{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "# Modeling Expected Goals\n", "\n", "\n", "\n", "\n", "In Part I, we took a deep dive into the data and trends of shots based on three key variables; the distance, angle and a categorical variable to identify headed shots. We developed an understanding of the distributions and probabilities associated with shots and goals by representing, transforming and visualizing the data. Here, we use this data to develop a model to predict goals. \n", "\n", "## Classification\n", "\n", "First some housekeeping, lets import our data from Part I and our libraries" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n" ], "text/plain": [ "" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "#make our plots center for jupyster notebook\n", "from IPython.core.display import HTML\n", "HTML(\"\"\"\n", "\n", "\"\"\")" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Importing Jupyter notebook from xG_model_part1.ipynb\n" ] }, { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stderr", "output_type": "stream", "text": [ "xG_model_part1.ipynb:49: RuntimeWarning: invalid value encountered in arccos\n", " \"source\": [\n" ] } ], "source": [ "#for extended notes and descriptions, visit part 1\n", "#use nbimporter to extract our shot_matrix function from part 1\n", "import nbimporter\n", "from xG_model_part1 import shot_matrix\n", "import pandas as pd\n", "import numpy as np\n", "import os\n", "import json\n", "import seaborn as sns \n", "import matplotlib.pyplot as plt\n", "from matplotlib.patches import Arc\n", "from PlotPitch import draw_pitch\n", "directory = '/Users/Ian/Desktop/IDanalytics/event_data'\n", "jsonfiles = []\n", "for path in os.listdir(directory):\n", " jsonfiles.append(os.path.join(directory,path))\n", "all_leagues = []\n", "for file in jsonfiles:\n", " all_leagues.append(shot_matrix(file))\n", "df = pd.concat(all_leagues)" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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GoalxyplayeridteamidmatchidheaderYXCenter_disDistanceAngle RadiansAngle Degrees
213165725699237992500686038.766.307.07.8960500.75557643.291300
3020174233455237722500686128.5617.858.018.6605490.37206921.317963
49814432638937722500686029.244.207.06.3480390.85194848.813019
5770162127692037722500686014.2816.8029.025.9059530.18483810.590449
6290275136676037992500686034.6828.351.028.3581540.25663714.704224
..........................................
64294502845856116332500098030.6029.405.029.5959460.24451714.009788
643023114334117416332500098022.4414.7017.018.7008980.30964617.741433
64305101262787916232500098042.1612.6012.015.0115160.41044423.516712
643055083814569216232500098025.848.4012.011.7109180.46114326.421528
64314901450800516332500098134.0014.700.014.7000000.48803627.962409
\n", "

40458 rows × 13 columns

\n", "
" ], "text/plain": [ " Goal x y playerid teamid matchid header Y X \\\n", "213 1 6 57 256992 3799 2500686 0 38.76 6.30 \n", "302 0 17 42 334552 3772 2500686 1 28.56 17.85 \n", "498 1 4 43 26389 3772 2500686 0 29.24 4.20 \n", "577 0 16 21 276920 3772 2500686 0 14.28 16.80 \n", "629 0 27 51 366760 3799 2500686 0 34.68 28.35 \n", "... ... .. .. ... ... ... ... ... ... \n", "642945 0 28 45 8561 1633 2500098 0 30.60 29.40 \n", "643023 1 14 33 41174 1633 2500098 0 22.44 14.70 \n", "643051 0 12 62 7879 1623 2500098 0 42.16 12.60 \n", "643055 0 8 38 145692 1623 2500098 0 25.84 8.40 \n", "643149 0 14 50 8005 1633 2500098 1 34.00 14.70 \n", "\n", " Center_dis Distance Angle Radians Angle Degrees \n", "213 7.0 7.896050 0.755576 43.291300 \n", "302 8.0 18.660549 0.372069 21.317963 \n", "498 7.0 6.348039 0.851948 48.813019 \n", "577 29.0 25.905953 0.184838 10.590449 \n", "629 1.0 28.358154 0.256637 14.704224 \n", "... ... ... ... ... \n", "642945 5.0 29.595946 0.244517 14.009788 \n", "643023 17.0 18.700898 0.309646 17.741433 \n", "643051 12.0 15.011516 0.410444 23.516712 \n", "643055 12.0 11.710918 0.461143 26.421528 \n", "643149 0.0 14.700000 0.488036 27.962409 \n", "\n", "[40458 rows x 13 columns]" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "#lets drop nan values and make sure our binary data is numeric for later\n", "df = df.dropna()\n", "#df = df.drop(columns = ['x','y','Center_dis'])\n", "df['header'] = pd.to_numeric(df['header'])\n", "df['Goal'] = pd.to_numeric(df['Goal'])\n", "df" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "Since our response variable (shot result) is categorical, we must apply classification methods to create a predictive model. To introduce this type of approach, let’s look at an illustrative example. Assume we plot a random selection of shots from our data and classify them based on their result, only taking the distance into account. " ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "scrolled": false }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "#we are going to plot specific point for a demonstration of what the Heaviside function does\n", "from PlotPitch import draw_pitch\n", "#choose specific goals and misses\n", "idx_goal = np.where((df['Goal']==1) & (df['Distance'] < 12)) \n", "df_HS_goal = df.iloc[idx_goal]\n", "idx_miss = np.where((df['Goal']==0) & (df['Distance']> 13)) \n", "df_HS_miss = df.iloc[idx_miss]\n", "\n", "#plot them with a bounday line between\n", "prob=np.array(df['Goal'])\n", "fig, ax = plt.subplots(figsize=(11, 7))\n", "draw_pitch(orientation=\"vertical\",\n", " aspect=\"half\",\n", " pitch_color='white',\n", " line_color=\"black\",\n", " ax=ax)\n", "goals = plt.scatter(data = df_HS_goal.head(100),x='Y', y='X',alpha=.7)\n", "misses = plt.scatter(data = df_HS_miss.head(100),x='Y', y='X',alpha=.7,marker='x')\n", "ax.set_xlim(0,68)\n", "plt.legend((goals,misses),('Goal','Miss'))\n", "ax.set_ylim(52.5,0)\n", "circle = plt.Circle((34,0),13,fill=False, color = 'Green')\n", "ax.add_artist(circle)\n", "plt.axis('off')\n", "\n", "plt.show()\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Above we can see that there is a clear distinction between the blue and orange clusters. If we assume this is the true nature of the relationship between shots and distance, and we want to predict future shot results based on this data, what model could we adopt?\n", "\n", "Since the data is easily separable, we can draw a boundary line between the two clusters. This line will represent a discriminant function, which we will use to classify each shot outcome as a goal or miss. In the case above, the discriminant function maps out a distance r from the center of the goal. \n", "\n", "This discriminant function, drawn in green, is defined by the equation 𝑦=αx+β, where x is the distance from goal and y is the binary response. Specifically for the data above, y = x -12. We can translate this into a classification model by applying the so-called Heaviside function to our discriminant, which will return a value of 0 or 1 as the response variable is based on the value of y:\n", "\n", "\n", "\n", "$$\n", "\\begin{array}{rcl}\n", " H(y) & \\equiv & \\left\\{\\begin{array}{ll}\n", " 0 & \\mathrm{if}\\ y > 0\n", " \\\\\n", " 1 & \\mathrm{if}\\ y \\leq 0\n", " \\end{array}\\right..\n", "\\end{array}\n", "$$\n", "\n", "The Heaviside function is a hard classifier and the simplest classification model, but it requires the data to be cleanly separable.\n" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0.5, 1.0, 'Heaviside Function Classification for Shots')" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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aX5KkVUFfb/zph1X97nJpPLRuSvPGH0nSRJr0N/5IkiRpcjFkSpIkqThDpiRJkoozZEqSJKk4Q6YkSZKKM2RKkiSpOEOmJEmSijNkSpIkqThDpiRJkoozZEqSJKk4Q6YkSZKKM2RKkiSpOEOmJEmSijNkSpIkqThDpiRJkoozZEqSJKk4Q6YkSZKKM2RKkiSpOEOmJEmSijNkSpIkqThDpiRJkoozZEqSJKk4Q6YkSZKKM2RKkiSpOEOmJEmSijNkSpIkqThDpiRJkoozZEqSJKk4Q6YkSZKKM2RKkiSpOEOmJEmSijNkSpIkqThDpiRJkoozZEqSJKk4Q6YkSZKKM2RKkiSpOEOmJEmSijNkSpIkqThDpiRJkoozZEqSJKk4Q6YkSZKKM2RKkiSpOEOmJEmSijNkSpIkqThDpiRJkoozZEqSJKk4Q6YkSZKKM2RKkiSpOEOmJEmSijNkSpIkqThDpiRJkoozZEqSJKk4Q6YkSZKKM2RKkiSpOEOmJEmSijNkSpIkqThDpiRJkoozZEqSJKk4Q6YkSZKKM2RKkiSpOEOmJEmSiutryIyI/SPi2ohYHBEndJi+ZUScFxGXRMTlEXFgP+uRJEnS+OhbyIyIAeAk4ABgJ+CIiNipbbb/B3w7M58FHA58rl/1SJIkafz0sydzD2BxZl6XmY8CZwCHtM2TwLr14/WAW/pYjyRJksZJP0PmXOCmxvCSelzTB4AjI2IJcDbwt50WFBFHR8SiiFi0bNmyftQqSZKkgib6xp8jgFMzc3PgQOAbEbFSTZl5cmYuyMwFc+bMGfciJUmSNDb9DJk3A1s0hjevxzW9Cfg2QGb+BlgT2LiPNUmSJGkc9DNkLgTmR8TWETGT6saeM9vm+RPwYoCI2JEqZHo+XJIkaZLrW8jMzOXAW4FzgKup7iK/KiI+FBEH17MdB7w5Ii4DTgfekJnZr5okSZI0Pqb3c+GZeTbVDT3Nce9rPP49sHc/a5AkSdL4m+gbfyRJkrQaMmRKkiSpOEOmJEmSijNkSpIkqThDpiRJkoozZEqSJKk4Q6YkSZKKM2RKkiSpOEOmJEmSijNkSpIkqThDpiRJkoozZEqSJKk4Q6YkSZKKM2RKkiSpOEOmJEmSijNkSpIkqThDpiRJkoozZEqSJKk4Q6YkSZKKM2RKkiSpOEOmJEmSijNkSpIkqThDpiRJkoozZEqSJKk4Q6YkSZKKM2RKkiSpOEOmJEmSijNkSpIkqThDpiRJkoozZEqSJKk4Q6YkSZKKM2RKkiSpOEOmJEmSijNkSpIkqThDpiRJkoozZEqSJKk4Q6YkSZKKM2RKkiSpOEOmJEmSijNkSpIkqThDpiRJkoozZEqSJKk4Q6YkSZKKM2RKkiSpOEOmJEmSijNkSpIkqThDpiRJkoozZEqSJKk4Q6YkSZKKM2RKkiSpOEOmJEmSijNkSpIkqThDpiRJkoozZEqSJKk4Q6YkSZKKM2RKkiSpOEOmJEmSijNkSpIkqThDpiRJkoozZEqSJKm4vobMiNg/Iq6NiMURcUKXeV4VEb+PiKsi4pv9rEeSJEnjY3q/FhwRA8BJwEuAJcDCiDgzM3/fmGc+8B5g78y8KyI26Vc9kiRJGj/97MncA1icmddl5qPAGcAhbfO8GTgpM+8CyMylfaxHkiRJ46SfIXMucFNjeEk9rmk7YLuIuCAifhsR+3daUEQcHRGLImLRsmXL+lSuJEmSSpnoG3+mA/OBfYEjgC9FxPrtM2XmyZm5IDMXzJkzZ3wrlCRJ0pj1M2TeDGzRGN68Hte0BDgzMx/LzOuB/6UKnZIkSZrE+hkyFwLzI2LriJgJHA6c2TbPD6h6MYmIjalOn1/Xx5okSZI0DvoWMjNzOfBW4BzgauDbmXlVRHwoIg6uZzsHuCMifg+cBxyfmXf0qyZJkiSNj759hBFAZp4NnN027n2Nxwm8s/6RJEnSamKib/yRJEnSasiQKUmSpOJGDZkRsXcv4yRJkqSWXnoyP9PjOEmSJAkY4cafiHgO8FxgTkQ0b8xZFxjod2GSJEmavEa6u3wmsE49z+zG+HuBV/SzKEmSJE1uXUNmZv4c+HlEnJqZN45jTZIkSZrkRjpd/t9A1o9Xmp6ZB680UpIkSWLk0+WfGLcqJEmStFoZ7XS5JEmSNGajfq1kRFxPfdq8KTOf1peKJEmSNOn18t3lCxqP1wReCWzYn3IkSZK0Ohj1w9gz847Gz82Z+SngoP6XJkmSpMmql9PluzUGp1H1bPbSAypJkqQpqpew+K+Nx8uBG4BX9aUaSZIkrRZGDZmZ+cLxKESSJEmrj1GvyYyIt0fEulE5JSJ+FxEvHY/iJEmSNDmNGjKBN2bmvcBLgY2A1wIn9rUqSZIkTWq9hMzWd0oeCHw9M69qjJMkSZJW0kvIvDgizqUKmedExGxgsL9lSZIkaTLr5e7yNwG7Atdl5oMRsRHwV32tSpIkSZNaLz2ZCewEvK0eXpvqm38kSZKkjnoJmZ8DngMcUQ/fB5zUt4okSZI06fVyunzPzNwtIi4ByMy7ImJmn+uSJEnSJNZLT+ZjETFAddqciJiDN/5IkiRpBL2EzE8D3wc2iYgPA78CPtrXqiRJkjSp9fK1kqdFxMXAi6k+H/NQ4E99rkuSJEmT2IghMyLmAk8FLs/MayJiE+AdwBuAzfpenSRJkialrqfLI+IdwKXAZ4DfRsRRwNXALODZ41GcJEmSJqeRejKPBrbPzDsjYkvgf4G9M/Pi8SlNkiRJk9VIN/48nJl3AmTmn4BrDZiSJEnqxUg9mZtHxKcbw09tDmfm2zo8R5IkSRoxZB7fNmwvpiRJknrSNWRm5tfGsxBJkiStPnr5MHZJkiRpTAyZkiRJKm7UkBkRe/cyTpIkSWrppSfzMz2OkyRJkoARbvyJiOcAzwXmRMQ7G5PWBQb6XZgkSZImr5E+wmgmsE49z+zG+HuBV/SzKEmSJE1uI32E0c+Bn0fEqZl5Y0SsU4+/f9yqkyRJ0qQ0Uk9my+yIuATYECAibgden5lX9rUySZIkTVq93PhzMvDOzNwqM7cCjqvHSZIkSR31EjLXzszzWgOZeT6wdt8qkiRJ0qTXy+ny6yLiH4Fv1MNHAtf1ryRJkiRNdr30ZL4RmAN8r/6ZU4+TJEmSOhq1JzMz7wLeNg61SJIkaTUxasiMiO2AvwfmNefPzBf1ryxJkiRNZr1ck/mfwBeAU4AV/S1HkiRJq4NeQubyzPx83yuRJEnSamOk7y7fsH743xHx18D3gUda0zPzzj7XJkmSpElqpJ7Mi4EEoh4+vjEtgaf1qyhJkiRNbiN9d/nW41mIJEmSVh9dPyczInaPiKc0hl8XEf8VEZ9unEqXJEmSVjLSh7F/EXgUICKeD5wIfB24B7+7XJIkSSMY6ZrMgcbNPYcBJ2fmd4HvRsSlfa9MkiRJk9ZIPZkDEdEKoS8GftaY1stHH0mSJGmKGiksng78PCJuBx4CfgkQEdtSnTKXJEmSOhrp7vIPR8RPgacC52Zm1pOmAX87HsVJkiRpchrxtHdm/rbDuP/tXzmSJElaHYx0TeaTFhH7R8S1EbE4Ik4YYb7/GxEZEQv6WY8kSZLGR99CZkQMACcBBwA7AUdExE4d5psNvB24sF+1SJIkaXz1sydzD2BxZl6XmY8CZwCHdJjvn4CPAQ/3sRZJkiSNo36GzLnATY3hJfW4x0XEbsAWmXnWSAuKiKMjYlFELFq2bFn5SiVJklRUX6/JHElETAM+CRw32ryZeXJmLsjMBXPmzOl/cZIkSXpS+hkybwa2aAxvXo9rmQ3sDJwfETcAewFnevOPJEnS5NfPkLkQmB8RW0fETOBw4MzWxMy8JzM3zsx5mTkP+C1wcGYu6mNNkiRJGgd9C5mZuRx4K3AOcDXw7cy8KiI+FBEH92u9kiRJmnh9/Q7yzDwbOLtt3Pu6zLtvP2uRJEnS+JmwG38kSZK0+jJkSpIkqThDpiRJkoozZEqSJKk4Q6YkSZKKM2RKkiSpOEOmJEmSijNkSpIkqThDpiRJkoozZEqSJKk4Q6YkSZKKM2RKkiSpOEOmJEmSijNkSpIkqThDpiRJkoozZEqSJKk4Q6YkSZKKM2RKkiSpOEOmJEmSijNkSpIkqThDpiRJkoozZEqSJKk4Q6YkSZKKM2RKkiSpOEOmJEmSijNkSpIkqThDpiRJkoozZEqSJKk4Q6YkSZKKM2RKkiSpOEOmJEmSijNkSpIkqThDpiRJkoozZEqSJKk4Q6YkSZKKM2RKkiSpOEOmJEmSijNkSpIkqThDpiRJkoozZEqSJKk4Q6YkSZKKM2RKkiSpOEOmJEmSijNkSpIkqThDpiRJkoozZEqSJKk4Q6YkSZKKM2RKkiSpOEOmJEmSijNkSpIkqThDpiRJkoozZEqSJKk4Q6YkSZKKM2RKkiSpOEOmJEmSijNkSpIkqThDpiRJkoozZEqSJKk4Q6YkSZKKM2RKkiSpuL6GzIjYPyKujYjFEXFCh+nvjIjfR8TlEfHTiNiqn/VIkiRpfPQtZEbEAHAScACwE3BEROzUNtslwILMfAbwHeBf+lWPJEmSxk8/ezL3ABZn5nWZ+ShwBnBIc4bMPC8zH6wHfwts3sd6JEmSNE76GTLnAjc1hpfU47p5E/CjThMi4uiIWBQRi5YtW1awREmSJPXDKnHjT0QcCSwAPt5pemaenJkLMnPBnDlzxrc4SZIkjdn0Pi77ZmCLxvDm9bhhImI/4B+AF2TmI32sR5IkSeOknz2ZC4H5EbF1RMwEDgfObM4QEc8CvggcnJlL+1iLJEmSxlHfQmZmLgfeCpwDXA18OzOviogPRcTB9WwfB9YB/jMiLo2IM7ssTpIkSZNIP0+Xk5lnA2e3jXtf4/F+/Vy/JEmSJsYqceOPJEmSVi+GTEmSJBVnyJQkSVJxhkxJkiQVZ8iUJElScYZMSZIkFWfIlCRJUnGGTEmSJBVnyJQkSVJxhkxJkiQVZ8iUJElScYZMSZIkFWfIlCRJUnGGTEmSJBVnyJQkSVJxhkxJkiQVZ8iUJElScYZMSZIkFWfIlCRJUnGGTEmSJBVnyJQkSVJxhkxJkiQVZ8iUJElScYZMSZIkFWfIlCRJUnGGTEmSJBVnyJQkSVJxhkxJkiQVZ8iUJElScYZMSZIkFWfIlCRJUnGGTEmSJBVnyJQkSVJxhkxJkiQVZ8iUJElScYZMSZIkFWfIlCRJUnGGTEmSJBVnyJQkSVJxhkxJkiQVZ8iUJElScYZMSZIkFWfIlCRJUnGGTEmSJBVnyJQkSVJxhkxJkiQVZ8iUJElScYZMSZIkFWfIlCRJUnGGTEmSJBVnyJQkSVJxhkxJkiQVZ8iUJElScYZMSZIkFWfIlCRJUnGGTEmSJBVnyJQkSVJxhkxJkiQVZ8iUJElScYZMSZIkFdfXkBkR+0fEtRGxOCJO6DB9jYj4Vj39woiY1896JPUgs/ppDg8OrjxPu/Z5li8fPr71e8WKldfVnDY4ODTPihXVT2t9remt4dbj9npH2pZO01qPM6u6W7W3tmP58uHPHRwcXkfz+d3aqDlv+/hu83bS3s7tw510qjNzeNt22s9PRHvt7fu70/7vpjkvwKOPDn9ea3ovbdhp37S3R7MN2o+xlvbh1nOa45rHS+tY6bZNox2T7fWMVEv78Ejal9esd6T6mtpff51eB6X1sl+7DT+ZdZRa9hQzvV8LjogB4CTgJcASYGFEnJmZv2/M9ibgrszcNiIOBz4GHNavmiSN4ryPwuKfwOYLYP8Tq3FfejHccxMs+Ct44XurP67/8x5Ycz144Xuqeb56IDxyLxz9C5g2Db58ANz6O5g2AzacB0edD6fsCw/cBSsegjk7wLznwcN3w1U/gByEjbaFJRdVz5m+JsxYCx66E1Y8BuvMgRiAB+8AAjbZEd70Yzj5BfDg7bDuXNh2v6qWh++B/T8K558ID90NAay5Pux7wlDdMLSda6xXPYeEi74EDMLAGvDct8ELToB/nlONm7kOvGcJnP9RWPRVePR+mLMjHPWTark3L6xqa68jYqjN/nw5POUZw8efUs9/1E+Gz9ts35b2dh4chJOfD2usC391dvd9+vA9sOa6sPinMPfZsGQR3H4tDMyEDbauan7kHrjye7Dx/O7L6uX4aW73Vw6o1rPgqGr4Dz+Gu66v9t8bzoL/OaGqZdv9Vt7Wf9sZHnsQjvsDDAzAJ3aE+2+t9sOc7eEpz4KrvwfT14IdDxq+nPY6mm3a2jet9th8Ady0sF5pwj1L4Nl/VbXzrZfBHYthvS3gzT+t9v21Z8O0mTD/JdUx9ckdq+Xt9rrqNfPVg+CWi6vjavrMoXWuuR5stTcs+jJsvAO88eyV62o/JpdcNLyeNdeFh++t5r/hl3D7H2Cn/wMHfqxa1snPhwduh91ev3J7dtpPa6xbLfdlH4Fz3lsdn4/cC9sdCC96b+d2a7XpeR+pXgfTBmDHQ6rx7a+DkWp4InrZr52mjaWOTusYy2tUw/QtZAJ7AIsz8zqAiDgDOARohsxDgA/Uj78DfDYiItN/EaRxl1mFspsXVT+tcbdcXD2+5uwqdJ3zXrjw87DnsUP/4T9yL/z5iupN7qjzq4C5/GHgkWr8iXOr4RiAXAHLroFNd4aLvji0/gduBwZhcDksfwgevmto2n23Vm/sg3VP1i0Xwyfmw0N3DE3f7NkwLeDCLwAJCVz0hWr6nsfAj06ohvc8BgZzaDs33QVuu2J4W6x4BH79abjg36uaoAqVZx0Pf/oNPLB0qI4vPg9uu3LouXOfDcTQultvvhd+Hp6yS/X78fEnDLX1j06AA04cmrfVvhHV9MHB4e189C+q33++olru4GAVPNv36cP3VMtrbWdrfS0P3Vltb2sb1tmk87JG01wXwEs/XAXMB++AhV+CXV45dCwtvRp+9O6h/T93wfBtXbGiCpgP3gH/Oh/ecU0VMEl49L7hx+j0B+p9Xi9ncHB4Hc323/OYoeNi052rbW5vD4BFp1TrXmuj6vcDS+Gsd8GS31Tt3VrXj95dHXtQ1TA4WG3j8oern1kbVv+gAWzy9CpgPngH3H5NtY3n/kNV1x7HVNvW7Zhs1fOUXar17/6W6lh4YCksrNvwpl8P1fbgXcPbs9t+ai3vxl9Vv1vbC1WAfvy1fszw19PLPgLXnDX0OrjoC9Uyhr0OFnSv4YloP7667deVph3bex0d1zGG16hWEv3KcxHxCmD/zDyqHn4tsGdmvrUxz5X1PEvq4T/W89zebbkLFizIRYs6/FGQppD4oH/UJEmd5fvHr68uIi7OzAWdpk2KG38i4uiIWBQRi5YtWzbR5UiSJGkU/TxdfjOwRWN483pcp3mWRMR0YD3gjvYFZebJwMlQ9WT2pVppEunbf6mZQ6eVm9pP3+157NA1SzB0beCfG/NMX7M+Zd6meUqulD2OqU5jwdCprE5adUPn7exmYCasePTJ1bHnsUPXvg0b33aqr1ln+2m4Tu38lF2GrtHspHX9WLc2adp0Z3jLL8d+qnykdY22v1tt1r6tK1ZUp8qHPTeoGmuU5XSqo7nve20PGDql3M2ex8D1v4SlV/W2vPb2GOsx2Zq/dQ1me227v6W6RnOkU7gjHRPt2ztSu7UuOWjXbZ8+WWPdr91eR2NexxheoxqmnyFzITA/IramCpOHA69um+dM4PXAb4BXAD/zekxpgrQHzD2PqcZd9MUqYG66C7zlF8NDUvub3VN2qa7JbF2D2QoFrcDZunlnrY1g51cMvyaTaTx+/WMnzWsyAWZtNHRN5kVfqOpoXZPZ/qbQGr7w81U9gzl0LVunazKhuvkns1pnK2AueHN1TebSxhtr8432ovp60NY1ma03otabVuvat8fHnzB0PWHrjbn5BtctyLeCZWu4dY1mp2syW8vrtp3Nbbjtyuoa0ycSNJvr2vPY6prMVkictWF1TWZrfzeHW/uoGUqaAXOtjaprMj+yCR0DZuvYal6P17xuuNn+zWt1uwUkGAqCa200FLgWHD38mszd31Id3hc2gsfuR8MlXx/652rWhtU1r1Bdk3n/n4eWe9wfhq7JzKxqu6jLMdmqp3VN7+Dg8Gswd3/L0HDruO4WNJv7qRUoW79b29s6vh5/rTfarfXPUvu1yCu9DigbNNuPr277daVp9B4GO65jDK9RraRvITMzl0fEW4FzgAHgK5l5VUR8CFiUmWcCXwa+ERGLgTupgqikiRABs9avLthv3l2+ZFF188IOB1bBo9VrsOZ61XMiqrtUmz1qT91t9LvLZ21Qhb9Sd5evtUFVV+vN4fwTqzeF5t3lEUN3ora2c436rt9e7i4/6OPVHcYPLO1+d/mstjoihtrsz5e3jT+xal8YekNub9+WadNWbudW0Fxj3c6hsLW9ex5b3Zk8fY3ud5fP26e6u3zN9Z5YT2ZzXa3t23j74XeXb/bsobvLD6hD0JJF1XHX3NaBgWr/r8XQ3eXrPHX0u8tnrV/V3l5Hs01b+2bNdavjrNe7yw/6l2rfQ/UPz1obVMfU1WcOv7v8tquG312+7mZD697hoKG7ywcGVq6r/ZjsdHf5VvtU86+xLqy9See7y9faoHvwae6nNerldbq7vP213mq3VpvucBDcv7T73eXt+/TJ6nR8jVRft9fRmNcxhteoVtK3G3/6xRt/pD5r/U1o/fFs3UHeDB6d7qhsvyN5+XKYPn1ofOv3ihXVG2xzXa3lr1gxdLpzYGDoMwWnTavGt6a3fgYHh+po1tt83Mu05t/B1jqnTx/aDqjqafYqtp7b/vxO62oOdxrffF639m1pb+de7gRvrrvTslrT2vfzE9Fee/v+Hhxcef9329bmc6H6nMyZM4d/puPAQG9t2L7vO7VHa9q0aUPztI6x5r5vDrfarTlu+fKh46V1rLTatX2bRjsm2+tp/8SBkWobSfvymtvb7bXe3qbtr79Or4PSetmv3eZ9MuuAMsteDY10408/T5dLmoza/3B2etPq9Me1PZy0QlprfOt38w22PSA2p/Uy3K33rlud3aY1H09v+7PYPtxpvZ3ao9u6e2nLkd682tfdSyjstu72fVHiTXO0dXTa/9207++ZM4c/rzV9LO3ffDzS81q/R2vvTu3WPGba52/fptGOyW6/e6ltJN2WO9Kx3b6dvbwOSuv1Nf1k6nmyr1E9blLcXS5JkqTJxZApSZKk4gyZkiRJKs6QKUmSpOIMmZIkSSrOkClJkqTiDJmSJEkqzpApSZKk4gyZkiRJKs6QKUmSpOIMmZIkSSousvmF9pNARCwDbhzHVW4M3D6O65ssbJeV2Sad2S6d2S6d2S4rs006s106G+922Soz53SaMOlC5niLiEWZuWCi61jV2C4rs006s106s106s11WZpt0Zrt0tiq1i6fLJUmSVJwhU5IkScUZMkd38kQXsIqyXVZmm3Rmu3Rmu3Rmu6zMNunMdulslWkXr8mUJElScfZkSpIkqThDpiRJkoozZHYREftHxLURsTgiTpjoelYVEXFDRFwREZdGxKKJrmeiRMRXImJpRFzZGLdhRPw4Iv5Q/95gImucCF3a5QMRcXN9zFwaEQdOZI3jLSK2iIjzIuL3EXFVRLy9Hj+lj5cR2mWqHy9rRsRFEXFZ3S4frMdvHREX1u9J34qImRNd63gaoV1OjYjrG8fLrhNc6riLiIGIuCQiflgPrzLHiiGzg4gYAE4CDgB2Ao6IiJ0mtqpVygszc9dV5XO4JsipwP5t404AfpqZ84Gf1sNTzams3C4A/1YfM7tm5tnjXNNEWw4cl5k7AXsBf1P/PZnqx0u3doGpfbw8ArwoM58J7ArsHxF7AR+japdtgbuAN01ciROiW7sAHN84Xi6dqAIn0NuBqxvDq8yxYsjsbA9gcWZel5mPAmcAh0xwTVqFZOYvgDvbRh8CfK1+/DXg0PGsaVXQpV2mtMy8NTN/Vz++j+rNYC5T/HgZoV2mtKzcXw/OqH8SeBHwnXr8VDxeurXLlBYRmwMHAafUw8EqdKwYMjubC9zUGF6Cf/xaEjg3Ii6OiKMnuphVzKaZeWv9+M/AphNZzCrmrRFxeX06fUqdFm6KiHnAs4AL8Xh5XFu7wBQ/XurTn5cCS4EfA38E7s7M5fUsU/I9qb1dMrN1vHy4Pl7+LSLWmLgKJ8SngHcBg/XwRqxCx4ohU2O1T2buRnUpwd9ExPMnuqBVUVafDTbl/8uufR7YhuoU163Av05oNRMkItYBvgu8IzPvbU6bysdLh3aZ8sdLZq7IzF2BzanOrO0wsRWtGtrbJSJ2Bt5D1T67AxsC7564CsdXRLwcWJqZF090Ld0YMju7GdiiMbx5PW7Ky8yb699Lge9T/QFU5baIeCpA/XvpBNezSsjM2+o3h0HgS0zBYyYiZlAFqdMy83v16Cl/vHRqF4+XIZl5N3Ae8Bxg/YiYXk+a0u9JjXbZv77sIjPzEeCrTK3jZW/g4Ii4geqyvhcB/84qdKwYMjtbCMyv79CaCRwOnDnBNU24iFg7Ima3HgMvBa4c+VlTypnA6+vHrwf+awJrWWW0glTt/zDFjpn6GqkvA1dn5icbk6b08dKtXTxeYk5ErF8/ngW8hOp61fOAV9SzTcXjpVO7XNP4Ry2orj2cMsdLZr4nMzfPzHlUOeVnmfkaVqFjxW/86aL+2IxPAQPAVzLzwxNb0cSLiKdR9V4CTAe+OVXbJSJOB/YFNgZuA94P/AD4NrAlcCPwqsycUjfBdGmXfalOfSZwA/CWxrWIq72I2Af4JXAFQ9dNvZfq+sMpe7yM0C5HMLWPl2dQ3awxQNUR9O3M/FD99/cMqlPClwBH1r13U8II7fIzYA4QwKXAMY0bhKaMiNgX+PvMfPmqdKwYMiVJklScp8slSZJUnCFTkiRJxRkyJUmSVJwhU5IkScUZMiVJklScIVPSlBURKyLi0oi4KiIui4jjImJaPW1BRHx6hOfOi4hXj1+1K61/VkT8PCIGxvCct0bEG/tZlyS1+BFGkqasiLg/M9epH28CfBO4IDPf38Nz96X+XLq+Ftl9/X8DTM/Mfx/Dc9ai2r5n9a8ySarYkylJPP5VqUcDb43KvhHxQ4CIeEHd43lpRFxSf/PVicDz6nF/V/ds/jIiflf/PLd+7r4RcX5EfCciromI0+pvJyEido+IX9e9qBdFxOyIGIiIj0fEwoi4PCLe0qXk11B/k0e9jp9HxH9FxHURcWJEvKZe5hURsU29jQ8CN0TEVPrqPUkTZPros0jS1JCZ19Wnnzdpm/T3wN9k5gURsQ7wMHACjZ7MupfwJZn5cETMB04HFtTPfxbwdOAW4AJg74i4CPgWcFhmLoyIdYGHgDcB92Tm7hGxBnBBRJybmde3iqm/7vZpmXlDo8ZnAjsCdwLXAadk5h4R8Xbgb4F31PMtAp4HXPSkGkuSRmHIlKTRXQB8MiJOA76XmUvqzsimGcBnI2JXYAWwXWPaRZm5BCAiLgXmAfcAt2bmQoDMvLee/lLgGRHR+u7h9YD5wPWN5W0M3N22/oWtr1+MiD8C59bjrwBe2JhvKbBDj9stSU+YIVOSavV3/q6gCmI7tsZn5okRcRZwIFXP4ss6PP3vqL6v/ZlUlyI93JjW/N7gFYz8tzeAv83Mc0aY5yFgzbZxzXUMNoYH29a3Zv18Seorr8mUJCAi5gBfAD6bbXdERsQ2mXlFZn4MWEjVE3gfMLsx23pUPZODwGuB0e76vhZ4akTsXq9jdkRMB84Bjo2IGfX47SJi7eYTM/MuYCAi2oNmL7YDrnwCz5OkMbEnU9JUNqs+fT0DWA58A/hkh/neEREvpOoVvAr4Uf14RURcBpwKfA74bkS8Dvgf4IGRVpyZj0bEYcBnImIWVe/ifsApVKfTf1ffILQMOLTDIs4F9gF+0vvmArA38IExPkeSxsyPMJKkSSgidgP+LjNfO4bnPAt451ieI0lPlKfLJWkSyszfAeeN5cPYqW4Y+sc+lSRJw9iTKUmSpOLsyZQkSVJxhkxJkiQVZ8iUJElScYZMSZIkFWfIlCRJUnH/H606CnLDTwjDAAAAAElFTkSuQmCC\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "#plot the heaviside function on top of the responses for the seperable data above\n", "df_HS_predictor = np.append(df_HS_goal['Distance'].head(100), df_HS_miss['Distance'].head(100))\n", "df_HS_response = np.append(df_HS_goal['Goal'].head(100), df_HS_miss['Goal'].head(100))\n", "\n", "fig, axes = plt.subplots(figsize=(11,7))\n", "\n", "goals = plt.scatter(df_HS_goal['Distance'].head(100),df_HS_goal['Goal'].head(100))\n", "misses = plt.scatter(df_HS_miss['Distance'].head(100),df_HS_miss['Goal'].head(100),marker='x')\n", "plt.plot([0,12], [1, 1], 'k-', lw=2,c='green')\n", "plt.plot([12,12], [0, 1], 'k-', lw=2,c='green')\n", "plt.plot([12,40], [0, 0], 'k-', lw=2,c='green')\n", "plt.xlabel('Distance (m)')\n", "plt.ylabel('Shot Result')\n", "plt.title('Heaviside Function Classification for Shots')\n", "\n", "\n", " " ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "#we are going to create a contour plot to see how the heaviside function classifies onto a pitch\n", "#first we must simulate the data above and we can do that by initializing \n", "#some numpy arrays what have certain properties\n", "from PlotPitch import draw_pitch \n", "\n", "#heaviside returns 0 if y is negative and 1 otherwise\n", "def heaviside(Y):\n", " A = np.where(Y<=0, 0, 1)\n", " return A\n", "\n", "#plot contour plot over the pitch from before\n", "fig, ax = plt.subplots(figsize=(11, 7))\n", "draw_pitch(orientation=\"vertical\",\n", " aspect=\"half\",\n", " pitch_color='white',\n", " line_color=\"black\",\n", " ax=ax)\n", "\n", "x0 = np.linspace(0, 68, 100)\n", "x1 = np.linspace(0,53 , 100)\n", "x11 = np.linspace(53,0 , 100)\n", "x0_grid, x1_grid = np.meshgrid(x0, x1)\n", "h_grid = heaviside(144-(x0_grid-34)**2-(x1_grid-53)**2)\n", "plt.contourf(x0, x11, h_grid,cmap='OrRd',alpha=.8,levels=10)\n", "plt.xlabel('X (m)')\n", "plt.ylabel('Y (m)')\n", "plt.title('Heaviside Function Classification for Shots')\n", "\n", "plt.axis('off')\n", "ax.set_xlim(0,68)\n", "ax.set_ylim(52.5,0)\n", "plt.colorbar()\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In reality, the data describing shots is not cleanly separable, making goals difficult to predict with any kind of certainty. Nevertheless, the Heaviside function serves as a natural progression into more advanced classification models. \n", "\n", "If we take a real sample of the data, it might resemble the plot below." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# for a real representation of the data, let's try different characteristics\n", "#remember these are just for demonstration\n", "\n", "idx = np.where((df['Goal']==1) & (df['Distance'] < 25)) \n", "df_log_goal = df.iloc[idx]\n", "idx = np.where((df['Goal']==0) & (df['Distance']> 5)) \n", "df_log_miss = df.iloc[idx]\n", "\n", "\n", "#same as before\n", "prob=np.array(df['Goal'])\n", "fig, ax = plt.subplots(figsize=(11, 7))\n", "draw_pitch(orientation=\"vertical\",\n", " aspect=\"half\",\n", " pitch_color='white',\n", " line_color=\"black\",\n", " ax=ax)\n", "goals = plt.scatter(data = df_log_goal.head(150),x='Y', y='X',alpha=.7)\n", "misses = plt.scatter(data = df_log_miss.head(150),x='Y', y='X',alpha=.7,marker='x')\n", "classifer = Arc(xy=(10,10),width=12,height=12)\n", "ax.set_xlim(0,68)\n", "ax.set_ylim(52.5,0)\n", "plt.legend((goals,misses),('Goal','Miss'))\n", "plt.axis('off')\n", "\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In the event where the data is not cleanly separable, we must look to model the probability as opposed to assigning hard zero and ones. We have already seen in our data exploration that there are clear trends for the probability with respect to the distance and angle variables. What function should we adopt to model these trends? There are numerous functions that map out probabilities and fit non-separable data, but we use the logistic function (also known as the sigmoid function) due to its simplicity.\n", "\n", "$$\n", "\\begin{array}{rcl}\n", " G(y) & \\equiv & \\dfrac{1}{1 + e^{-y}} \\equiv \\dfrac{1}{1+e^{-(\\alpha x_{1} +\\beta)}}\n", "\\end{array}\n", "$$\n", "\n", "Similar to the heaviside function, the logistic function takes in our predictors (distance in this case), but instead outputs values between zero and one. \n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The logistic function takes any value in the domain $(-\\infty, +\\infty)$ and produces a value in the range $(0, 1)$. Thus, given a value $y$, we can interpret $G(y)$ as a conditional probability that the shot results in a goal, $G(y) \\equiv \\mathrm{Pr}[\\mbox{label is }1 \\,|\\, y]$." ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "scrolled": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "#plot a general logistic function for demonstration\n", "fig, ax = plt.subplots(figsize=(11, 7))\n", "rand_t=np.random.normal(5,5,50)\n", "rand_f=np.random.normal(-5,5,50)\n", "plt.scatter(rand_t,np.random.randint(1,2,50))\n", "plt.scatter(rand_f,np.random.randint(0,1,50))\n", "\n", "y = np.linspace(-15,15,100)\n", "plt.plot(y,1/(1+np.exp(-(.5*y))),c='Green',label='')\n", "plt.plot(y,1/(1+np.exp(-(.5*y))),c='Green',label='Logistic Function')\n", "plt.plot(y,1/(1+np.exp(-(.5*y))),c='Green',label='Logistic Function')\n", "\n", "plt.xlabel('Predictor')\n", "plt.ylabel('Response')\n", "plt.title('Logistic Function')\n", "plt.legend()\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The logistic function is an S-shaped curve that changes in slope and trajectory based on the values of the coefficients. Now the question is, how do we use the logistic function to model our shot data? Well, for each predictor variable we employ, we optimize the corresponding coefficient (α, β, etc.) to best fit the data. What do we optimize on? Something known as the log-likelihood. The process of maximizing the log-likelihood is beyond the scope here, but if you are interested in the process, here is a good jumping off point. For a slower-paced visual demonstration, StatsQuest does a good job. \n", "\n", "# The xG model\n", "\n", "Our goal is to create a model to accurately describe our existing data as well as possible, and to eventually predict future events. Before applying logistic regression to our entire dataset, we must split our data into training and test sets. The training set serves at the data we build our model on, and the testing set is the data we use to evaluate how well our model performs. Fitting the training data to the logistic function will produce coefficients for our predictors ( I will do this by using the Scikit-learn library in Python). If we start by only fitting the distance variable, we should arrive at the optimal parameters to describe the training data:" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[-0.14641592]] [0.09763449]\n" ] }, { "data": { "text/html": [ "
\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
coef
Distance-0.146416
\n", "
" ], "text/plain": [ " coef\n", "Distance -0.146416" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "#we are going to split the data into a test and train set(20% of it will go towards testing)\n", "#for now we are going to model just the distance predictor\n", "from sklearn import metrics \n", "from sklearn.model_selection import train_test_split\n", "train_dis = df[['Goal','Distance']].copy()\n", "x_train_dis, x_test_dis, y_train_dis, y_test_dis = train_test_split(train_dis.drop('Goal',axis=1), \n", " train_dis['Goal'], test_size=0.20, \n", " random_state=10)\n", "from sklearn.linear_model import LogisticRegression\n", "lgm_dis = LogisticRegression()\n", "lgm_dis.fit(x_train_dis,y_train_dis)\n", "log_odds = lgm_dis.coef_[0]\n", "print(lgm_dis.coef_, lgm_dis.intercept_)\n", "pd.DataFrame(log_odds, \n", " x_train_dis.columns, \n", " columns=['coef']).sort_values(by='coef', ascending=False)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$\n", "\\begin{array}{rcl}\n", " G(y) = \\dfrac{1}{1+e^{(0.146*distance - 0.097)}}\n", "\\end{array}\n", "$$" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0.5, 1.0, 'Logistic Regression Model for Shots')" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "#compare this model to the sample data from before\n", "df_HS_predictor = np.append(df_log_goal['Distance'].head(100), df_log_miss['Distance'].head(100))\n", "df_HS_response = np.append(df_log_goal['Goal'].head(100), df_log_miss['Goal'].head(100))\n", "\n", "fig, axes = plt.subplots(figsize=(11,7))\n", "goals = plt.scatter(df_log_goal['Distance'].head(100),df_log_goal['Goal'].head(100))\n", "misses = plt.scatter(df_log_miss['Distance'].head(100),df_log_miss['Goal'].head(100),marker='x')\n", "y = np.linspace(0,40,100)\n", "\n", "plt.plot(y,1/(1+np.exp(-(lgm_dis.coef_[0][0]*y+lgm_dis.intercept_[0]))),c='Green',label='Log Model')\n", "\n", "plt.xlabel('Distance (m)')\n", "plt.ylabel('Shot Result')\n", "plt.legend()\n", "plt.title('Logistic Regression Model for Shots')\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "While the graph above produces some certification that our coefficients produce a reasonable fit, it is not very clear graphically how good this fit is, especially considering this is just a small sample of our training data. Instead of measuring the goodness of fit numerically, let’s examine another graphic. As we constructed in Part I, we can bin the data by distance, calculate the ratio of shots that resulted in a goal per bin, and then scatter plot the bins onto a graph. If we now superimpose the logistic model onto the scatter plot, we can see how well the function maps the data." ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "#use the seaborn library to inspect the distribution of the shots by result (goal or no goal) \n", "fig, axes = plt.subplots(figsize=(11, 5))\n", "#first we want to create bins to calc our probability\n", "#pandas has a function qcut that evenly distibutes the data \n", "#into n bins based on a desired column value\n", "df['Goal']=df['Goal'].astype(int)\n", "df['Distance_Bins'] = pd.qcut(df['Distance'],q=100)\n", "#now we want to find the mean of the Goal column(our prob density) for each bin\n", "#and the mean of the distance for each bin\n", "dist_prob = df.groupby('Distance_Bins',as_index=False)['Goal'].mean()['Goal']\n", "dist_mean = df.groupby('Distance_Bins',as_index=False)['Distance'].mean()['Distance']\n", "dist_trend = sns.scatterplot(x=dist_mean,y=dist_prob)\n", "dist_trend.set(xlabel=\"Distance (m)\",\n", " ylabel=\"Probabilty of Goal\",\n", " title=\"Probability of Scoring Based on Distance\")\n", "dis = np.linspace(0,50,100)\n", "sns.lineplot(x = dis,y = 1/(1+np.exp((0.146*dis-.097))),color='green',legend='auto',label='Logistic Fit')\n", "\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Remember that we did not fit our model to the points in figure 6 and 7, but rather to the 32,000 shots in our training set. The purpose of these graphs is to gauge where our model performs well and where it does not. Plotting 32,000 points on a graph is not great for visualization, so we decide to plot a sample representation of the population. \n", "\n", "We can see from figure 7 that the model predicts the data well for values greater than 6 meters, yet it undervalues the probability of goals from closer distances. This is the sort of advantage a graphical approach will offer. We can try to better predict shots closer to goal by adding a quadratic term to the logistic function. That is, " ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[-0.21632621 0.00206089]] [0.58419379]\n" ] } ], "source": [ "# we are going to have to use the pipe line function from sklearn to mesh a polynomial \n", "#function with logisitic regression\n", "from sklearn.preprocessing import PolynomialFeatures\n", "from sklearn.pipeline import Pipeline\n", "from sklearn.pipeline import make_pipeline\n", "df_dis_2 = df[['Goal','Distance']].copy()\n", "x_train_dis_2, x_test_dis_2, y_train_dis_2, y_test_dis_2 = train_test_split(df_dis_2.drop('Goal',axis=1), \n", " df_dis_2['Goal'], test_size=0.20, \n", " random_state=10)\n", "\n", "poly = PolynomialFeatures(degree = 2, interaction_only=False, include_bias=False)\n", "lgm_dis_2 = LogisticRegression()\n", "lgm_dis_2.fit(x_train_dis_2,y_train_dis_2)\n", "pipe = Pipeline([('polynomial_features',poly), ('logistic_regression',lgm_dis_2)])\n", "pipe.fit(x_train_dis_2, y_train_dis_2)\n", "\n", "\n", "\n", "print(lgm_dis_2.coef_,lgm_dis_2.intercept_)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$\n", "\\begin{array}{rcl}\n", " G(y) = \\dfrac{1}{1+e^{(0.216*distance - 0.002*distance^2 - 0.584)}}\n", "\\end{array}\n", "$$" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "#use the seaborn library to inspect the distribution of the shots by result (goal or no goal) \n", "fig, axes = plt.subplots(figsize=(11, 5))\n", "#first we want to create bins to calc our probability\n", "#pandas has a function qcut that evenly distibutes the data \n", "#into n bins based on a desired column value\n", "df['Goal']=df['Goal'].astype(int)\n", "df['Distance_Bins'] = pd.qcut(df['Distance'],q=100)\n", "#now we want to find the mean of the Goal column(our prob density) for each bin\n", "#and the mean of the distance for each bin\n", "dist_prob = df.groupby('Distance_Bins',as_index=False)['Goal'].mean()['Goal']\n", "dist_mean = df.groupby('Distance_Bins',as_index=False)['Distance'].mean()['Distance']\n", "dist_trend = sns.scatterplot(x=dist_mean,y=dist_prob)\n", "dist_trend.set(xlabel=\"Distance (m)\",\n", " ylabel=\"Probabilty of Goal\",\n", " title=\"Probability of Scoring Based on Distance\")\n", "dis = np.linspace(0,50,100)\n", "sns.lineplot(x = dis,y = 1/(1+np.exp((0.21632621*dis-0.00206089*dis**2-0.58419379))),color='green',\n", " label='Log Fit with Quadratic Term')\n", "\n", "\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now that is an improvement! If we add a quadratic term for the distance variable, we do a much better job at predicting shots close to goal. A numerical evaluation does not offer us this luxury. This sort of analysis is more of an art and less of a science, so it is important to play around with different options. Of course this is merely an ad hoc method of evaluating our model, for the purpose of graphically representing how the model compares to the data. We will explore a more concrete method of assessing the accuracy of the model soon, but let’s first add the angle predictor to the mix. We fit these two variables to the data and graph the probability via a contour map onto a pitch:" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\n", "I am going to explore some different variables and polynomials. Some of them I have deleted or modified but if you are following along, try to play around with your own model. " ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[0.05221106]] [-3.60645775]\n" ] }, { "data": { "text/html": [ "
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coef
Angle Degrees0.052211
\n", "
" ], "text/plain": [ " coef\n", "Angle Degrees 0.052211" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "#similar to before but using ang variable\n", "train_ang = df[['Goal','Angle Degrees']].copy()\n", "x_train_ang, x_test_ang, y_train_ang, y_test_ang = train_test_split(train_ang.drop('Goal',axis=1), \n", " train_ang['Goal'], test_size=0.20, \n", " random_state=10)\n", "from sklearn.linear_model import LogisticRegression\n", "lgm_ang = LogisticRegression()\n", "lgm_ang.fit(x_train_ang,y_train_ang)\n", "log_odds_ang = lgm_ang.coef_[0]\n", "print(lgm_ang.coef_, lgm_ang.intercept_)\n", "pd.DataFrame(log_odds_ang, \n", " x_train_ang.columns, \n", " columns=['coef']).sort_values(by='coef', ascending=False)" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "#same for the angle\n", "fig, axes = plt.subplots(figsize=(11, 5))\n", "df['Angle_Bins'] = pd.qcut(df['Angle Degrees'],q=100)\n", "angle_prob = df.groupby('Angle_Bins',as_index=False)['Goal'].mean()['Goal']\n", "angle_mean = df.groupby('Angle_Bins',as_index=False)['Angle Degrees'].mean()['Angle Degrees']\n", "angle_trend = sns.scatterplot(x=angle_mean,y=angle_prob)\n", "angle_trend.set(xlabel=\"Avg. Angle of Bin\",\n", " ylabel=\"Probabilty of Goal\",\n", " title=\"Probability of Scoring Based on Angle\")\n", "ang = np.linspace(0,100,100)\n", "sns.lineplot(x = ang,y = 1/(1+np.exp(-(lgm_ang.coef_[0][0]*ang+lgm_ang.intercept_[0]))),color='green',\n", " label='Log Fit')\n", "\n", "\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[ 0.08400573 -0.00035088]] [-4.14642689]\n" ] } ], "source": [ "df_poly_ang = df[['Goal','Angle Degrees']].copy()\n", "X_train, X_test, Y_train, Y_test = train_test_split(df_poly_ang.drop('Goal',axis=1), \n", " df_poly_ang['Goal'], test_size=0.20, \n", " random_state=10)\n", "\n", "poly = PolynomialFeatures(degree = 2, interaction_only=False, include_bias=False)\n", "lr_ang_poly = LogisticRegression()\n", "pipe = Pipeline([('polynomial_features',poly), ('logistic_regression',lr_ang_poly)])\n", "pipe.fit(X_train, Y_train)\n", "\n", "log_odds = lr_ang_poly.coef_[0]\n", "\n", "\n", "print(lr_ang_poly.coef_,lr_ang_poly.intercept_)" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "#same for the angle\n", "fig, axes = plt.subplots(figsize=(11, 5))\n", "df['Angle_Bins'] = pd.qcut(df['Angle Degrees'],q=100)\n", "angle_prob = df.groupby('Angle_Bins',as_index=False)['Goal'].mean()['Goal']\n", "angle_mean = df.groupby('Angle_Bins',as_index=False)['Angle Degrees'].mean()['Angle Degrees']\n", "angle_trend = sns.scatterplot(x=angle_mean,y=angle_prob)\n", "angle_trend.set(xlabel=\"Avg. Angle of Bin\",\n", " ylabel=\"Probabilty of Goal\",\n", " title=\"Probability of Scoring Based on Angle\")\n", "ang = np.linspace(0,100,100)\n", "sns.lineplot(x = ang,y = 1/(1+np.exp(-(lr_ang_poly.coef_[0][0]*ang + lr_ang_poly.coef_[0][1]*ang**2\n", " + lr_ang_poly.intercept_[0]))),color='green',\n", " label='Log Fit')\n", "\n", "\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[-0.08801449 1.41598327]] [-1.48107418]\n", " coef\n", "Angle Radians 1.415983\n", "Distance -0.088014\n" ] } ], "source": [ "train_2 = df[['Goal','Distance','Angle Radians']].copy()\n", "x_train_2, x_test_2, y_train_2, y_test_2 = train_test_split(train_2.drop('Goal',axis=1), \n", " train_2['Goal'], test_size=0.20, \n", " random_state=10)\n", "\n", "\n", "lgm_2 = LogisticRegression(random_state=0)\n", "lgm_2.fit(x_train_2,y_train_2)\n", "log_odds = lgm_2.coef_[0]\n", "print(lgm_2.coef_, lgm_2.intercept_)\n", "print(pd.DataFrame(log_odds, \n", " x_train_2.columns, \n", " columns=['coef']).sort_values(by='coef', ascending=False))\n" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "def Logistic(Y):\n", " g_y = 1 + np.exp(-Y)\n", " return np.reciprocal(g_y)\n", "\n", "\n", "x0 = np.linspace(-34, 34, 100)\n", "x1 = np.linspace(.1, 53 , 100)\n", "x_0 = np.linspace(0, 68, 100)\n", "x0_grid, x1_grid = np.meshgrid(x0, x1)\n", "c=7.32\n", "a=np.sqrt((x0_grid-7.32/2)**2 + x1_grid**2)\n", "b=np.sqrt((x0_grid+7.32/2)**2 + x1_grid**2)\n", "h_grid = Logistic(lgm_2.coef_[0][1]*np.arccos((c**2-a**2-b**2)/(-2*a*b))\n", " +lgm_2.coef_[0][0]*np.sqrt((x1_grid)**2+(x0_grid)**2)+lgm_2.intercept_[0])\n", "\n", "\n", "fig, ax = plt.subplots(figsize=(11, 7))\n", "draw_pitch(orientation=\"vertical\",\n", " aspect=\"half\",\n", " pitch_color='white',\n", " line_color=\"black\",\n", " ax=ax)\n", "\n", "\n", "CS =plt.contourf(x_0,x1, h_grid,alpha=.85,cmap='OrRd',levels=50)\n", "\n", "\n", "plt.title('xG Model')\n", "\n", "#plt.axis('off')\n", "ax.set_xlim(0,68)\n", "ax.set_ylim(52.5,0)\n", "plt.colorbar()\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This represents the simplest expected goals model. If we flip back to part one and compare the two dimensional density plot with the xG model, we see that our two parameter model matches the probability distribution to a reasonable extent. Now for a closer look at the contour plot:" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(22.0, 0.0)" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import matplotlib\n", "import numpy as np\n", "import matplotlib.cm as cm\n", "import matplotlib.mlab as mlab\n", "import matplotlib.ticker as ticker\n", "import matplotlib.pyplot as plt\n", "\n", "matplotlib.rcParams['xtick.direction'] = 'out'\n", "matplotlib.rcParams['ytick.direction'] = 'out'\n", "\n", "def Logistic(Y):\n", " g_y = 1 + np.exp(-Y)\n", " return np.reciprocal(g_y)\n", "\n", "\n", "x0 = np.linspace(-34, 34, 100)\n", "x1 = np.linspace(.1, 53 , 100)\n", "x_0 = np.linspace(0, 68, 100)\n", "x0_grid, x1_grid = np.meshgrid(x0, x1)\n", "c=7.32\n", "a=np.sqrt((x0_grid-7.32/2)**2 + x1_grid**2)\n", "b=np.sqrt((x0_grid+7.32/2)**2 + x1_grid**2)\n", "h_grid = Logistic(1.57148079*np.arccos((c**2-a**2-b**2)/(-2*a*b))\n", " -0.11023242*np.sqrt((x1_grid)**2+(x0_grid)**2)-1.02645936)\n", "\n", "\n", "fig, ax = plt.subplots(figsize=(11, 7))\n", "draw_pitch(orientation=\"vertical\",\n", " aspect=\"half\",\n", " pitch_color='white',\n", " line_color=\"black\",\n", " ax=ax)\n", "\n", "\n", "CS =plt.contour(x_0,x1, h_grid,alpha=1,cmap='OrRd',levels=7)\n", "\n", "# Define a class that forces representation of float to look a certain way\n", "# This remove trailing zero so '1.0' becomes '1'\n", "class nf(float):\n", " def __repr__(self):\n", " str = '%.1f' % (self.__float__(),)\n", " if str[-1] == '0':\n", " return '%.0f' % self.__float__()\n", " else:\n", " return '%.1f' % self.__float__()\n", "\n", "\n", "# Recast levels to new class\n", "CS.levels = [nf(val*100) for val in CS.levels]\n", "\n", "# Label levels with specially formatted floats\n", "if plt.rcParams[\"text.usetex\"]:\n", " fmt = r'%r \\%%'\n", "else:\n", " fmt = '%r %%'\n", "plt.clabel(CS, CS.levels[1::2],inline=True, fmt=fmt, fontsize=12)\n", "\n", "plt.title('xG Model')\n", "\n", "#plt.axis('off')\n", "ax.set_xlim(10,58)\n", "ax.set_ylim(22,0)\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This is where we need to invoke some footballing knowledge. While the probability of values in central positions resembles the density plot from Part I, they are far too large for small angle positions near the goal line. Is it at all plausible to score from 5 meters out and effectively zero angle with the goal? Never mind having a 15% chance! This is a clear flaw with this simplified model. This does however represent a chance to experiment with different possibilities and variables. We can choose to add polynomial terms and interaction terms (such as δ*distance*angle) or add another variable all together. I tried a number of options and found that adding a “distance to center” of the pitch variable to produce the most reasonable contour plot: " ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[-0.08812064 1.41583297 -0.00209564]] [-1.40900091]\n" ] } ], "source": [ "#playing around with polynomials and variables to try to get better values for small angs\n", "from sklearn_pandas import DataFrameMapper\n", "from sklearn.compose import ColumnTransformer\n", "from sklearn.preprocessing import PolynomialFeatures, FunctionTransformer\n", "df_3 = df[['Goal','Distance','Angle Radians','Y']].copy()\n", "x_train_3, x_test_3, y_train_3, y_test_3 = train_test_split(df_3.drop('Goal',axis=1), \n", " df_3['Goal'], test_size=0.20, \n", " random_state=10)\n", "#ct = ColumnTransformer([('poly_X0X1', PolynomialFeatures(degree = 2, interaction_only=True, include_bias=False), \n", "# ['Distance','Angle Radians']),\n", "# ('poly_x0**2', FunctionTransformer(func=lambda x: x**2), ['Distance']),\n", "# ('Y',FunctionTransformer(func=lambda x: x),['Y'])])\n", "\n", "#poly_train = ct.fit_transform(X_train)\n", "#poly_test = ct.fit_transform(X_test)\n", "\n", "\n", "lgm_3 = LogisticRegression()\n", "\n", "lgm_3.fit(x_train_3, y_train_3)\n", "#print('dis, ang, Y')\n", "print(lgm_3.coef_,lgm_3.intercept_)\n" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(27.0, 0.0)" ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "def Logistic(Y):\n", " g_y = 1 + np.exp(-Y)\n", " return np.reciprocal(g_y)\n", "\n", "x0 = np.linspace(-34, 34, 100)\n", "x1 = np.linspace(.1, 53 , 100)\n", "x_0 = np.linspace(0, 68, 100)\n", "x0_grid, x1_grid = np.meshgrid(x0, x1)\n", "c=7.32\n", "a=np.sqrt((x0_grid-7.32/2)**2 + x1_grid**2)\n", "b=np.sqrt((x0_grid+7.32/2)**2 + x1_grid**2)\n", "ang = np.arccos((c**2-a**2-b**2)/(-2*a*b))\n", "dis = np.sqrt((x1_grid)**2+(x0_grid)**2)\n", "#h_grid_poly = Logistic(lr.coef_[0][0]*dis +lr.coef_[0][1]*ang + lr.coef_[0][2]*dis*ang +\n", "# lr.coef_[0][3]*(ang**2)+lr.coef_[0][3]*x0_grid+lr.intercept_[0])\n", "\n", "h_grid_Y = Logistic(lgm_3.coef_[0][0]*dis +lgm_3.coef_[0][1]*ang +lgm_3.coef_[0][2]*(x0_grid) +lgm_3.intercept_[0])\n", "\n", "\n", "\n", "fig, ax = plt.subplots(figsize=(11, 7))\n", "draw_pitch(orientation=\"vertical\",\n", " aspect=\"half\",\n", " pitch_color='white',\n", " line_color=\"black\",\n", " ax=ax)\n", "\n", "\n", "CS =plt.contourf(x_0,x1, h_grid_Y,alpha=.9,cmap='OrRd',levels=50)\n", "\n", "\n", "#plt.title('xG Model')\n", "\n", "plt.axis('off')\n", "\n", "ax.set_xlim(10,58)\n", "ax.set_ylim(27,0)\n", "#ax.set_xlim(0,68)\n", "#ax.set_ylim(53,0)\n", "#plt.colorbar()\n" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(22.0, 0.0)" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "matplotlib.rcParams['xtick.direction'] = 'out'\n", "matplotlib.rcParams['ytick.direction'] = 'out'\n", "\n", "fig, ax = plt.subplots(figsize=(11, 7))\n", "draw_pitch(orientation=\"vertical\",\n", " aspect=\"half\",\n", " pitch_color='white',\n", " line_color=\"black\",\n", " ax=ax)\n", "\n", "\n", "\n", "CS =plt.contour(x_0,x1, h_grid_Y,alpha=1,cmap='OrRd',levels=10)\n", "\n", "# Define a class that forces representation of float to look a certain way\n", "# This remove trailing zero so '1.0' becomes '1'\n", "class nf(float):\n", " def __repr__(self):\n", " str = '%.1f' % (self.__float__(),)\n", " if str[-1] == '0':\n", " return '%.0f' % self.__float__()\n", " else:\n", " return '%.1f' % self.__float__()\n", "\n", "\n", "# Recast levels to new class\n", "CS.levels = [nf(val*100) for val in CS.levels]\n", "\n", "# Label levels with specially formatted floats\n", "if plt.rcParams[\"text.usetex\"]:\n", " fmt = r'%r \\%%'\n", "else:\n", " fmt = '%r %%'\n", "plt.clabel(CS, CS.levels[:3],inline=True, fmt=fmt, fontsize=10)\n", "\n", "plt.title('xG Model (with added distance to center variable)')\n", "\n", "plt.axis('off')\n", "ax.set_xlim(10,58)\n", "ax.set_ylim(22,0)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Adding this new variable decreases the chance of scoring from small angles close to goal, but does little for further distances. This is probably because there are few shots taken from those positions and of the shots recorded, some might be miss-hit crosses that resulted in unlikely goals. Players rarely take shots from these wide, low angle positions. If we had 10 seasons worth of data, we would see the model begin to undervalue those types of shots. We could also choose to add artificial data in the form of misses on the goal line to fix this flaw, but for now we choose to live with it. Remember that while I have tried to add polynomial factors and this new variable to fix this flaw, the optimization in logistic regression will still fit the training data best it can. That is, as much as I want to tell the model to undervalue these types of shots, logistic regression only knows how to maximize the likelihood. I can merely add more flexibility to the model but I cannot tell it how and where to curve. \n", "\n", "While we have visualized these models, we still do not have anything concrete on how well they perform at predicting future data. If we also want to add more variables, such as a categorical header variable, the visualization is going to become more cumbersome and difficult. For that we are going to need to employ some statistical analysis.\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Model Evaluation" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If we want to assess the accuracy of our model, we have to test how well it can predict future events. But this raises another concern. How do we classify a shot with our new expected goals model? Unlike the Heaviside function, which gives hard classifications, the logistic regression model returns a probability of a shot resulting in a goal.\n", "\n", " In order to make a classification, we have to define a threshold. This threshold essentially splits the logistic function, assigning goals for where the model lies above the threshold and misses below. For example:" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0.5, 1.0, 'Logistic Regression Model for Shots')" ] }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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YsCDL45es5VtLpjHmPWPMfmPMxgyWG2PMJGPMNmPMemNMZH7FIoVPcnLKZ2tTTycmOvPc85OSUqZdjQKe7Vz/zGOt7+2Sk9Ov5/2eUQyQel9pt0lbZnJyyvbu6bTreE+7l7u3SUxMXS8ZHWdGx+CrfO/53sfmrk83dyy+pr239bWeL+66yOg7TBv7uZDZd+Erloy+a1/LMtrubGLN6zIzKjez7z678aSdTvuznVl9+VtYWBgxMTF88sknnv6PvrRs2ZIBAwbwzjvveFomW7RowbPPPssLL7zAzp07KVWqFAsXLmT16tU0adKEiIgIFi5cyF9//cWvv/5K27ZtqVatGsWLF+e2227zuZ9OnTrx119/ceedd/LHH3/QqFEjYmNjAWjatCm1a9cmICCAiIgIYmJi2LJlC/Xq1eOKK64AoH///ixdujTP6mfSpEmEh4fTvHlz/v77b7Zu3coll1zCX3/9xf3338+3337rSVbDwsLo06cPH330EcWKZb9968cff6Rnz56eZLhy5cqAcy/VTp06ERoayksvvcSmTZsyLScuLo4jR47Qpk0bIH1d3HTTTQA0btyYmJiYbMcnmcvPlsxpwGtARj1urwMud72aAW+43gu96RumM2bhGHbF7aJOhTqM7zCePqF9sr39PfPu4a3Vb5Fsnd/GZYLK8NYNb2VZhvd+K5dyfhAPnTyUoxi8yyhTvAzHzxzHYgk0gQxtPJSWdVoyZuEYdsbt9Ll9lVJVuLXhrczfOp+dcTsxGCzOXw6DYVjUMF6//nXumXcPb0a/6VnmfZzv3N+HuDhYvRqeegoOH4YlS6BiRdixA/bsgerVwRioXBn27oVTp6BCBTh0CJo0gXbtnO0A1q1zyjp50tmudm1n/d9/d8po1Mh579QJ4uJg7VqIiIAJE5z51sJFFzmJ0O7dEBAATzwBr78OwcFObNbCqFFOjADffgvNmjnT334LO13VNXQofPedM12smBPLzz/DVVc5ZTRvDnPmQKVKsG+fM++yyyA62jmuY8ecYzxxwtm393FWquTENWpU6mN48klnnRUrnOO59lr46iu44Qb4/nv4+2+nXrp1g8WLYfNmuOQSuO46ePxxqFULAgOd9dq1c+qoVStYvx7CwmDZMud7qVfPmV+5srNd48bOd7J4ccr50batcyxly8LFFzvH++mnzjFVr+7Us/t7qFgRxo3L8pQ9a+PGpf6+jhxx6n3lSt+xjBvnrONdt2nr330euNdzn0fuZbk9Lu9951WZGZV70UXOvMGDYeJEZ15kJBw4AEOGONtkFU/a5U88AXPnOueaMRnXXaocKxstjvmpW7duPPTQQyxevJiDBw/6XOfNN9/k119/Zd68eTRu3JjVq1dz++2306xZM+bNm0eXLl146623sNbSv39/nnvuuVTbf/nll9mOp3Llytx+++3cfvvtdO3alaVLl1KlShXPpW2AwMBAEt3/mebQZZddxq5duzh69GimrZmLFy9mwYIF/PLLL5QuXZq2bdty6tQpKlWqxLp16/juu+948803+eyzz3jvvfeYN28eS5cu5auvvmL8+PFs2LAhV/G53X///TzwwAN069aNxYsXM+4sf1m46+9s6k7Sy7ck01q71BhTN5NVbgQ+sE7HkRXGmIrGmAuttXvzK6ZzYfqG6Qz9aignEpxRezvjdjL0q6EA2Ury7pl3D29Ev5Fq3vGE4/T7vF+mZaTd78GTKb8MsxtD2jLiz8R7liXZJN6IfoN31rxDYnLGP4AHTx5MFb93EmmxvBH9BktilrD5wOZ02x5POM4ds/tz0b/XsWtLZSIjoU0bmDTJWR4WBvv3O616e/Y483bvTtk+3hXuxo1OguXeLiQkZdnevc7L28qVzvvp0ynJ2auvOvMmTIARI1L207ixkyS9/rrzx3bzZif5fPBBZ5vhw50/tL/+6rzCwpxkzG3KFCehctu92/nDvW5dSixVq6YkpZCSbP70k/MeGOjsc9Om1Mc5fDiMHOlMu4/B3TLkXgdg+3Yn9n/+cd7BqU9rnXgOHHBezZo5sf37r7PO/fenJOFr1zrHNnmys6xkyZT599/v1JO7LpOTncQ8OdlJOI4fd1779qXUvTuGPXtSvocRI5yY8vN2idY6iY77+4qIcPbtljYWcI7BV9161//w4amXTZjgJFCvvpr747I2Zd95VWZG5Y4cmXLOu49hyZKU8/Tw4ZTvM6N40i5/5RUnwXTXb6tWKeePd925xrQUGIMGDaJixYqEhoay2Ps/Ji/bt2+nWbNmNGvWjG+++Ya///6buLg4LrnkEoYPH86uXbtYv3491157LTfeeCOjRo2ievXqHDp0iGPHjtGsWTNGjBjBwYMHKV++PDNnziQ8PDzdfn788UeaN29O6dKlOXbsGNu3b6dOnTocP37cZ1z169cnJiaGbdu2cdlll/Hhhx96WvLKlSvHsWPH0l0uL126NIMHD2bEiBG89dZbFC9enNjYWBYvXkzPnj0968XFxVGpUiVKly7NH3/8wYoVKwA4cOAAxYsX5+abb6Z+/fr07duX5ORk/v77b9q1a8fVV1/Np59+Snx8PNnRvn17evTowQMPPECVKlU4dOgQlStXJi4uzjMQ6/333/esX65cOY4ePZqunAoVKlCpUiWWLVtGq1atUtWF5B9/9smsBfztNf2Pa16hTjLHLBzjSdLcTiScYMzCMdlKMt9e/bbP+ckkZ1qGr/3mNIasygAyTTCzy1eC6WZNEnZoJBEfxrB2bcofNUhJ1kqWdFoifalSBQ4eTJ1UbfTZYSM9dzLxyivwwAPOH0f3H8j773da7NaudVogwUkGDxxImR4xwvlDC84f+0mTUieYkDrBdPM+RkhJ/NzSXrZNSkrZt/dxuj+nPYa03OWn3U/aONwJQERE6oTAzfvYvL8P7+1Wr3YSTHDe16xJnVT74v4e3K1f+ckYp5UOnPrzTjAzisX9HaetW+/69z4PvM+jszkuY1LvOy/KzKzc4cOdVuj161OfZ8OHO3WWnXh8LXcn8t51nbbu/vgjd8eSH2rXrs1w938NGRg9ejRbt27FWkuHDh0IDw/nhRde4MMPPyQoKIgaNWrw3//+l8qVK/PMM89w7bXXkpycTFBQEFOmTKF58+aMGzeOFi1aULFiRSIiInzuZ/Xq1dx3330UK1aM5ORkhgwZQpMmTTJMfkuWLMnUqVPp2bMniYmJNGnSxDPaeujQoXTu3JmaNWuyaNGiVNs988wzjB07luDgYEqWLEmZMmV46qmnUq3TuXNn3nzzTRo0aED9+vVp3rw5ALt372bgwIEku/pFPPfccyQlJdG3b1/i4uKw1jJ8+HAqupv7s9CwYUPGjBlDmzZtCAwMpFGjRkybNo1x48bRs2dPKlWqRPv27dmxYwcAN9xwA7fccgtz5sxhcppfWu+//z7Dhg3jxIkTXHLJJUydOjVbMUjuGZuPnWBcLZlfW2tDfCz7GnjeWvuTa3oh8Ii1NtrHukOBoQB16tRpvNO7maeACXgyIFXrnZvBkPxEBp3UvNd7MuO/FJmVkdF+cxJDdso4FwyGxMeSCQz0vTwhAYKCfC9LTExJ+nIjOTnlsp87OXLPd7ciZrQv97aQfvu8ltlxZnQMuZWU5JSX07KSknxvk5xMht+t9zrn8oEvmdWVr1iyu76v8+hsjys/ysyo3LTnvK/9ZRVP2uVJSRl//+5tf//9dxo0aJD7gxGRfOHrZ9MYs9paG+VrfX/ewmg3cJHXdG3XvHSstW9ba6OstVHVqlU7J8HlVp0KdXI0P61Ak/Ff38zKyE75Wa2T3RjzW+1ydWjcOOPl5cplvOyCC85u36NGOX/oRo1KPX/ECNLFVKNG+m3dAxlGjjy7OLKSdt9p4/B1DLnVuHHuLmE2bpx+8E9ystOSmRV3XZ4LWX1faWNx9zvMan1f653tceVHmRmVO3Kk0185rZEjU7euZxaPr+WZ/Wyfy+9dRPKfP5PMuUA/1yjz5kBcYe+PCTC+w3hKB6W+uW3poNKM7zA+W9sPbTzU5/wAAjItw9d+cxpDVmUAFAs4+x4WwVWDM1xmbCDm7TWsXQvh4Sl928DpA5jZpXJwLpVXrpx6u5B07ei+ufsxNm6cul/Z/fc7l4DdfQwTE1MuV1et6kyPGOFsM3Kk89m7H6k318DIVNJ2vUrTRcrTKuR+Dwx09l2lSurjHD7ceXkfg3uer/LT7ic8PPW8++935q1d6xz/vfc6x+/mfWwlS6bezn1J1DvRdCeYmV0qh5Tv4VwkHO4E0/19pb1KmTYWd9Lkq26963/kSOflfR65z5HcHpf3vvOqzIzKHT48dXeP4cNTztNJk5xjc/8jk1E8aZcnJaWcFxERznniq+7y6p8jEfG/fOuTaYz5BGgLVDXG/AM8AQQBWGvfBOYDXYBtwAlgYH7Fci65+zzmdnT569e/DpDj0eVp95ub0eVpy/Db6PLFlalcKmV0+fDhKaPLq1fPenR5SIgzWtWdAKxb54xmzs7o8jZt0vfDe/VV+Pxz54+ku4/hPfekjC4PDEzpe+buZtSsWcpo5ZIlcz66vHbt7I0u9z5O9whdY1Ifw5NPOuvkdHR55cpOH0r36PLJk53R5e4+muvXp/RV3bEDrrwyZXT56tUpo8u9+2RWrAhlymQ9urxNG2fdc9Ens1Kl1N9X69apR5enjaVixfR1m7b+3eeBr/6JuT0ud7l5WWZG5U6cCLNnZzy6vFKllO8zo3h8LXc/IMc9ujyzuhORwi9f+2Tmh6ioKBsdna7bppxn3COSIaUFyT2dmJjSpyvtMu/+fu5T290/0bsvmHs7Y1K3FLrnpR2pm3Y/kL5vmfc2afftng4ISL1v73XcjEnfr9LdB9NdL2mPxb2ddxy+4vEu3x2Le7n72Nx9Kd3bumPxNe1dL77Wy6hPZtp4vffvq/7zW9rvyy2jWDL6rn0tS3se5UWfzLwuM6Ny0/6MpP2OsxNP2um0P9uQvr7UJ1OkYMppn0w98UcKJO/kJO0fNe8BL2n/uHonfd7LjMl8u7Tz0y5PG0PaffnaX0bb+ior7bR3wgUpsbvnZ3ScGR1DVuV7L097XGkTxYy+m8zWy2y+r+/iXCaYafeX1XeTk/WzU1ZO5UeZGZWb0XmTk3gyKyO/jkVECgZ/9skUERERkfOUkkwREZE09u3bx+23384ll1xC48aNadGiBV988UWuyoqJiSEkgxGIf/75J126dOHyyy8nMjKSW2+9lX379rF48WK6du16NoeQypAhQ9i82blH8cyZM2nQoAHt2rUjOjo6y/uAZmTixImcOJFyb+UuXbqkey65FG26XC4iIuLFWkv37t3p378/H3/8MQA7d+5k7ty5ebqfU6dOcf311/PKK69www03AM7jGt3PI89L7777rufz//73P9555x2uvvpqAKKifHany9LEiRPp27cvpUs7dyWZP3/+2Qcq5xW1ZIqIiHj58ccfKV68uOfpOAAXX3wx97vuu3Tq1CkGDhxIaGgojRo18jwxJyYmhlatWhEZGUlkZCQ///xzpvv5+OOPadGihSfBBGjbtm26Vs+VK1fSokULGjVqxFVXXcWWLVsA2LRpE02bNiUiIoKwsDC2bt3K8ePHuf766wkPDyckJIQZM2Z4yo2Ojuapp57ip59+YvDgwYwePTpVi2l8fLznuMLCwpg9ezYAd999N1FRUTRs2JAnnngCgEmTJrFnzx7atWtHu3btAKhbty4HXI8Se+WVVwgJCSEkJISJrsdqxcTE0KBBA+68804aNmzItddey8mTJ3P47UhhopZMEREpsEZ+O5K1/67N0zIjakQwsfPEDJdv2rSJyEyeGjBlyhSMMWzYsIE//viDa6+9lj///JPq1avzww8/ULJkSbZu3Urv3r3J7G4oGzdupHFmd6d3ufLKK1m2bBnFihVjwYIF/Pe//2X27Nm8+eabjBgxgj59+nDmzBmSkpKYP38+NWvWZN68eYDzjHFvjz/+OD/++CMvv/wyUVFRqR5J+fTTT1OhQgU2bNgAwOHDhwEYP348lStXJikpiQ4dOrB+/XqGDx/OK6+8wqJFi9I9/3z16tVMnTqVX3/9FWstzZo1o02bNlSqVImtW7fyySef8M4773Drrbcye/Zs+vbtm2UdSOGklkwREZFM3HvvvYSHh9OkSRMAfvrpJ09idOWVV3LxxRfz559/kpCQwJ133kloaCg9e/b09IE8W3FxcfTs2ZOQkBBGjRrFpk2bAGjRogXPPvssL7zwAjt37qRUqVKEhobyww8/8Mgjj7Bs2TIqVKiQ7f0sWLCAe++91zNdqVIlAD777DMiIyNp1KgRmzZtyvK4fvrpJ3r06EGZMmUoW7YsN910E8uWLQOgXr16nmezN27cmJiYmBzUhBQ2askUEZECK7MWx/zSsGFDz6VicFouDxw4kGXfxQkTJnDBBRewbt06kpOTKen9KKwM9rNkyZIs43nsscdo164dX3zxBTExMbRt2xaA22+/nWbNmjFv3jy6dOnCW2+9Rfv27VmzZg3z589n7NixdOjQgccffzzrg87Ajh07ePnll1m1ahWVKlViwIABnMrssWtZKFGihOdzYGCgLpef59SSKSIi4qV9+/acOnWKN954wzPPexR1q1atmD59OuCMDt+1axf169cnLi6OCy+8kICAAD788EOSkpIy3c/tt9/Ozz//7Lm0DbB06VI2btyYar24uDhq1aoFwLRp0zzz//rrLy655BKGDx/OjTfeyPr169mzZw+lS5emb9++jB49mjVr1mT7uDt27MiUKVM804cPH+bo0aOUKVOGChUqsG/fPr755hvP8nLlynHs2LF05bRq1Yovv/ySEydOcPz4cb744gtatWqV7Tjk/KEkU0RExIsxhi+//JIlS5ZQr149mjZtSv/+/XnhhRcAuOeee0hOTiY0NJTbbruNadOmUaJECe655x7ef/99wsPD+eOPPyhTpkym+ylVqhRff/01kydP5vLLLyc4OJjXX3+datWqpVrv4Ycf5j//+Q+NGjUiMTHRM/+zzz4jJCSEiIgINm7cSL9+/diwYYNnMNCTTz7J2LFjs33cY8eO5fDhw4SEhBAeHs6iRYsIDw+nUaNGXHnlldx+++20bNnSs/7QoUPp3LmzZ+CPW2RkJAMGDKBp06Y0a9aMIUOG0KhRo2zHIecPPVZSREQKFD1WUqRgyuljJdWSKSIiIiJ5TkmmiIiIiOQ5JZkiIiIikueUZIqIiIhInlOSKSIiIiJ5TkmmiIiIiOQ5JZkiIiJeDh48SEREBBEREdSoUYNatWoRERFBxYoVCQ4OzvP9jRs3jpdffjlH25QtW9bn/AEDBjBr1qxcxfHcc89x2WWXUb9+fb777juf6wwePJjw8HDCwsK45ZZbiI+Pz9W+pGhQkikiIuKlSpUqrF27lrVr1zJs2DBGjRrlmQ4IyPrPpvcN0wuLzZs38+mnn7Jp0ya+/fZb7rnnHp9PLJowYQLr1q1j/fr11KlTh9dee80P0UphoSRTREQkm5KSkrjzzjtp2LAh1157refZ223btmXkyJFERUXx6quvsnr1atq0aUPjxo3p1KkTe/fuBWDSpEkEBwcTFhZGr169POVu3ryZtm3bcskllzBp0iTP/FdeeYWQkBBCQkKYOHFiunistdx3333Ur1+fa665hv379+fquObMmUOvXr0oUaIE9erV47LLLmPlypXp1itfvrxnvydPnsQYk6v9SdFQzN8BiIiIZKatj3m3AvcAJ4AuPpYPcL0OALekWbb4LGLZunUrn3zyCe+88w633nors2fPpm/fvgCcOXOG6OhoEhISaNOmDXPmzKFatWrMmDGDMWPG8N577/H888+zY8cOSpQowZEjRzzl/vHHHyxatIhjx45Rv3597r77btavX8/UqVP59ddfsdbSrFkz2rRpk+oRjV988QVbtmxh8+bN7Nu3j+DgYAYNGpQu7pdeesnzvHVvrVu3ZtKkSezevZvmzZt75teuXZvdu3f7rIOBAwcyf/58goOD+b//+7/cVqUUAUoyRUREsqlevXpEREQA0LhxY2JiYjzLbrvtNgC2bNnCxo0b6dixI+C0fl544YUAhIWF0adPH7p370737t09215//fWUKFGCEiVKUL16dfbt28dPP/1Ejx49PM9Av+mmm1i2bFmqJHPp0qX07t2bwMBAatasSfv27X3GPXr0aEaPHp0ndTB16lSSkpK4//77mTFjBgMHDsyTcuX8oyRTREQKtMWZLCudxfKqWSzPqRIlSng+BwYGei6XA55k0FpLw4YN+eWXX9JtP2/ePJYuXcpXX33F+PHj2bBhg89y87pfZ1YtmbVq1eLvv//2zP/nn3+oVatWhuUFBgbSq1cvXnzxRSWZkiH1yRQREclD9evXJzY21pNkJiQksGnTJpKTk/n7779p164dL7zwAnFxcZmOzm7VqhVffvklJ06c4Pjx43zxxRe0atUq1TqtW7dmxowZJCUlsXfvXhYtWuSzrNGjR3sGL3m/3P0/u3Xrxqeffsrp06fZsWMHW7dupWnTpqnKsNaybds2z+e5c+dy5ZVX5rqe5PynlkwREZE8VLx4cWbNmsXw4cOJi4sjMTGRkSNHcsUVV9C3b1/i4uKw1jJ8+HAqVqyYYTmRkZEMGDDAk+wNGTIk1aVygB49evDjjz8SHBxMnTp1aNGiRa5ibtiwIbfeeivBwcEUK1aMKVOmEBgYCECXLl149913qVGjBv379+fo0aNYawkPD+eNN97I1f6kaDDWWn/HkCNRUVE2Ojra32GIiEg++f3332nQoIG/wxCRNHz9bBpjVltro3ytr8vlIiIiIpLnlGSKiIiISJ5TkikiIiIieU5JpoiIiIjkOSWZIiIiIpLnlGSKiIiISJ5TkikiIuLl4MGDREREEBERQY0aNahVq5Zn+syZM3myj7Zt21K/fn3Cw8Np2bIlW7ZsyXEZXbp04ciRIxw5coTXX3/dM3/Pnj3cckvaJ7afGy+//DJXXnklERERNGnShA8++OCc7Xvt2rXMnz/fMz1t2jTuu+++bG8/btw4z3cdEhLC3Llzcx1LTEwMISEhWa4XHx/P3XffzaWXXkpkZCSNGzfmnXfeyfV+y5Ytm+tt84OSTBERES9VqlTxPBFn2LBhjBo1yjNdvHjxPHvk4/Tp01m3bh39+/fP1XPF58+fT8WKFdMlmTVr1mTWrFl5EmNOvPnmm/zwww+sXLmStWvXsnDhQnJyL+6kpKRMp7OSNsnMDfd3PXPmTAYNGkRycnKq5Xn9uM8hQ4ZQqVIltm7dypo1a/j22285dOhQnu7Dn5RkiohIoTZ9w3TqTqxLwJMB1J1Yl+kb0j+j+2wNGDCAYcOG0axZMx5++GHGjRvHyy+/7FkeEhJCTEwMAB999BFNmzYlIiKCu+66K8tkqXXr1mzbtg1rLaNHjyYkJITQ0FBmzJgBwN69e2ndurWnhW3ZsmUA1K1blwMHDvDoo4+yfft2IiIiGD16dKpWtObNm7Np0ybPvtq2bUt0dDTHjx9n0KBBNG3alEaNGjFnzpyzrqNnn32WN954g/LlywNQvnx5+vfvD8DChQtp1KgRoaGhDBo0iNOnT3uO4ZFHHiEyMpKZM2emm/7+++9p0aIFkZGR9OzZ0/MYzlWrVnHVVVcRHh5O06ZNiYuL4/HHH2fGjBlERER46g7g2LFj1KtXj4SEBACOHj2aatqXBg0aUKxYMQ4cOEDbtm0ZOXIkUVFRvPrqq6xevZo2bdrQuHFjOnXqxN69ewFYvXo14eHhhIeHM2XKlCzra/v27axcuZJnnnmGgAAnHatWrRqPPPIIQIbnQ3x8PB06dCAyMpLQ0NA8+e7yi5JMEREptKZvmM7Qr4ayM24nFsvOuJ0M/WpoviSa//zzDz///DOvvPJKhuv8/vvvzJgxg+XLl7N27VoCAwOZPj3zWL766itCQ0P5/PPPWbt2LevWrWPBggWMHj2avXv38vHHH9OpUyfPsoiIiFTbP//881x66aWsXbuWl156KdWy2267jc8++wxwktW9e/cSFRXF+PHjad++PStXrmTRokWMHj2a48ePp9r22LFjnm4CaV+bN29Ote7Ro0c5duwYl1xySbrjO3XqFAMGDGDGjBls2LCBxMTEVI+jrFKlCmvWrKFXr16ppq+55hqeeeYZFixYwJo1a4iKiuKVV17hzJkz3Hbbbbz66queuipTpgxPPfUUt912G2vXruW2227zlF+uXDnatm3LvHnzAPj000+56aabCAoKyvA7+fXXXwkICKBatWoAnDlzhujoaIYPH87999/PrFmzWL16NYMGDWLMmDEADBw4kMmTJ7Nu3boMy/W2adMmwsPDPQlmWhmdDyVLluSLL75gzZo1LFq0iAcffDBHLcbnkp5dLiIihdaYhWM4kXAi1bwTCScYs3AMfUL75Om+evbs6Xmed0YWLlzI6tWradKkCQAnT56kevXqPtft06cPpUqVom7dukyePJlXXnmF3r17ExgYyAUXXECbNm1YtWoVTZo0YdCgQSQkJNC9e/d0SWZmbr31Vq699lqefPJJPvvsM09fze+//565c+d6WmNPnTrFrl27Uj0ysFy5cqxduzbb+8rIli1bqFevHldccQUA/fv3Z8qUKYwcORIgVULoPb1ixQo2b95My5YtASfRa9GiBVu2bOHCCy/01LG75TQzQ4YM4cUXX6R79+5MnTo1w36PEyZM4KOPPqJcuXLMmDEDY0yqmLZs2cLGjRvp2LEj4FzSv/DCCz19Y1u3bg3AHXfcwTfffJPtOgIYP348M2fOZP/+/ezZs4effvrJ5/lw3XXX8d///pelS5cSEBDA7t272bdvHzVq1MjR/s4FJZkiIlJo7YrblaP5Z6NMmTKez8WKFUvVX+/UqVOAc4mzf//+PPfcc1mWN336dKKifD7yOZXWrVuzdOlS5s2bx4ABA3jggQfo169ftmKuVasWVapUYf369cyYMYM333zTE+fs2bOpX79+htseO3aMVq1a+Vz28ccfExwc7JkuX748ZcuW5a+//vLZmpkZ73r1nrbW0rFjRz755JNUyzds2JCj8gFatmxJTEwMixcvJikpKcNBOaNGjeKhhx7KMEZrLQ0bNuSXX35JtfzIkSM5jik4OJh169aRnJxMQEAAY8aMYcyYMVkO3pk+fTqxsbGsXr2aoKAg6tat6zn/ChpdLhcRkUKrToU6OZqfV+rWrcuaNWsAWLNmDTt27ACgQ4cOzJo1i/379wNw6NAhdu7cma0yW7VqxYwZM0hKSiI2NpalS5fStGlTdu7cyQUXXMCdd97JkCFDPPt1K1euHMeOHcuw3Ntuu40XX3yRuLg4wsLCAOjUqROTJ0/2XGb97bff0m3nbsn09fJOMN3+85//cO+993L06FHA6Tv4wQcfUL9+fWJiYti2bRsAH374IW3atMmyPpo3b87y5cs92x0/fpw///yT+vXrs3fvXlatWgU4yXBiYmKW9dCvXz9uv/12Bg4cmOW+M1K/fn1iY2M9SWZCQgKbNm2iYsWKVKxYkZ9++gkgyy4SAJdddhlRUVGMHTvW02/31KlTnu8ko/MhLi6O6tWrExQUxKJFi7J9fvmDkkwRESm0xncYT+mg0qnmlQ4qzfgO4/N1vzfffDOHDh2iYcOGvPbaa55LwcHBwTzzzDNce+21hIWF0bFjR8/AkKz06NGDsLAwwsPDad++PS+++CI1atRg8eLFhIeH06hRI2bMmMGIESNSbVelShVatmxJSEiIz1Hqt9xyC59++im33nqrZ95jjz1GQkICYWFhNGzYkMcee+wsasNx9913065dO5o0aUJISAitWrUiICCAkiVLMnXqVHr27EloaCgBAQEMGzYsy/KqVavGtGnT6N27N2FhYbRo0YI//viD4sWLM2PGDO6//37Cw8Pp2LEjp06dol27dmzevDndwB+3Pn36cPjwYXr37p3rYyxevDizZs3ikUceITw8nIiICH7++WcApk6dyr333ktERESqPpJ79uyhS5cuPst79913OXjwoCfh7NixIy+++CKQ8fnQp08foqOjCQ0N5YMPPuDKK6/M9fHkN1NQO4tmJCoqykZHR/s7DBERySe///57qr6BWZm+YTpjFo5hV9wu6lSow/gO4/O8P6YUfrNmzWLOnDl8+OGH/g6l0PL1s2mMWW2t9dnvQ30yRUSkUOsT2kdJpWTq/vvv55tvvjnr+2hKzijJFBERkfPa5MmT/R1CkaQ+mSIiIiKS55RkioiIiEieU5IpIiIiInlOSaaIiIiI5DklmSIiImkEBgamelZ3TExMhutm9YSW7BgwYAD16tUjIiKCyMjIdE+UyY4hQ4Z4nin+7LPPplp21VVXnXWMOTVu3DjPYysLorVr16YabT5t2jTuu+++bG8/btw4atWqRUREBCEhIcydOzfXscTExGT4FCJv8fHx3H333Vx66aVERkbSuHHjDB+RmR15ce5mRkmmiIgUamlv95wXt38uVapUqifc1K1b9+wLzcJLL73E2rVref7557nrrrtyvP27777reRJP2iTTfcPw84n7KTkZTWclbZKZG6NGjWLt2rXMnDmTQYMGpXrUKEBiYuJZlZ/WkCFDqFSpElu3bmXNmjV8++23HDp0KE/3kZeUZIqISKE1bhyMGpWSWFrrTI8bl7f7iY+Pp0OHDkRGRhIaGsqcOXPSrbN3715at27tadlatmwZAN9//z0tWrQgMjKSnj17Eh8fn+m+Wrdu7XmU4iuvvEJISAghISFMnDgRcB6veP311xMeHk5ISIjn6TZt27YlOjqaRx99lJMnTxIREUGfPs79Q90tVr169WLevHmefQ0YMIBZs2aRlJTE6NGjadKkCWFhYbz11ltnV2FptG3blkceeYSmTZtyxRVXeOomKSmJhx56iJCQEMLCwjy3Glq4cCGNGjUiNDSUQYMGcfr0acB5nOcjjzxCZGQkM2fOTDedUV2vWrWKq666ivDwcM+jGR9//HFmzJiR7glBx44do169eiQkJABw9OjRVNO+NGjQgGLFinHgwAHatm3LyJEjiYqK4tVXX2X16tW0adOGxo0b06lTJ88ToFavXk14eDjh4eFMmTIlyzrcvn07K1eu5JlnniEgwEnfqlWrxiOPPAI4z1UfPXo0ISEhhIaGeo4pO+duvrHWFqpX48aNrYiInL82b96crfWSk60dMcJacN59TedWQECADQ8Pt+Hh4bZ79+42ISHBxsXFWWutjY2NtZdeeqlNdu2gTJky1lprX375ZfvMM89Ya61NTEy0R48etbGxsbZVq1Y2Pj7eWmvt888/b5988sl0++vfv7+dOXOmtdbazz77zDZt2tRGR0fbkJAQGx8fb48dO2aDg4PtmjVr7KxZs+yQIUM82x45csRaa22bNm3sqlWrUsXk5p7+/PPPbb9+/ay11p4+fdrWrl3bnjhxwr711lv26aefttZae+rUKdu4cWP7119/pYvz6quv9tSL9+uHH35It+4TTzxhX3rpJU9sDzzwgLXW2nnz5tkOHTpYa619/fXX7c0332wTEhKstdYePHjQnjx50tauXdtu2bLFWmvtHXfcYSdMmGCttfbiiy+2L7zwgmcf3tMZ1fXp06dtvXr17MqVK6211sbFxdmEhAQ7depUe++993rK8p4eMGCA/eKLL6y11r711lue2DM6vhUrVtgLL7zQJicn2zZt2ti7777bWmvtmTNnbIsWLez+/futtdZ++umnduDAgdZaa0NDQ+2SJUustdY+9NBDtmHDhun24W3OnDm2e/fuGS6fNWuWveaaa2xiYqL9999/7UUXXWT37NmTrXM3u3z9bALRNoOcTTdjFxGRQskYmDDB+fzqq84LYMQIZ74xuS/bfbncLSEhgf/+978sXbqUgIAAdu/ezb59+6hRo4ZnnSZNmjBo0CASEhLo3r07ERERLFmyhM2bN9OyZUsAzpw5Q4sWLXzuc/To0TzzzDNUq1aN//3vfyxcuJAePXpQpkwZAG666SaWLVtG586defDBB3nkkUfo2rUrrVq1yvZxXXfddYwYMYLTp0/z7bff0rp1a0qVKsX333/P+vXrmTVrFgBxcXFs3bqVevXqpdre3QKZGzfddBMAjRs39vRxXbBgAcOGDaNYMScdqVy5MuvWraNevXqe58H379+fKVOmMHLkSABuu+22VOW6p1esWOGzrrds2cKFF15IkyZNAChfvnyWsQ4ZMoQXX3yR7t27M3Xq1Az7PU6YMIGPPvqIcuXKMWPGDIzrpHPHtGXLFjZu3EjHjh0Bp+X2wgsv5MiRIxw5coTWrVsDcMcdd/DNN99kGZe38ePHM3PmTPbv38+ePXv46aef6N27N4GBgVxwwQW0adOGVatWcd1112V57uYXJZkiIlJouRNNd4IJZ59g+jJ9+nRiY2NZvXo1QUFB1K1bl1OnTqVap3Xr1ixdupR58+YxYMAAHnjgASpVqkTHjh355JNPstzHSy+9xC233OKZXrhwoc/1rrjiCtasWcP8+fMZO3YsHTp04PHHH8/WcZQsWZK2bdvy3XffMWPGDHr16gU4VzUnT55Mp06dMt2+VatWHDt2LN38l19+mWuuuSbTbUuUKAE4g6rOpq+iO+lOO22t9VnXGzZsyPE+WrZsSUxMDIsXLyYpKSnDQTmjRo3ioYceyjBGay0NGzZMN5DryJEjOY4pODiYdevWkZycTEBAAGPGjGHMmDFZDt7JzrmbX9QnU0RECi13H0xv3n0080pcXBzVq1cnKCiIRYsWsXPnznTr7Ny5kwsuuIA777yTIUOGsGbNGpo3b87y5cs9fSyPHz/On3/+ma19tmrVii+//JITJ05w/PhxvvjiC1q1asWePXsoXbo0ffv2ZfTo0axZsybdtkFBQRn2IbztttuYOnWqp1UUoFOnTrzxxhuebf7880+OHz+ebttly5alGhDlfmWVYGakY8eOvPXWW56k89ChQ9SvX5+YmBhPnX344Ye0adMmy7Iyquv69euzd+9eVq1aBTh9LhMTEylXrpzPhNmtX79+3H777QwcODBXxwZQv359YmNjPUlmQkICmzZtomLFilSsWJGffvoJcBLBrFx22WVERUUxduxYzyCnU6dOYV0ne6tWrZgxYwZJSUnExsaydOlST//TrM7d/KIkU0RECiV3gvnqq84l8uRk5/3VV/M+0ezTpw/R0dGEhobywQcfcOWVV6ZbZ/HixYSHh9OoUSNmzJjBiBEjqFatGtOmTaN3796EhYXRokUL/vjjj2ztMzIykgEDBtC0aVOaNWvGkCFDaNSoERs2bKBp06ZERETw5JNPMnbs2HTbDh06lLCwMM/AH2/XXnstS5Ys4ZprrqF48eKAc3k4ODiYyMhIQkJCuOuuu/J8ZLQvQ4YMoU6dOoSFhREeHs7HH39MyZIlmTp1Kj179iQ0NJSAgACGDRuWZVkZ1XXx4sWZMWMG999/P+Hh4XTs2JFTp07Rrl07Nm/enG7gj1ufPn04fPgwvXv3zvXxFS9enFmzZvHII48QHh5ORESEZ6T/1KlTuffee4mIiPAkigB79uyhS5cuPst79913OXjwoCfh7NixIy+++CIAPXr08NRj+/btefHFF6lRo0a2zt38Ymxe/7uXz6Kiomx0dLS/wxARkXzy+++/06BBg2ytO24cHDmSconcnXhWrJj3I8ylaJk1axZz5szhww8/9HcoBYavn01jzGprbZSv9dUnU0RECq1x45zE0t0H091HM6/7ZErRcv/99/PNN9+c9X00izolmSIiUqilTSiVYMrZct+vU86O+mSKiIiISJ5TkikiIiIieU5JpoiIiIjkuXxNMo0xnY0xW4wx24wxj/pYXscYs8gY85sxZr0xxveYfREREREpVPItyTTGBAJTgOuAYKC3MSY4zWpjgc+stY2AXsDr+RWPiIhIdhw8eJCIiAgiIiKoUaMGtWrV8kyfOXMmT/bRtm1boqJS7voSHR1N27Zt86Rsb9OmTWPPnj2e6SFDhrB58+Y8309WVq5cSevWralfvz6NGjViyJAhnDhx4pzt/9lnn001ndVTcrzFxMRQqlQpIiIiCA4OZtiwYSQnJ+c6lrZt25LVrRjHjRuHMcZzY3mAiRMnYozxbNulS5dcPTnoXMrPlsymwDZr7V/W2jPAp8CNadaxgPshohWAPYiIiPhRlSpVPE+yGTZsGKNGjfJMFy9ePM9uUr5///4cP686p9Imme+++y7BwWnbe/LXvn376NmzJy+88AJbtmzht99+o3Pnzpk+bcdb2vrOTf2nTTJz6tJLL2Xt2rWsX7+ezZs38+WXX551TFkJDQ3l008/9UzPnDmThg0beqbnz59PxYoV83y/eSk/k8xawN9e0/+45nkbB/Q1xvwDzAfu91WQMWaoMSbaGBMdGxubH7GKiEhhtWM6fFkXPg5w3ndk/Yi+nBowYADDhg2jWbNmPPzww4wbN46XX37ZszwkJISYmBgAPvroI88Tee666y7PIwDTGj16NOPHj083PykpidGjR9OkSRPCwsJ46623AEhOTuaee+7hyiuvpGPHjnTp0oVZs2YB8NRTT9GkSRNCQkIYOnQo1lpmzZpFdHQ0ffr0ISIigpMnT3pa0d58801Gjx7t2ee0adO47777chR/dk2ZMoX+/fvTokULz7xbbrmFCy64gEOHDtG9e3fCwsJo3rw569evB5yWvDvuuIOWLVtyxx13pJuOjY3l5ptvpkmTJjRp0oTly5cDEB8fz8CBAwkNDSUsLIzZs2fz6KOPcvLkSSIiItI9Aalfv36pEsY+ffowZ86cDI+lWLFiXHXVVWzbto1p06bRrVs32rdvT4cOHTh+/DiDBg2iadOmNGrUyFPOyZMn6dWrFw0aNKBHjx6cPHkyW/XWvXt3Txnbt2+nQoUKVK1a1bO8bt26HDhwgOPHj3P99dcTHh5OSEiI5+lFjz76KMHBwYSFhfl8vvq54O+BP72Badba2kAX4ENjTLqYrLVvW2ujrLVR1apVO+dBiohIAbVjOqwcCid2AtZ5Xzk0XxLNf/75h59//plXXnklw3V+//13ZsyYwfLly1m7di2BgYEZPpe6RYsWFC9enEWLFqWa/7///Y8KFSqwatUqVq1axTvvvMOOHTv4/PPPiYmJYfPmzXz44Yee52ED3HfffaxatYqNGzdy8uRJvv76a2655RaioqKYPn06a9eupVSpUp71b775Zr744gvP9IwZM+jVq1e24x81apSnC4H36/nnn0+37saNG2ncuLHPOnjiiSdo1KgR69ev59lnn6Vfv36eZZs3b2bBggV88skn6aZHjBjBqFGjWLVqFbNnz2bIkCEAPP3001SoUIENGzawfv162rdvz/PPP0+pUqVYu3ZtumMZPHgw06ZNA5zn0//8889cf/31PmMFOHHiBAsXLiQ0NBSANWvWMGvWLJYsWcL48eNp3749K1euZNGiRYwePZrjx4/zxhtvULp0aX7//XeefPJJVq9enWH53sqXL89FF13Exo0b+fTTT7ntttt8rvftt99Ss2ZN1q1bx8aNG+ncuTMHDx7kiy++YNOmTaxfv97no0fPhfy8Gftu4CKv6dqued4GA50BrLW/GGNKAlWB/fkYl4iInC/WjYGkNH37kk448+ulf2732ejZsyeBgYGZrrNw4UJWr15NkyZNAKcVq3r16hmuP3bsWJ555hleeOEFz7zvv/+e9evXe1op4+Li2Lp1Kz/99BM9e/YkICCAGjVq0K5dO882ixYt4sUXX+TEiRMcOnSIhg0bcsMNN2S432rVqnHJJZewYsUKLr/8cv744w9atmzJlClTshX/hAkTMq2H7Prpp5+YPXs2AO3bt+fgwYMcPXoUgG7duqVKjL2nFyxYkKpv6dGjR4mPj2fBggWpLjFXqlQp0/23adOGe+65h9jYWGbPns3NN99MsWLpU6Pt27cTERGBMYYbb7yR6667jmnTptGxY0cqV64MON/b3LlzPS3cp06dYteuXSxdupThw4cDEBYWRlhYWLbrp1evXnz66ad89913LFy4kKlTp6ZbJzQ0lAcffJBHHnmErl270qpVKxITEylZsiSDBw+ma9eudO3aNdv7zEv5mWSuAi43xtTDSS57AbenWWcX0AGYZoxpAJQEdD1cRESy58SunM0/C2XKlPF8LlasWKrBH6dOnQLAWkv//v157rnnslVm+/btGTt2LCtWrPDMs9YyefJkOnXqlGrdjB5xeOrUKe655x6io6O56KKLGDdunCeezPTq1YvPPvuMK6+8kh49emCMyXb8o0aNStcC6y7z0UdT30ymYcOGrF69mhtvTDssI3Pe9Z12Ojk5mRUrVlCyZMkclelLv379+Oijj/j00099JnGQ0iczsxittcyePZv69eufdUxuXbt2ZfTo0URFRVG+fHmf61xxxRWsWbOG+fPnM3bsWDp06MDjjz/OypUrWbhwIbNmzeK1117jxx9/zLO4sivfLpdbaxOB+4DvgN9xRpFvMsY8ZYzp5lrtQeBOY8w64BNggLXW5ldMIiJynildJ2fz80jdunVZs2YN4Fwy3bFjBwAdOnRg1qxZ7N/vXJA7dOgQO3fuzLSssWPH8uKLL3qmO3XqxBtvvEFCQgIAf/75J8ePH6dly5bMnj2b5ORk9u3bx+LFi4GUBLdq1arEx8d7WkABypUrl+EAmx49ejBnzhw++eQTevXqlaP4J0yY4BkM5f1Km2CCcyn//fff59dff/XM+/zzz9m3bx+tWrXyXMJevHgxVatWzTCZ8nbttdemevSjOwHs2LEjU6ZM8cw/fPgwAEFBQZ76TGvAgAFMnDgR4KwGRXXq1InJkyfjTmN+++03AFq3bs3HH38MOF0H3P1Os6N06dK88MILjBkzJsN19uzZQ+nSpenbty+jR49mzZo1xMfHExcXR5cuXZgwYQLr1q3L9XGdjXx9drm1dj7OgB7veY97fd4MtMzPGERE5DwWPt7pg+l9yTywtDM/H91888188MEHNGzYkGbNmnHFFVcATpLyzDPPcO2115KcnExQUBBTpkzh4osvzrCsLl264D3eYMiQIcTExBAZGYm1lmrVqvHll19y8803s3DhQoKDg7nooouIjIykQoUKVKxYkTvvvJOQkBBq1KjhudQNKQOWSpUqlaoPJziXkhs0aMDmzZtp2rRpruPPygUXXMCnn37KQw89xP79+wkICKB169Z07tyZcePGMWjQIMLCwihdujTvv/9+tsqcNGkS9957L2FhYSQmJtK6dWvefPNNxo4dy7333ktISAiBgYE88cQT3HTTTQwdOpSwsDAiIyPT9cu84IILaNCgAd27d8/1MQI89thjjBw5krCwMJKTk6lXrx5ff/01d999NwMHDqRBgwY0aNAgVf/UIUOGMGzYsFS3s0rL/Q9ARjZs2MDo0aMJCAggKCiIN954g2PHjnHjjTdy6tQprLWZ9iPOT6awNRxGRUXZrO4vJSIihdfvv/9OgwYNsr/BjulOH8wTu5wWzPDxed4fs6CIj4+nbNmyHDx4kKZNm7J8+XJq1Kjh77AKtRMnThAaGsqaNWuoUKGCv8Mp0Hz9bBpjVltrfWbJ+dqSKSIiku/q9Tlvk8q0unbtypEjRzhz5gyPPfaYEsyztGDBAgYPHsyoUaOUYOYDJZkiIiKFhLsfpuSNa665Jss+s5J7/r5PpoiIiIich5RkioiIiEieU5IpIiIiInlOSaaIiIiI5DklmSIiImkEBgameiZ3TExMhuuWLVv2rPc3YMAAatWqxenTpwE4cOAAdevWPety0/ryyy9TPY7x8ccfZ8GCBXm+n8zExMQQEhJyTveZU88++2yq6Zx8xzExMZQqVYqIiAiCg4MZNmxYqqdD5VTbtm3J6taN48aNwxjDtm3bPPMmTpyIMcazbZcuXThy5Eiu48gNJZkiIlK4pb3fcx7c/7lUqVKpnmSTHwlfWoGBgbz33nv5uo+0SeZTTz3FNddck6/7PNcSExMznc6OtElmTrkfQ7l+/Xo2b97Ml19+edYxZSU0NDTVc9tnzpxJw4YNPdPz58+nYsWKeb7fzCjJFBGRwmvcOBg1KiWxtNaZHjcuT3cTHx9Phw4diIyMJDQ0lDlz5qRbZ+/evbRu3ZqIiAhCQkJYtmwZAN9//z0tWrQgMjKSnj17Eh8f73MfI0eOZMKECT4TkJdeeokmTZoQFhbGE0884Zn/9NNPU79+fa6++mp69+7Nyy+/DMA777xDkyZNCA8P5+abb+bEiRP8/PPPzJ07l9GjRxMREcH27dsZMGAAs2bN4ttvv6Vnz56echcvXkzXrl1zFH9uTJs2jZtuuonOnTtz+eWX8/DDD3uWffvtt0RGRhIeHk6HDh0A5zGX3bt3JywsjObNm3se0Thu3DjuuOMOWrZsyR133JFuOjY2lptvvpkmTZrQpEkTli9fDjjf68CBAwkNDSUsLIzZs2fz6KOPcvLkSSIiIujTJ/X9V/v165cqYezTp4/Pc8GtWLFiXHXVVWzbto1p06bRrVs32rdvT4cOHTh+/DiDBg2iadOmNGrUyFPOyZMn6dWrFw0aNKBHjx6cPHkyW3XZvXt3Txnbt2+nQoUKVK1a1bO8bt26HDhwgOPHj3P99dcTHh5OSEgIM2bMAODRRx8lODiYsLAwHnrooWztM0vW2kL1aty4sRURkfPX5s2bs7dicrK1I0ZYC867r+lcCggIsOHh4TY8PNx2797dJiQk2Li4OGuttbGxsfbSSy+1ya7yy5QpY6219uWXX7bPPPOMtdbaxMREe/ToURsbG2tbtWpl4+PjrbXWPv/88/bJJ59Mt7/+/fvbmTNn2oEDB9r33nvPxsbG2osvvthaa+13331n77zzTpucnGyTkpLs9ddfb5csWWJXrlxpw8PD7cmTJ+3Ro0ftZZddZl966SVrrbUHDhzwlD1mzBg7adKkVPtJu9+EhAR70UUXeeIcNmyY/fDDD7Md/4svvuipL+/X/fffn27dHTt22IYNG1prrZ06daqtV6+ePXLkiD158qStU6eO3bVrl92/f7+tXbu2/euvv6y11h48eNBaa+19991nx40bZ621duHChTY8PNxaa+0TTzxhIyMj7YkTJ3xO9+7d2y5btsxaa+3OnTvtlVdeaa219uGHH7YjRozwxHbo0KFU36mbe3rx4sX2xhtvtNZae+TIEVu3bl2bkJCQ4fEdP37cRkVF2fnz59upU6faWrVqeY7lP//5j/3www+ttdYePnzYXn755TY+Pt7+3//9nx04cKC11tp169bZwMBAu2rVqnT16O2JJ56wL730ku3Ro4fdsGGDfeaZZ+y0adNsmzZtPNtefPHFNjY21s6aNcsOGTLEs+2RI0fsgQMH7BVXXOE5pw8fPuxzP75+NoFom0HOppuxi4hI4WQMTJjgfH71VecFMGKEM9+YXBftvlzulpCQwH//+1+WLl1KQEAAu3fvZt++fameuNOkSRMGDRpEQkIC3bt3JyIigiVLlrB582ZatmwJwJkzZ2jRokWG+/3Pf/7DjTfeyPXXX++Z9/333/P999/TqFEjwGl927p1q+f51CVLlqRkyZLccMMNnm02btzI2LFjOXLkCPHx8XTq1CnT4y1WrBidO3fmq6++4pZbbmHevHm8+OKL2Y5/9OjRjB49OtN9ZKRDhw6ep+0EBwezc+dODh8+TOvWralXrx4AlStXBuCnn35i9uzZALRv356DBw9y9OhRALp160apUqU85XpPL1iwIFU3gaNHjxIfH8+CBQtSXWKuVKlSprG2adOGe+65h9jYWGbPns3NN99MsWLpU6nt27cTERGBMYYbb7yR6667jmnTptGxY0fPsXz//ffMnTvX0/p86tQpdu3axdKlSxk+fDgAYWFhhIWFZbcq6dWrF59++infffcdCxcuZOrUqenWCQ0N5cEHH+SRRx6ha9eutGrVisTEREqWLMngwYPp2rWrpxX7bCnJFBGRwsudaLoTTDjrBNOX6dOnExsby+rVqwkKCqJu3bqcOnUq1TqtW7dm6dKlzJs3jwEDBvDAAw9QqVIlOnbsyCeffJKt/Vx++eVERETw2WefeeZZa/nPf/7DXXfdlWrdiRMnZljOgAED+PLLLwkPD2fatGnZelJQr169eO2116hcuTJRUVGUK1cOa2224n/ppZeYPn16uvmtW7dm0qRJmW5bokQJz+fAwMBc91csU6ZMhtPJycmsWLGCkiVL5qpsb/369eOjjz7i008/9ZnEQUqfzMxitNYye/Zs6tevf9YxuXXt2pXRo0cTFRVF+fLlfa5zxRVXsGbNGubPn8/YsWPp0KEDjz/+OCtXrmThwoXMmjWL1157jR9//PGs41GfTBERKbzcfTC9effRzCNxcXFUr16doKAgFi1a5PNRhDt37uSCCy7gzjvvZMiQIaxZs4bmzZuzfPlyz6jf48eP8+eff2a6rzFjxnhatwA6derEe++95+kLuXv3bvbv30/Lli356quvOHXqFPHx8Xz99deebY4dO8aFF15IQkJCquSvXLlyHDt2zOd+27Rpw5o1a3jnnXfo1asXQLbjHz16dKqBUu5XVglmRpo3b87SpUvZsWMH4PTFBGjVqpXneBYvXkzVqlUzTKa8XXvttUyePNkz7U4AO3bsyJQpUzzzDx8+DEBQUBAJCQk+yxowYIAnwQ8ODs7ZgXnp1KkTkydPxrrO1d9++w1wEvOPP/4YcFqk3f1Os6N06dK88MILjBkzJsN19uzZQ+nSpenbty+jR49mzZo1xMfHExcXR5cuXZgwYQLr1q3L9XF5U5IpIiKFkzvBfPVV5xJ5crLz/uqreZ5o9unTh+joaEJDQ/nggw+48sor062zePFiwsPDadSoETNmzGDEiBFUq1aNadOm0bt3b8LCwmjRogV//PFHpvtq2LAhkZGRnulrr72W22+/nRYtWhAaGsott9zCsWPHaNKkCd26dSMsLIzrrruO0NBQz2Xnp59+mmbNmtGyZctUsfbq1YuXXnqJRo0asX379lT7DQwMpGvXrnzzzTeey6W5iT8vVKtWjbfffpubbrqJ8PBwbrvtNsAZ4LN69WrCwsJ49NFHef/997NV3qRJk4iOjiYsLIzg4GDefPNNAMaOHcvhw4cJCQkhPDycRYsWATB06FDCwsLSDfwBuOCCC2jQoAEDBw48q2N87LHHSEhIICwsjIYNG/LYY48BcPfddxMfH0+DBg14/PHHady4sWebIUOGZHk7o169eqU6f9LasGEDTZs2JSIigieffJKxY8dy7NgxunbtSlhYGFdffTWvvPLKWR2bm7F5/N9efouKirJZVbCIiBRev//+Ow0aNMjeyuPGwZEjKZfI3YlnxYp5PsK8IIqPj6ds2bKcOHGC1q1b8/bbb2eaYMjZO3HiBKGhoaxZs8aT1BcVvn42jTGrrbVRvtZXn0wRESm8xo1zEkt3H0x3H8087pNZUA0dOpTNmzdz6tQp+vfvrwQzny1YsIDBgwczatSoIpdg5oaSTBERKdzSJpRFJMEEPH335Ny45pprfPbHFd/UJ1NERAqcwtaVS+R8l5ufSSWZIiJSoJQsWZKDBw8q0RQpIKy1HDx4MMe3gNLlchERKVBq167NP//8Q2xsrL9DERGXkiVLUrt27RxtoyRTREQKlKCgIM+TXkSk8NLlchERERHJc0oyRURERCTPKckUERERkTynJFNERERE8pySTBERERHJc0oyRURERCTPKckUERERkTynJFNERERE8pySTBERERHJc0oyRURERCTPKckUERERkTynJFNERERE8pySTBERERHJc0oyRURERCTPKckUERERkTynJFNERERE8pySTBERERHJc0oyRURERCTPKckUERERkTynJFNERERE8pySTBERERHJc0oyRURERCTPKckUERERkTynJFNERERE8pySTBERERHJc0oyRURERCTPKckUERERkTynJFNERERE8pySTBERERHJc0oyRURERCTPKckUERERkTynJFNERERE8pySTBERERHJc0oyRURERCTPKckUERERkTynJFNERERE8pySTBERERHJc0oyRURERCTP5WuSaYzpbIzZYozZZox5NIN1bjXGbDbGbDLGfJyf8YiIiIjIuVEsvwo2xgQCU4COwD/AKmPMXGvtZq91Lgf+A7S01h42xlTPr3hERERE5NzJz5bMpsA2a+1f1tozwKfAjWnWuROYYq09DGCt3Z+P8YiIiIjIOZKfSWYt4G+v6X9c87xdAVxhjFlujFlhjOnsqyBjzFBjTLQxJjo2NjafwhURERGRvOLvgT/FgMuBtkBv4B1jTMW0K1lr37bWRllro6pVq3ZuIxQRERGRHMvPJHM3cJHXdG3XPG//AHOttQnW2h3AnzhJp4iIiIgUYvmZZK4CLjfG1DPGFAd6AXPTrPMlTismxpiqOJfP/8rHmERERETkHMi3JNNamwjcB3wH/A58Zq3dZIx5yhjTzbXad8BBY8xmYBEw2lp7ML9iEhEREZFzw1hr/R1DjkRFRdno6Gh/hyEiIiJS5BljVltro3wt8/fAHxERERE5DynJFBEREZE8l2WSaYxpmZ15IiIiIiJu2WnJnJzNeSIiIiIiQCbPLjfGtACuAqoZYx7wWlQeCMzvwERERESk8MowyQSKA2Vd65Tzmn8UuCU/gxIRERGRwi3DJNNauwRYYoyZZq3deQ5jEhEREZFCLrPL5V8B1vU53XJrbbd0M0VEREREyPxy+cvnLAoREREROa9kdblcRERERCTHMmvJBMAYswPXZXNv1tpL8iUiERERESn0skwyAe/nUZYEegKV8yccERERETkfZHkzdmvtQa/XbmvtROD6/A9NRERERAqr7Fwuj/SaDMBp2cxOC6iIiIiIFFHZSRb/z+tzIhAD3Jov0YiIiIjIeSHLJNNa2+5cBCIiIiIi548s+2QaY0YYY8obx7vGmDXGmGvPRXAiIiIiUjhlmWQCg6y1R4FrgSrAHcDz+RqViIiIiBRq2Uky3c+U7AJ8YK3d5DVPRERERCSd7CSZq40x3+Mkmd8ZY8oByfkbVsHw9JKneXXFq/4OQ0RERKTQyc7o8sFABPCXtfaEMaYKMDBfoyoAkm0ya/et5fPfP2dv/F6e6/AcxqgBV0RERCQ7stOSaYFgYLhrugzOk3/OawEmgM9u+YxhjYfxwvIXGDx3MInJif4OS0RERKRQyE5L5us4l8fbA08Bx4DZQJN8jKtACAwI5PXrX6dG2RqMWzKO2BOxzLhlBqWDSvs7NBEREZECLTstmc2stfcCpwCstYeB4vkaVQFijOGJtk/wxvVvMO/PeVzzwTUcOnnI32GJiIiIFGjZSTITjDGBOJfNMcZUo4gM/PE2LGoYM3vOZPXe1bSa2oq/4/72d0giIiIiBVZ2ksxJwBdAdWPMeOAn4Ll8jaqAujn4Zr7r+x3/HP2Hq967is2xm/0dkoiIiEiBlGWSaa2dDjyMk1juBboD8/I3rIKrbd22LBmwhISkBFpNbcUvf//i75BERERECpxMk0xjTC1jTBTO7YumAJ/hPPFn67kIrqCKqBHBz4N/pnKpynT4oAPzt873d0giIiIiBUqGSaYxZiSwFpgMrDDGDAF+B0oBjc9FcAXZJZUuYfmg5QRXC6bbJ934YN0H/g5JREREpMDI7BZGQ4H61tpDxpg6wJ9AS2vt6nMTWsFXvUx1FvVfRI8ZPej/ZX/2xe9jdMvR/g5LRERExO8yu1x+ylp7CMBauwvYogQzvXIlyjHv9nnc2vBWHl7wMA9+9yDJtsgNvhcRERFJJbOWzNrGmEle0xd6T1trh/vYpkgqUawEn9z8CdVLV+eVFa+w/8R+3uv2HkGBQf4OTURERMQvMksy0173VStmJgJMAJOum0SNsjUYu2gsB04cYGbPmZQtXtbfoYmIiIiccxkmmdba989lIOcDYwxjWo+hRtkaDP16KB0+6MC82+dRtXRVf4cmIiIick5l52bskkODIwfz+a2fs37feq5+72p2Htnp75BEREREziklmfnkxitv5Ic7fmDf8X1c9d5VbNi3wd8hiYiIiJwzWSaZxpiW2Zkn6V1d52qWDlgKQKuprVi2c5mfIxIRERE5N7LTkjk5m/PEh9ALQvl50M/UKFuDaz+6li//+NLfIYmIiIjkuwwH/hhjWgBXAdWMMQ94LSoPBOZ3YOeTiytezE+DfqLrx125+bObefP6N7mz8Z3+DktEREQk32TWklkcKIuTiJbzeh0Fbsn/0M4vVUtXZWG/hXS6tBNDvx7K00uexlrr77BERERE8kVmtzBaAiwxxkyz1u40xpR1zY8/Z9GdZ8oUL8OcXnMY8tUQHl/8OHvj9zL5uskEBqhhWERERM4vmd2M3a2cMeY3oDKAMeYA0N9auzFfIztPBQUGMe3GadQoU4MXf36Rfcf3Mf2m6ZQsVtLfoYmIiIjkmewM/HkbeMBae7G19mLgQdc8ySVjDC90fIEJnSbw+e+f0/mjzhw5dcTfYYmIiIjkmewkmWWstYvcE9baxUCZfIuoCBnZfCSf3PwJP//9M62ntmb30d3+DklEREQkT2QnyfzLGPOYMaau6zUW+Cu/AysqeoX04ps+37DjyA6ueu8q/jjwh79DEhERETlr2UkyBwHVgM9dr2queZJHOlzSgSUDlnAq8RQt32vJL3//4u+QRERERM5KlkmmtfawtXa4tTbS9RphrT18LoIrSiIvjOSXwb9QuVRlOnzQga+2fOXvkERERERyLTuPlbzCGPO2MeZ7Y8yP7te5CK6ouaTSJSwftJyG1RvSfUZ33l3zrr9DEhEREcmV7NzCaCbwJvAukJS/4Uj1MtVZ1H8RPWf25M6v7mTPsT081voxjDH+Dk1EREQk27KTZCZaa9/I90jEo2zxssztNZc7v7qTJxY/we6ju5ly/RSKBWTn6xIRERHxv8yeXV7Z9fErY8w9wBfAafdya+2hfI6tSAsKDGLqjVOpWa4mz/30HP8e/5dPbv6E0kGl/R2aiIiISJYyaxpbDVjAfZ12tNcyC1ySX0GJwxjDsx2epVa5Wtz/zf3OgKDeX1G1dFV/hyYiIiKSqcyeXV7vXAYiGbu36b3ULFeT3rN70/K9lnzb51vqVdLXIyIiIgVXhqPLjTFNjDE1vKb7GWPmGGMmeV1Kl3OkR4MeLOi3gNjjsbT4XwvW7F3j75BEREREMpTZLYzeAs4AGGNaA88DHwBx6NnlfnF1natZPmg5JYqVoPXU1ny77Vt/hyQiIiLiU2ZJZqDX4J7bgLettbOttY8Bl+V/aOJLg2oN+GXwL1xW+TK6ftyVqb9N9XdIIiIiIulkmmQaY9x9NjsA3jdg1710/KhmuZosHbiU9vXaM2juIJ5a8hTWWn+HJSIiIuKRWZL5CbDEGDMHOAksAzDGXIZzyVz8qHyJ8nx9+9f0C+/HE4ufYOhXQ0lMTvR3WCIiIiJA5qPLxxtjFgIXAt/blKayAOD+cxGcZK54YHGm3TiNi8pfxPhl49l9bDef9fyMssXL+js0ERERKeIyvextrV3hY96f+ReO5JQxhmfaP0OdCnW4Z949tJnWhq97f82F5S70d2giIiJShGV2ufysGWM6G2O2GGO2GWMezWS9m40x1hgTlZ/xnM+GNh7K3N5z2XJgCy3+14LNsZv9HZKIiIgUYfmWZBpjAoEpwHVAMNDbGBPsY71ywAjg1/yKpajocnkXlgxYwumk07R8ryWLYxb7OyQREREpovKzJbMpsM1a+5e19gzwKXCjj/WeBl4ATuVjLEVG45qN+WXwL9QoW4NOH3Xi4w0f+zskERERKYLyM8msBfztNf2Pa56HMSYSuMhaOy+zgowxQ40x0caY6NjY2LyP9DxTt2Jdfh70My1qt6DP530Yv3S8bnEkIiIi51S+9snMjDEmAHgFeDCrda21b1tro6y1UdWqVcv/4M4DlUpV4ru+39EntA9jF43lzq/uJCEpwd9hiYiISBGRnzdV3w1c5DVd2zXPrRwQAiw2xgDUAOYaY7pZa6PzMa4io0SxEnzY40PqVazHM8ueYVfcLmb2nEmFkhX8HZqIiIic5/KzJXMVcLkxpp4xpjjQC5jrXmitjbPWVrXW1rXW1gVWAEow85gxhqfbP8173d5jUcwirp56Nbvidvk7LBERETnP5VuSaa1NBO4DvgN+Bz6z1m4yxjxljOmWX/sV3wY2Gsg3fb5hV9wumr3bjOg9yuVFREQk/5jCNiAkKirKRkcrQcqtTfs3cf3H1xN7IpaPb/qYG6/0NeBfREREJGvGmNXWWp/3OffbwB/xj4bVG7JiyAoaVmtIjxk9mPDLBI08FxERkTynJLMIqlG2BosHLKZHgx488P0D3DPvHhKTE/0dloiIiJxHlGQWUaWDSjOz50wevuph3lz9Jl0/7krcqTh/hyUiIiLnCSWZRViACeCFji/w7g3vsnDHQlq+15Idh3f4OywRERE5DyjJFAZHDua7vt+x+9humr3bjJ///tnfIYmIiEghpyRTAGhfrz0rBq+gfInytHu/HdPXT/d3SCIiIlKIKckUj/pV6/PrkF9pUbsFfb/oy2M/PkayTfZ3WCIiIlIIKcmUVKqUrsL3d3zP4EaDeWbZM9w26zZOJJzwd1giIiJSyCjJlHSKBxbnnRve4eWOLzN782xaT23N7qO7s95QRERExEVJpvhkjOHBqx5kbu+5bDm4hSbvNGHl7pX+DktEREQKCSWZkqmuV3Tll8G/UKJYCdpMa8MnGz7xd0giIiJSCCjJlCyFVA9h5ZCVNKnZhNs/v50xC8doQJCIiIhkSkmmZEu1MtVY0G8Bd0beybM/PctNM27i2Olj/g5LRERECiglmZJtxQOL81bXt5jUeRJf//k1Lf7Xgr8O/+XvsERERKQAUpIpOWKM4f5m9/Nd3+/Yc2wPTd5pwsK/Fvo7LBERESlglGRKrnS4pAOr7lzFhWUvpNNHnXh1xatYa/0dloiIiBQQSjIl1y6tfCm/DP6FG+rfwMjvRjJwzkBOJZ7yd1giIiJSACjJlLNSrkQ5Zt86myfaPMH7696n9dTW/HP0H3+HJSIiIn6mJFPOWoAJYFzbcXxx2xf8fuB3Gr/dmGU7l/k7LBEREfEjJZmSZ7pf2Z1fh/xKhRIVaP9Be6asnKJ+miIiIkWUkkzJU8HVgll550o6X9aZ+765j0FzB3Ey4aS/wxIREZFzTEmm5LmKJSsyp9ccHm/9ONPWTuPqqVez88hOf4clIiIi55CSTMkXASaAJ9s9ydxec9l2aBuN327MD9t/8HdYIiIico4oyZR8dUP9G4i+M5oaZWvQeXpnnlv2nJ57LiIiUgQoyZR8d3mVy1kxZAW3NryV//74X26acRNxp+L8HZaIiIjkIyWZck6ULV6Wj2/6mFc7v8q8rfNo/HZj1v27zt9hiYiISD5RkinnjDGG4c2Gs7j/Yk4mnqT5/5ozbe00f4clIiIi+UBJppxzLeu0ZM3QNbSo3YKBcwZy59w7dZsjERGR84wpbDfLLhcVZRtHR6eadytwD3AC6OJjmwGu1wHgFh/L7wZuA/4G7vCx/EHgBmALcJeP5WOBa4C1wEgfy58FrgJ+Bv7rY/lEIAJYADzjY/lbQH3gK+D/fCz/ELgImAG84WP5LKAqMM31Sms+UBp4HfjMx/LFrveXga/TLCsFfOP6/DSwMM3yKsBs1+f/AL94LbPWcvDfdWx6uxER5asSPng1MeXrpNr+CuBt1+ehwJ9pyo/AqT+AvkDaB1q2AJ5zfb4ZOJhmeQfgMdfn64C0qW5X4CHX57akp3OvcJ57ALWBj1yfR+LUoTedezr3QOdeW9LTuadzD1LOvSXGrLbWRqU/ErVkih8ZY4i4MIKvb3yDnccPsmfnXDi1399hiYiISB4odC2ZUVFRNjpNS6YUfgdi11L1t3vgwC9w+b0Q+X8QWMLfYYmIiEgmjFoypaCrWi0CrlkCVz4IW6fA91fBse3+DktERERySUmmFBwBQRD5MrSeA/F/wbeRsGumv6MSERGRXFCSKQVP7W5w3W9QvgH8dCusHAaJGn0uIiJSmCjJlIKpbF3ouAwaPAzb3oLvm0Hc7/6OSkRERLJJSaYUXAFB0OgFaPsNnPwXvo2C7e9BIRusJiIiUhQpyZSCr2ZnuG4tVG0Ovw6G5b3gzBF/RyUiIiKZUJIphUPpmtDuewh/Dv7+HOaHQ+xyf0clIiIiGVCSKYVHQCA0fBQ6LoeAYrCgNWx4EpIT/R2ZiIiIpKEkUwqfqk2d0ecX3w4bxsGCNhC/w99RiYiIiBclmVI4BZWHqz6EFh9B3Ebn8vlf72tQkIiISAGhJFMKt3p9oMt6qNwIVgxw7qt5+pC/oxIRESnylGRK4VfmYmj/I0Q8D7vnwPxQ2Pu9v6MSEREp0pRkyvkhIBCCH4FrV0BQBVjUCVbdB4nH/R2ZiIhIkaQkU84vlSOh82qoPwq2ToFvGsGBFf6OSkREpMhRkinnn2KloPEr0OFHSDoNP7SEdWMh6Yy/IxMRESkylGTK+euCds6goHr9YNN4+K4JHPrN31GJiIgUCUoy5fxWvAI0nwptvoJT++G7pq4buCf4OzIREZHzmpJMKRpqdYXrN8HFvZwbuH/XFA6v83dUIiIi5y0lmVJ0lKjs3MC91Rdwcg98GwXrn1BfTRERkXygJFOKnou6w/WbnVbNjU/Bt43h4Cp/RyUiInJeUZIpRVOJKk6rZpuv4cxh+L45/PYwJJ70d2QiIiLnBSWZUrTVut7pq3nJYPj9JedpQf8u9HdUIiIihZ6STJHiFaDZ2859NTHw4zWwYiCcPujvyERERAotJZkibu77agb/B3Z8BF83gJhPwFp/RyYiIlLoKMkU8VasFEQ86zyaskxd+Pl2WHwdHNvu78hEREQKFSWZIr5UCoNrf4HGkyD2Z5gfAhvH63ZHIiIi2aQkUyQjAYFQ/37o+jvUugHWj4VvImDfEn9HJiIiUuApyRTJSulacPVn0GYeJJ2EhW3h5zvg5L/+jkxERKTAUpIpkl21uji3O2o4FnZ9Bl/Xhz9eheREf0cmIiJS4ORrkmmM6WyM2WKM2WaMedTH8geMMZuNMeuNMQuNMRfnZzwiZ61YaQh/GrpshKotYM1I54lB+5f5OzIREZECJd+STGNMIDAFuA4IBnobY4LTrPYbEGWtDQNmAS/mVzwiear85dD2G2g123li0ILWsPx2OPGPvyMTEREpEPKzJbMpsM1a+5e19gzwKXCj9wrW2kXW2hOuyRVA7XyMRyRvGQMX3eQMDAp5DP7+HL6qD5uehaRT/o5ORETEr/IzyawF/O01/Y9rXkYGA9/4WmCMGWqMiTbGRMfGxuZhiCJ5oFgZCHvKSTZrdoZ1Y2BeQ/j7C93IXUREiqwCMfDHGNMXiAJe8rXcWvu2tTbKWhtVrVq1cxucSHaVredcPm//AwSWgmU3wcJ2cOg3f0cmIiJyzuVnkrkbuMhrurZrXirGmGuAMUA3a+3pfIxH5NyocQ1ctxaavA5xm5yBQSsGw8m9/o5MRETknMnPJHMVcLkxpp4xpjjQC5jrvYIxphHwFk6CuT8fYxE5twKKweV3ww1bocGDEPMhfHU5bHgKEo/7OzoREZF8l29JprU2EbgP+A74HfjMWrvJGPOUMaaba7WXgLLATGPMWmPM3AyKEymcileERi/B9ZvhwutgwxNOsrntXUhO8nd0IiIi+cbYQjYwISoqykZHR/s7DJHcif0ZfnsIDvwCFRpCxAtQs4szUl1ERKSQMcasttZG+VpWIAb+iBQZ1a6CjsudAUJJp2FJV1jQxkk+RUREziNKMkXONc/9NTc7g4OObYUfWsKSG+HIJn9HJyIikieUZIr4S0CQMzio2zYIHw/7F8P8UPi5H8T/5e/oREREzoqSTBF/K1YGGv4Xuv3ljET/e6bz5KCVd+kxlSIiUmgpyRQpKEpUcUaid/sLLrsL/poKcy+D1SPh5L/+jk5ERCRHlGSKFDSlLoQmrzn32KzXF/58DebWg9UPKNkUEZFCQ0mmSEFV5mJo9i50/QMu7gV/TlKyKSIihYaSTJGCrtxl0Hxq+mQz+n44/re/oxMREfFJSaZIYeFJNrdA3T6w9U346lL49U44tt3f0YmIiKSiJFOksCl3qXMZvdt2uHQo7PgQvr4ClveBw+v9HZ2IiAigJFOk8CpTxxkgdOMOqD8Kds+Fb8Jh8fWwfxkUskfGiojI+UVJpkhhV+pCiHwZbtwJYU/DwVWwoLXzFKG/v4DkJH9HKCIiRZCSTJHzRYnKEDIWboyBqNfg5F5YdhN8fSX8+ToknvB3hCIiUoQoyRQ53xQrDVfc69xn8+rPnOQz+l748iJYN9ZJPkVERPKZkkyR81VAMajTE65dAdcsg+qtYdOzMOdi+LkvHIz2d4QiInIeK+bvAEQknxkD1a92Xse2OU8Q2v4exEyHqldB/RFwUQ8ICPJ3pCIich5RS6ZIUVLuMmg8EXr8A5ET4dQ+WH6b07q54UldShcRkTyjJFOkKAoqD1eOcG7s3uZrqBgOG8bBl3Xgp166BZKIiJw1XS4XKcoCAqHW9c7r6FbY+gb89R7smgHlG8Dlw6BePyhe0d+RiohIIaOWTBFxlL8cGr8CPfZAs/cgqBysHgFf1IQVAyH2F7VuiohItinJFJHUipWGSwdCp1+h82qodwfsmgk/XAXzQ+CPCXDqgL+jFBGRAk5JpohkrHIkNH0Leux1npderDyseQC+rAk/3Qp7voHkRH9HKSIiBZD6ZIpI1oLKwaWDndeRjbD9fxDzkdPCWepCqHsHXDIAKjTwd6QiIlJAGFvI+lhFRUXZ6GjdRFrE75LOwJ558Nc0590mQeUmzuX1i3tByWr+jlBERPKZMWa1tTbK1zJdLheR3Aks7tzEvc0c6L4bGv0f2ARYPRy+uBAWd4WdM/TMdBGRIkotmSKSt45sdC6lx0yHE/9AsbJQ+0a4uDdceK2eLCQich7JrCVTSaaI5A+bDPuXQMwn8PcsOHMYileGOrdAnducZ6kHqFu4iEhhpiRTRPwr6Qzs/Q52fgL/zIGkE1CiGlx0M1x8K1Rr7dwYXkRECpXMkkw1I4hI/gssDrVvcF6JJ5xbH+36DHZ8ANvedBLO2t2dpPOCds76IiJSqCnJFJFzq1hpqHOz80o8Dnvmw67ZTivn9ncgqALUusEZVHRhJyhWxt8Ri4hILijJFBH/KVYG6vR0XkmnYO8P8M/nziX1mI8goATUuMYZOFTrBihVw98Ri4hINinJFJGCIbBkyiX15ASI/Qn+/hJ2z3Huw4mBKk2hVlfnVTEcjPF31CIikgEN/BGRgs1aOLLead3cMw8OrnTml64NNa+HmtfBBe2dpxKJiMg5pdHlInL+OPmvM3Boz9ew93tIjHfuvVntarjwOqjZGSqEqJVTROQcUJIpIuenpDNwYLkr6fwG4jY680tdCDWudW7+XuMaKFndv3GKiJynlGSKSNFw4h+ndXPv9/DvD3DmkDO/YjjU6AAXdHBuAh9U1r9xioicJ5RkikjRk5wEh3+Df7+HfxdC7HJIPg2mGFRtBtXbOffkrNoCipXyd7QiIoWSkkwRkcSTzqX1fxc6r8OrnUdfBhSHKs3ggrZOK2fVFro3p4hINinJFBFJK+Eo7P8J9i+GfYvg8Bon6TTFoHKkk3BWawVVr4KSVf0drYhIgaQkU0QkKwlHIfYXiF0K+5c6t0pKPuMsK18fqraEai2dpLP8FWAC/BuviEgBoGeXi4hkJag81OzkvMC5vH4o2unLGbsc/vkS/nrPWVa8knOJvWoLqNocqjRx5omIiIeSTBERX4qVguqtnBc4l9KPboEDv6S8NnwHuK4GlbvCeSJRlWZO0lkp3HmKkYhIEaUkU0QkO0wAVGjgvC4d5Mw7EweHVjmX1g+uhH8XOM9cB6dvZ8UQqBzlejV2ppV4ikgRoSRTRCS3ildwbvZe4xpn2lrnXp2Hop3XwWj4+3PY/q6z3BSDCsHOwKJKkVApAiqGOeWIiJxnlGSKiOQVY6DMRc7roh7OPGvh+A449Jszgv3QGtgzH/6alrJdmXrO5fWK4VApzEk8y16iwUUiUqgpyRQRyU/GOAlj2Uugzs3OPGvh5F44sg4Or3VeR9bBP3Pw9PEMLO1cXq8Q4npv6HwudaGeyy4ihYKSTBGRc80YKF3TedW8LmV+4gmI2wRHNrhe62HP1ymj2sEZxV4hGMo3cL0HO/1ES9dWy6eIFChKMkVECopipZ2R6VWapJ5/KtaVfG6EuI1w9Hfnlkruvp7gtHyWrw/lr3Tey9V3vV+uZ7WLiF8oyRQRKehKVoOSbZ1HX3o7FesknHGbndsrHf3DubXSzk/xXHYHKFXTucVSucuh3GUp72UvdRJbEZF8oCRTRKSwKlnNeVVvnXp+4kmI3wZH/4RjrtfRLU7r5+nY1OuWutBJNste4nq/FMrWc14la6j/p4jkmpJMEZHzTbFSUDHUeaV1Js5JQI+5XvHbnde/C+HkB6nXDSwJZeo6o9/L1oUyF7umXZ9LVlc/UBHJkJJMEZGipHgF58bwlRunX5Z4Eo7HQPwO57ZLnvcYOPgrnDmUev2A4lD6IlfyWQdK1XZu31Ta6xVUXq2hIkWUkkwREXEUK5XyVCNfEo7B8Z1OInp8l/P5xC7n894f4NRe5/Gbqcos44x8L1Ur5b2Ua2S9+3OpGhAQlO+HJyLnlpJMERHJnqByzj07K4b4Xp6cCCf3wIm/4fjfcPIfOLHbeQrSyd2wb5Fzf1CbmH7bElVdCeeFzqtkDedVyvVe8gIodQEEVVTLqEghoSRTRETyRkAx57J5mTpQLYN1bDKcPuAknyf3OMnnyb2pX3Gb4NQ+SE7wsY/iTl/QkhdAiequz65XiWrOq2Q1J2ktUc1pSVVSKuIXSjJFROTcMQEpSSGNMl7PJsOZw06yeXKv8+79OrnPGSnvSUhP+y4nsKQr4fR6Fa8CJapA8crOe4kqrnmVnXlBFSAgMF8OX6QoUZIpIiIFjwlISQArBGe+rrWQGO8km6cPOPcPPR3rfD4dC6cPuj4fcAYxnTkIZ46Q6l6iqXfuJJolKjtPWCrufq8ExSs670EVnc/u9+IVnW2KV3QSWxFRkikiIoWcMU5/0aByzk3msyM5CRKOuBLQg87I+TOH4PShlM9nDrumDzuDnBKOOJ99Xcb3FlDcGVUfVMGVeFZwpouVT/kcVB6KlXN9Luc1XQ6KlU151y2ipBBTkikiIkVPQGBKS2lOWAtJJ52W0DOHISHO+ZwQ50pCXZ/PxLnmuV7xf0HC0ZSXTcre/oqVcZJN78TTM10WAsu41vHxSrestPP40WKlIaCE+qpKvlOSKSIikl3GOElasdLObZhyw52oJhx1bguVeNTrc7zr/VjKtGee6/30QefWUQmuZYnHM+6TmuFxBEBgKSfpDCzlSkC93t2vYqUhoKTrs3t+yZT3gJKpp71fASXSfw5Q2lGU5Ou3bYzpDLwKBALvWmufT7O8BPAB0Bg4CNxmrY3Jz5gkj1ib+r/gtNNZbQsp66edFhE5n3knqqVq5E2ZyYlOsul+JZ3w8fmE67NrOulkynTSyZR5iced/qtJJ50b9Cd5vbLbApvhsQc4CWdACQj09V48/eeA4mmWFXd99vUKyvzdBLk+e73SznNPm0D9XTpL+ZZkGmMCgSlAR+AfYJUxZq61drPXaoOBw9bay4wxvYAXgNvyKybJI+PGwZEjMGGC8wNoLYwaBRUrOsuy2vbbb6FZM5g40Zk3ciT8+it07pz19gAr74Htb6f+ZWcCoVpb53F5J3ZB6ToQPh7q9cnx4QGwYzqsG5O6LEg9r+xlELvYicMEwqVDoenr2d8+p/HtmA7RIyDhoDNdvAo0ftV3uQAr74Kk4+nLKX1x5vv2tZ86t8Ke+ZnH7v29mEAoWx/it6T+nkpfDDW7pJQVVBkMzkCMjASWcVpLEg45rS5JJ0g1YCOoCkS9mvPvOu1xEgAkgykO9kzqdat3gMNrU9YNLOO0ypw5lHF9+DoHMqvz7K6btp69z7vMjnXdGDixM+U40zFw2bCsy8pK2mNJ+3NyNj+nC66B/QvTz/d1DmRWp971YQKd2IpXcU6rhIMp89zn667PUs7RgDJQLM13H7sctr1JynkZ6PqcDARAQClIPuGs733+ZxjXLmewka940q6/ekRKbLn5WUhbT+niezb1/tb+F07ucp7u1GA01OwMu2bBlslw+l/ntlJ1+0DVZpB0GpJPOe9Jp5xX8mnn5Z6XfCZl2vN+xtX39UzK/OQE17pe88424c0uE+R0r0g6g/M7IjBl8FdAMTDFvN6DUk97PgemmR+Y+rNnntdnzzZp52XxKl0Tqrc+N3WTBWOtzXqt3BRsTAtgnLW2k2v6PwDW2ue81vnOtc4vxphiwL9ANZtJUFFRUTY6OjpfYpZscCeUr74KI0Y4iWba6Yz+87PWSSgnTXKmhw933r2nJ07M/D/HlffAtjeyF2tgaWj6du6Sj5VDXcmMS0BxJ36bRYf/y+6Gai2zt31O4tsxHVYMTL9/UwwwqecHFHcNTMjkZzujfWe0n6y2z8n3kh9MEDSfmv3vOrvHmV1p68PXOZRZnWd33Yzq+bK7M04OfZWfmczKykpO9wXZ/znIKMF08z4HMqtTyHmMmTHFfN9cPrtyGpf3+r8OcpKuVPHk4GchO99XZvEFloZ6/WHH+9k7f/OaTXZacJPPwI6PYM0DkHwyZXlASWj4H6hxjStBTUh5twmu6YTU0wd+hV0z0/xucA++8vrnzARC5abOY1Rtolc5Sc60TXLFlmae9ZqXnOi1rnu9JK/1ff0zmA01roX23+Vu21wwxqy21kb5XJaPSeYtQGdr7RDX9B1AM2vtfV7rbHSt849rertrnQMZlaskswDwTjTdskowvbf1TjTdspNgAnxSLGf/vZa+GLrHZH99gC/rulp8csEEOv/hZ3f77MZ3NjHlZN852Y/39jn9XvJDTr7r/K7PjMrPSZ37WjejejaB0DuDRCenx5pZWVnJbb1m57v7OBuXLd3lZFankPff/dnKaVxZrZ/Xv1cy25+7lTW3MeSVnPwc5aYcX/L7GK31kXgmOXdGsJm8AktB2br5F1camSWZhaIHrjFmKDAUoE6dOn6ORjDGSSi9k8zsJJjubSdOTJ9kZifBhJwnMid25Wz93G7jZpNytn121z2bmHJSZm5j93eCCflT77ndf0bl56TOfc3PqJ4zq/+cHuvZfJe5rde8+j7c5eSkTguCnMaV1fp5/Xsls/UyOl/OdV3n1Xfu798j3oxxXa0qFKmaT/l5A67dwEVe07Vd83yu47pcXgFnAFAq1tq3rbVR1tqoatUyelaZnDPulkxvo0alDODJatuRI9PPHzkye9ubHD6Fo3Qu/inJzTZuJjBn22d33bOJKSdl5jb2nH4v+SE/6j23+8+o/JzUua/5GdVzZvWf02M9m+8yt/WaV9+Hu5zM6jQ/vvuzldO4slo/r3+vZLa/jM6Xc13POfk5yk05eVF2EZSfSeYq4HJjTD1jTHGgFzA3zTpzgf6uz7cAP2bWH1MKgLR9MpOTnfdXX8060fTVJ9O7X2Z2Es1Lh2Y/1sDSKYNgciJ8vLOtN/eoxKxcOjT72+ckvvDxvvdviqWfH1AcZzRNJjLad0b7yWr7nHwv+cEE5ey7zu5xZlfa+vB1DmRW59ldN6N6zqz+fZWfmbP5LnO6L8j+z0H1Dpkv9z4HMqvT3MSY6X7PspUpp3F5rx9Q3Ec8OfhZyM4+M4svsLRzvmT3/M1POfk5ymk5Z/v7uwjLtyTTWpsI3Ad8B/wOfGat3WSMecoY08212v+AKsaYbcADwKP5FY/kEWOcUeTefTAnTHCmK1bM/JK3MVCpkjOy3N0Hc+JE53OzZs6yrC6ZN33dGZiQ9r9nE+j8ESp9MWCc99x2PK/Xx9nWu6xm7zmd6b3nVe+QEocJTBkwkd3tcxJfvT7O9kFeN44uXgWaT0tfbrP3oMWHzghoXzLbd0b7uezuzGNP+72YQCgXnP57Kn1x6rKCXM+MzkxgGVc8xnVMac6RoCo5G/ST0XG6fx0aH3+4q3dIvW5gGVfcGdSHr3MgszrP7rq+6jmrgTqpyvc6znTM2Q36yehY0v6c5Pbn9JoFGSeaac+BzOo0bX24YyteJeU7ds9zn6/e52hAmu+++TRnnVTnZSAp9RzgbONeP6OfpbQxZxSP9/rN3ksdW05/FnzVU3bjcy9r+nr2z9/8lJOfo5yWc7a/v4uwfBv4k1808KeA0H0yRUREirxCP/BHCqC0CWFOEsSz2VZEREQKhfzskykiIiIiRZSSTBERERHJc0oyRURERCTPKckUERERkTynJFNERERE8pySTBERERHJc0oyRURERCTPKckUERERkTynJFNERERE8pySTBERERHJc0oyRURERCTPGWutv2PIEWNMLLDzHO6yKnDgHO6vsFC9pKc68U314pvqxTfVS3qqE99UL76d63q52FpbzdeCQpdknmvGmGhrbZS/4yhoVC/pqU58U734pnrxTfWSnurEN9WLbwWpXnS5XERERETynJJMEREREclzSjKz9ra/AyigVC/pqU58U734pnrxTfWSnurEN9WLbwWmXtQnU0RERETynFoyRURERCTPKckUERERkTynJDMDxpjOxpgtxphtxphH/R1PQWGMiTHGbDDGrDXGRPs7Hn8xxrxnjNlvjNnoNa+yMeYHY8xW13slf8boDxnUyzhjzG7XObPWGNPFnzGea8aYi4wxi4wxm40xm4wxI1zzi/T5kkm9FPXzpaQxZqUxZp2rXp50za9njPnV9TdphjGmuL9jPZcyqZdpxpgdXudLhJ9DPeeMMYHGmN+MMV+7pgvMuaIk0wdjTCAwBbgOCAZ6G2OC/RtVgdLOWhtRUO7D5SfTgM5p5j0KLLTWXg4sdE0XNdNIXy8AE1znTIS1dv45jsnfEoEHrbXBQHPgXtfvk6J+vmRUL1C0z5fTQHtrbTgQAXQ2xjQHXsCpl8uAw8Bg/4XoFxnVC8Bor/Nlrb8C9KMRwO9e0wXmXFGS6VtTYJu19i9r7RngU+BGP8ckBYi1dilwKM3sG4H3XZ/fB7qfy5gKggzqpUiz1u611q5xfT6G88egFkX8fMmkXoo064h3TQa5XhZoD8xyzS+K50tG9VKkGWNqA9cD77qmDQXoXFGS6Vst4G+v6X/QLz83C3xvjFltjBnq72AKmAustXtdn/8FLvBnMAXMfcaY9a7L6UXqsrA3Y0xdoBHwKzpfPNLUCxTx88V1+XMtsB/4AdgOHLHWJrpWKZJ/k9LWi7XWfb6Md50vE4wxJfwXoV9MBB4Gkl3TVShA54qSTMmpq621kThdCe41xrT2d0AFkXXuDVbk/8t2eQO4FOcS117g//wajZ8YY8oCs4GR1tqj3suK8vnio16K/PlirU2y1kYAtXGurF3p34gKhrT1YowJAf6DUz9NgMrAI/6L8NwyxnQF9ltrV/s7lowoyfRtN3CR13Rt17wiz1q72/W+H/gC5xegOPYZYy4EcL3v93M8BYK1dp/rj0My8A5F8JwxxgThJFLTrbWfu2YX+fPFV73ofElhrT0CLAJaABWNMcVci4r03ySveuns6nZhrbWngakUrfOlJdDNGBOD062vPfAqBehcUZLp2yrgctcIreJAL2Cun2PyO2NMGWNMOfdn4FpgY+ZbFSlzgf6uz/2BOX6MpcBwJ1IuPShi54yrj9T/gN+tta94LSrS50tG9aLzxVQzxlR0fS4FdMTpr7oIuMW1WlE8X3zVyx9e/6gZnL6HReZ8sdb+x1pb21pbFydP+dFa24cCdK7oiT8ZcN02YyIQCLxnrR3v34j8zxhzCU7rJUAx4OOiWi/GmE+AtkBVYB/wBPAl8BlQB9gJ3GqtLVKDYDKol7Y4lz4tEAPc5dUX8bxnjLkaWAZsIKXf1H9x+h8W2fMlk3rpTdE+X8JwBmsE4jQEfWatfcr1+/dTnEvCvwF9Xa13RUIm9fIjUA0wwFpgmNcAoSLDGNMWeMha27UgnStKMkVEREQkz+lyuYiIiIjkOSWZIiIiIpLnlGSKiIiISJ5TkikiIiIieU5JpoiIiIjkOSWZIlJkGWOSjDFrjTGbjDHrjDEPGmMCXMuijDGTMtm2rjHm9nMXbbr9lzLGLDHGBOZgm/uMMYPyMy4RETfdwkhEiixjTLy1tqzrc3XgY2C5tfaJbGzbFtd96fI1yIz3fy9QzFr7ag62KY1zfI3yLzIREYdaMkVE8DwqdSj8f3v3D1pnFcZx/PulDbZo7KKCm1gaLIK1YhysxRb8A05uHUpdHES02IiDi+AYEbpYxKGDIEUEFQRFGwQViUMisRoFHUw7FAUFtYo2iMnjcE/gNcQkN94iJb8PXLj3nPO857x3uBye933vw+P2HFDfBlDvbhnPM+pnrfLVOLC/tY21zObH6kx73dliD6gfqq+rX6unWnUS1FH1k5ZFnVKH1S3q8+q0+oX6yL8s+TCtkkeb4yP1LXVOHVcPt2POqjvbOf4BnFM3U+m9iPifbF17SETE5lBVc+3y83XLup4CHquqSfUqYB54mk4ms2UJ762qeXUX8Cpwe4vfC9wMfAdMAvvUKeA14FBVTatXAxeBh4ELVTWqXgFMqhNVdXZpMa3c7Y1Vda6zxj3AbuAnYA44WVV3qE8AR4FjbdynwH5g6j99WRERa8gmMyJibZPAcfUU8GZVnW/JyK4h4IR6K7AAjHT6pqrqPIB6BrgBuAB8X1XTAFX1a+u/D7hFXao9vAPYBZztHO8a4Jdl808vlV9UvwUmWvsscLAz7gfgpnWed0TEhmWTGRHRtJq/C/Q2YruX2qtqXH0HeIBeZvH+FcLH6NVr30PvVqT5Tl+3bvACq//2ChytqtOrjLkIbFvW1p1jsfN5cdl821p8RMQllXsyIyIA9VrgJeBELXsiUt1ZVbNV9RwwTS8T+Bsw3Bm2g15mchE4Aqz11Pc3wPXqaJtjWN0KnAYeVYda+4h6ZTewqn4GtqjLN5rrMQJ8uYG4iIi+JJMZEZvZ9nb5egj4C3gFOL7CuGPqQXpZwa+Ad9v7BfVz4GXgReAN9SHgPeD31Sauqj/VQ8AL6nZ62cV7gJP0LqfPtAeEfgQeXOEQE8BdwPvrP10A9gHP9hkTEdG3/IVRRMRlSL0NGKuqI33E7AWe7CcmImKjcrk8IuIyVFUzwAf9/Bk7vQeGnrlES4qI+IdkMiMiIiJi4JLJjIiIiIiByyYzIiIiIgYum8yIiIiIGLhsMiMiIiJi4LLJjIiIiIiB+xtdlz55q/y2pAAAAABJRU5ErkJggg==\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "#plot the heaviside function on top of the responses for the seperable data above\n", "threshold=0.3\n", "threshold_x=6.5\n", "df_goal = df_log_goal[:100]\n", "df_miss = df_log_miss[:100]\n", "TP = df_goal[df_goal['Distance']threshold_x]\n", "FP = df_goal[df_goal['Distance']>threshold_x]\n", "FN = df_miss[df_miss['Distance']" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "from sklearn.metrics import classification_report,confusion_matrix\n", "from sklearn.metrics import ConfusionMatrixDisplay\n", "threshold=[0.3]\n", "y_pred = (lgm_dis.predict_proba(x_test_dis)[:, 1] > threshold).astype('float')\n", "cm_dis_3 = confusion_matrix(y_test_dis, y_pred)\n", "cm_display = ConfusionMatrixDisplay(cm_dis_3).plot(cmap='OrRd')\n", "cm_display.im_.colorbar.remove()\n", "plt.title('Confusion Matrix for Threshold = 0.3')\n", "print(cm_dis_3)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "From the confusion matrix, we can gather for which classifications the model gives promising predictions and for which it does not. For the example above, the model does a fantastic job of predicting misses but a poor job of predicting goals, and this is understandable if we examine where the threshold intersects the model. We can define the model’s ability to correctly predict goals with a metric known as sensitivity and the model’s ability to correctly predict a miss is given by the specificity. \n", "\n", "\n", "$$\n", "\\begin{array}{rcl}\n", " Sensitivity = \\dfrac{True Positives}{True Positives + False Negatives}\n", "\\end{array}\n", "$$\n", "\n", "$$\n", "\\begin{array}{rcl}\n", " Specificity = \\dfrac{True Negatives}{False Positives + True Negatives}\n", "\\end{array}\n", "$$\n", "\n", "\n", "For the threshold value that we examined above, the model would produce the following confusion matrix on the entire testing data:" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "sensitivity = 0.19570135746606335\n", "specificity = 0.9741953385127636\n" ] } ], "source": [ "#sensitivity = the ability of the model to correctly identify shots that resulted in a goal.\n", "sensitivity_3 = cm_dis_3[1][1]/(cm_dis_3[1][1]+cm_dis_3[1][0])\n", "print('sensitivity = ' + str(sensitivity_3))\n", "#the ability of the model to correctly identify shots that did not result in a goal\n", "specificity_3 = cm_dis_3[0][0]/(cm_dis_3[0][1]+cm_dis_3[0][0])\n", "print('specificity = '+ str(specificity_3) )" ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0.5, 1.0, 'Logistic Regression Model for Shots')" ] }, "execution_count": 27, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "threshold=0.1\n", "threshold_x=16\n", "df_goal = df_log_goal[:100]\n", "df_miss = df_log_miss[:100]\n", "TP = df_goal[df_goal['Distance']threshold_x]\n", "FP = df_goal[df_goal['Distance']>threshold_x]\n", "FN = df_miss[df_miss['Distance']" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "threshold=[0.1]\n", "y_pred = (lgm_dis.predict_proba(x_test_dis)[:, 1] > threshold).astype('float')\n", "cm_dis_10 = confusion_matrix(y_test_dis, y_pred)\n", "cm_display = ConfusionMatrixDisplay(cm_dis_10).plot(cmap='OrRd')\n", "cm_display.im_.colorbar.remove()\n", "plt.title('Confusion Matrix for Threshold = 0.1')\n", "print(cm_dis_10)" ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "sensitivity = 0.7782805429864253\n", "specificity = 0.6104328523862376\n", "2808\n" ] } ], "source": [ "#sensitivity = the ability of the model to correctly identify shots that resulted in a goal.\n", "sensitivity_10 = cm_dis_10[1][1]/(cm_dis_10[1][1]+cm_dis_10[1][0])\n", "print('sensitivity = ' + str(sensitivity_10))\n", "#the ability of the model to correctly identify shots that did not result in a goal\n", "specificity_10 = cm_dis_10[0][0]/(cm_dis_10[0][0]+cm_dis_10[0][1])\n", "print('specificity = '+ str(specificity_10) )\n", "print(cm_dis_10[0][1])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we have the opposite effect. The logistic regression model produces a better classification of goals but misclassifies misses at a much high volume. If we split the difference and choose a threshold in between the previous two:" ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0.5, 1.0, 'Logistic Regression Model for Shots')" ] }, "execution_count": 30, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "\n", "threshold=0.02\n", "threshold_x=28\n", "df_goal = df_log_goal[:100]\n", "df_miss = df_log_miss[:100]\n", "TP = df_goal[df_goal['Distance']threshold_x]\n", "FP = df_goal[df_goal['Distance']>threshold_x]\n", "FN = df_miss[df_miss['Distance']" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "threshold=[0.02]\n", "y_pred = (lgm_dis.predict_proba(x_test_dis)[:, 1] > threshold).astype('float')\n", "cm_dis_02 = confusion_matrix(y_test_dis, y_pred)\n", "cm_display = ConfusionMatrixDisplay(cm_dis_02).plot(cmap='OrRd')\n", "cm_display.im_.colorbar.remove()\n", "plt.title('Confusion Matrix for Threshold = 0.02')\n", "print(cm_dis_02)" ] }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "sensitivity = 0.9671945701357466\n", "specificity = 0.19034406215316316\n", "5836\n" ] } ], "source": [ "#sensitivity = the ability of the model to correctly identify shots that resulted in a goal.\n", "sensitivity_02 = cm_dis_02[1][1]/(cm_dis_02[1][1]+cm_dis_02[1][0])\n", "print('sensitivity = ' + str(sensitivity_02))\n", "#the ability of the model to correctly identify shots that did not result in a goal\n", "specificity_02 = cm_dis_02[0][0]/(cm_dis_02[0][0]+cm_dis_02[0][1])\n", "print('specificity = '+ str(specificity_02) )\n", "print(cm_dis_02[0][1])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We now predict goals and misses at a more balanced rate. We have seen that three different thresholds produce vastly different predictions from our model. Where they vary is in their specificity and sensitivity; that is, their ability to correctly predict goals and misses. It’s a tradeoff. So, what threshold do we choose? Well, neither of them and all of them. \n", "\n", "Let’s take a step back. If we were using a logistic regression model to identify if a patient has cancer, then we would adopt a high threshold, to forgo a high specificity rate in favor of high sensitivity. We would much rather give out false positive results rather than false negatives. We do not want someone to walk away thinking they passed a cancer screening when in fact they have cancer. When we are trying to model goal probability, we do not have such a preference. In fact, trying to predict goals outright is not all that useful to begin with. As we will see in the next part, the power of the expected goal model does not lie in making a prediction for a single shot. So what was the purpose of investigating thresholds and confusion matrices? We can use them to compare different models using something known as a Receiver Operator Characteristic (ROC) graph." ] }, { "cell_type": "code", "execution_count": 33, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0.5, 1.0, 'ROC Graph')" ] }, "execution_count": 33, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "from sklearn.metrics import roc_curve\n", "fig, axes = plt.subplots(figsize=(11,7))\n", "y_score = lgm_dis.decision_function(x_test_dis)\n", "fpr, tpr, _ = roc_curve(y_test_dis,y_score, pos_label=lgm_dis.classes_[1])\n", "plt.plot(fpr,tpr,label='ROC for Distance Parameter xG model')\n", "\n", "plt.scatter(1-specificity_3,sensitivity_3,c='orange',label='Threshold= 0.3')\n", "plt.scatter(1-specificity_10,sensitivity_10,c='red',label='Threshold= 0.1')\n", "plt.scatter(1-specificity_02,sensitivity_02,c='green',label='Threshold= 0.02')\n", "y_45 = np.linspace(0,1,100) \n", "plt.plot(y_45,y_45,linestyle='dashed',c='cyan')\n", "plt.legend()\n", "plt.xlim([0, 1])\n", "plt.ylim([0, 1])\n", "plt.xlabel('False Positive Rate = 1- Specificity')\n", "plt.ylabel('True Positive Rate = Sensitivity')\n", "plt.title('ROC Graph')\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Using a small step size, the ROC curve plots the model’s ability to predict goals correctly versus its ability to incorrectly predict misses for different threshold values. As you move up the y-axis, the model better predicts goals, and as we move to the left along the x-axis, the model better predicts misses. It essentially maps the trade-off between predicting goals and predicting misses. The dashed line represents a model that has no predictive power and is essentially useless because for every correct classification, it also predicts an incorrect classification. Therefore, the further away our ROC curve is from the 45 degree line, the better overall job it does at classifying the test data. Another way of looking at it is that the larger the area under the curve, the better our model is in describing the test data. This is useful to us because we can use it to compare different models and see if there is any substantial advantage to adding more variables to our model." ] }, { "cell_type": "code", "execution_count": 34, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[-0.08812064 1.41583297 -0.00209564]] [-1.40900091]\n", "[[-0.10757759 1.59478695 -1.01155408]] [-1.07169239]\n" ] } ], "source": [ "train_3 = df[['Goal','Distance','Angle Radians','Y']].copy()\n", "x_train_3, x_test_3, y_train_3, y_test_3 = train_test_split(train_3.drop('Goal',axis=1), \n", " train_3['Goal'], test_size=0.20, \n", " random_state=10)\n", "\n", "\n", "lgm_3 = LogisticRegression()\n", "lgm_3.fit(x_train_3,y_train_3)\n", "log_odds = lgm_3.coef_[0]\n", "print(lgm_3.coef_, lgm_3.intercept_)\n", "\n", "\n", "train_4 = df[['Goal','Distance','Angle Radians','header']].copy()\n", "x_train_4, x_test_4, y_train_4, y_test_4 = train_test_split(train_4.drop('Goal',axis=1), \n", " train_4['Goal'], test_size=0.20, \n", " random_state=10)\n", "\n", "\n", "lgm_4 = LogisticRegression()\n", "lgm_4.fit(x_train_4,y_train_4)\n", "log_odds = lgm_4.coef_[0]\n", "print(lgm_4.coef_, lgm_4.intercept_)" ] }, { "cell_type": "code", "execution_count": 35, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0.5, 1.0, 'ROC Graph')" ] }, "execution_count": 35, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, axes = plt.subplots(figsize=(11,7))\n", "\n", "\n", "y_score = lgm_dis.decision_function(x_test_dis)\n", "fpr, tpr, _ = roc_curve(y_test_dis,y_score, pos_label=lgm_dis.classes_[1])\n", "plt.plot(fpr,tpr,label='Distance Predictor',c='green')\n", "\n", "y_score_2 = lgm_2.decision_function(x_test_2)\n", "fpr2, tpr2, _ = roc_curve(y_test_2,y_score_2, pos_label=lgm_2.classes_[1])\n", "plt.plot(fpr2,tpr2,label='Distance + Angle',c='orange',linewidth=2)\n", "\n", "y_score_3 = lgm_3.decision_function(x_test_3)\n", "fpr_3, tpr_3, _ = roc_curve(y_test_3,y_score_3, pos_label=lgm_3.classes_[1])\n", "plt.plot(fpr_3,tpr_3,label='Distance + Angle + Center Distance',c='blue')\n", "\n", "y_score_4 = lgm_4.decision_function(x_test_4)\n", "fpr_4, tpr_4, _ = roc_curve(y_test_4,y_score_4, pos_label=lgm_4.classes_[1])\n", "plt.plot(fpr_4,tpr_4,label='Distance + Angle + Header',c='red')\n", "plt.legend()\n", "\n", "#y_score_5 = lgm_5.decision_function(poly_test)\n", "#fpr_5, tpr_5, _ = roc_curve(y_test_5,y_score_5, pos_label=lgm_5.classes_[1])\n", "#plt.plot(fpr_4,tpr_4,label='Distance + Angle + Header',c='yellow')\n", "#plt.legend()\n", "\n", "y_45 = np.linspace(0,1,100) \n", "plt.plot(y_45,y_45,linestyle='dashed',c='cyan')\n", "\n", "plt.xlim([0, 1])\n", "plt.ylim([0, 1])\n", "\n", "plt.xlabel('False Positive Rate = 1- Specificity')\n", "plt.ylabel('True Positive Rate = Sensitivity')\n", "plt.title('ROC Graph')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we have something concrete when assessing our model. If we look closely, a model with distance and angle as input variables produces the same area under the curve (AUC) as the same model but with an added “distance to center” parameter. So, contrary to some of the assumptions we made earlier, the “distance to center”predictor does not add much to the performance of our model and we should exclude it. While the “distance to center” parameter showed a slight change to the model in areas close to the goal line, this change meant very little as so few shots are taken from those positions. The AUC therefore tells us that adding the center to distance variable is rather useless. Note that we could have just as easily used p-values to learn if the center to distance parameter is useful towards our model. \n", "\n", "Another advantage of the ROC curve is if we chose to use other classification techniques, such as SVM, random forests, neural networks, etc, we could compare and contrast the performance of those model to the one we created here. I think this is overkill for the problem at hand, but is an avenue for further exploration. While these alternative models would produce similar results, logistic regression provides us with a fairly simple and digestible method to describe shot results, whereas these other methods require a deeper and more sophisticated understanding of machine learning techniques. \n", "\n", " " ] }, { "cell_type": "code", "execution_count": 39, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0.1714345578023222\n" ] } ], "source": [ "train_5 = df[['Goal','Distance','Angle Radians','header']].copy()\n", "x_train_5, x_test_5, y_train_5, y_test_5 = train_test_split(train_5.drop('Goal',axis=1), \n", " train_5['Goal'], test_size=0.20, \n", " random_state=10)\n", "\n", "\n", "lgm_5 = LogisticRegression(fit_intercept=False, solver='lbfgs')\n", "lgm_5.fit(x_train_5,y_train_5)\n", "\n", "\n", "X = x_train_4\n", "from numpy.random import binomial, normal\n", "from scipy.stats import bernoulli, binom\n", "np.random.seed(37)\n", "\n", "def full_log_likelihood(w, X, y):\n", " score = np.dot(X, w).reshape(1, X.shape[0])\n", " return np.sum(-np.log(1 + np.exp(score))) + np.sum(y * score)\n", "\n", "def null_log_likelihood(w, X, y):\n", " z = np.array([w if i == 0 else 0.0 for i, w in enumerate(w.reshape(1, X.shape[1])[0])]).reshape(X.shape[1], 1)\n", " score = np.dot(X, z).reshape(1, X.shape[0])\n", " return np.sum(-np.log(1 + np.exp(score))) + np.sum(y * score)\n", "\n", "\n", "w = np.array(lgm_4.coef_).transpose()\n", "y_pred = lgm_5.predict_proba(X)[:, 1]\n", "\n", "n = 32366\n", "z = np.dot(X, np.array([1.0, 2.0, 3.0])) + normal(0.0, 1.0, n)\n", "p = 1.0 / (1.0 + np.exp(-z))\n", "y = binom.rvs(1, p)\n", "\n", "\n", "def mcfadden_rsquare(w, X, y):\n", " return 1.0 - (full_log_likelihood(w, X, y) / null_log_likelihood(w, X, y))\n", "\n", "def mcfadden_adjusted_rsquare(w, X, y):\n", " k = float(X.shape[1])\n", " return 1.0 - ((full_log_likelihood(w, X, y) - k) / null_log_likelihood(w, X, y))\n", " \n", "print(mcfadden_adjusted_rsquare(w,X,y))\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Before we close, I want to briefly touch on R-squared values. In linear regression, R-squared measures the percentage of the response variable variation that a linear model explains. An R-squared of zero means the model does not explain any of the variation in the response and an R-squared of one represents a model that perfectly describes the data. R-squared does not directly translate to classification and logistic regression, but there are a number of pseudo R-squared values that mimic the linear regression version. The most popular, and the one I have employed, is Mcfadden’s R-squared, which measures the log likelihood of a null model (essentially just an intercept value) versus our model. We can interpret it in a similar fashion to the analogous linear regression R-squared. Values approaching one represent a model that perfectly classifies the data (such as the example we used to introduce the Heaviside function). For our best model based on the AUC (using distance, angle and header variables), Mcfadden’s R-squared comes out to about 0.171. Now before you throw out the xG model, we must understand that there is no definite answer to what value represents a good model and what represents a bad model. Goals, as we have discussed earlier, are mostly random. We need to remember that every shot is unique, comprised of hundreds of different variables that we have tried to model using just three. For that we should not expect to predict goals with certainty or anywhere near it. Some of this is due to our inability to model all these variables. Consider that while distance and angle give us a good sense of the likelihood of shot resulting in a goal, we did not take into account where the goalkeeper is positioned, if the shot was taken with a weak foot or strong foot, shot height at point of contact, the game state, home field advantage, if there are many bodies between the goal and the shot, etc. These are just a handful of the quantifiable variables that have an influence. There are also variables that are not easily quantifiable: what is the state of the pitch (as in rugged or is it a carpet), is fatigue playing a role, morale and confidence, and other soft factors. Even after neglecting these other variables, there is also some level of intrinsic randomness to shots. We have tried to model a very complex situation with a simple 3 parameter model; we should not expect such a high R-squared value. Nonetheless, xG is far from useless and in fact has been revolutionary to the way we approach the game. \n", "\n", "In the next and final part, we will explore applications of the expected goals model, its strengths, weaknesses, the dangers of extrapolation and hopefully prove that expected goals are worthwhile. Until then. " ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.4" } }, "nbformat": 4, "nbformat_minor": 2 }