{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Influence of region, skill and patch on predictability in League of Legends\n", "\n", "Last month, I used [random forests to predict the winner of League of Legends games](http://www.trailofpapers.net/2015/10/playing-in-random-forests-in-league-of.html). Since then I have downloaded more datasets from different regions, different ELOs, and on different patches. In this notebook, I will show that Korean games are easier to predict due to \"open mids,\" high skill games are faster and easier to predict than low-skill games, and show how the Preseason 2016 patch influenced the game.\n", "\n", "Code used in this notebook can be found at https://github.com/map222/lolML.\n", "\n", "### Table of contents\n", "[Region differences](#regions)\n", "\n", "[Skill differences](#skill)\n", "\n", "[Team ranked vs solo queue](#team)\n", "\n", "[Preseason 2016](#2016)\n", "\n", "### Load libraries, API key, and datasets" ] }, { "cell_type": "code", "execution_count": 87, "metadata": { "collapsed": false }, "outputs": [], "source": [ "import requests, json\n", "import numpy as np\n", "from src import API_io\n", "import importlib\n", "import pandas as pd\n", "import pickle\n", "import os\n", "from src import feature_calc\n", "import matplotlib.pyplot as plt\n", "import src.plotting as lol_plt\n", "%matplotlib inline\n", "import pdb\n", "import warnings\n", "warnings.filterwarnings('ignore')" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# load sklearn package \n", "from sklearn.naive_bayes import GaussianNB\n", "from sklearn.metrics import confusion_matrix\n", "from sklearn import cross_validation\n", "from sklearn.ensemble import RandomForestClassifier" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [], "source": [ "working_dir = 'C:\\\\Users\\\\Me\\\\Documents\\\\GitHub\\\\lolML'\n", "os.chdir(working_dir)\n", "with open(working_dir+ '\\\\api_key.txt', 'r') as api_file:\n", " api_key = api_file.read()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Load the datasets in. These datasets were scraped using the Region Scraper Notebook which identifies good players in the featured games, and takes games from their history." ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": false }, "outputs": [], "source": [ "working_dir = 'C:\\\\Users\\\\Me\\\\Documents\\\\GitHub\\\\lolML\\\\notebooks'\n", "os.chdir(working_dir)\n", "with open('EUW combined_df.pickle', 'rb') as pickle_file:\n", " euw_timelines_df = pickle.load(pickle_file)\n", "with open('KR combined_df.pickle', 'rb') as pickle_file:\n", " kr_timelines_df = pickle.load(pickle_file)\n", "with open('NA combined_df.pickle', 'rb') as pickle_file:\n", " na_timelines_df = pickle.load(pickle_file)\n", "with open('Low ELO combined_df.pickle', 'rb') as pickle_file:\n", " low_timelines_df = pickle.load(pickle_file)\n", "with open('Preseason2016 combined_df.pickle', 'rb') as pickle_file:\n", " pre2016_timelines_df = pickle.load(pickle_file)\n", "with open('Season 2015 Team ranked combined_df.pickle', 'rb') as pickle_file:\n", " team_timelines_df = pickle.load(pickle_file)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Create some secondary features." ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "collapsed": false }, "outputs": [], "source": [ "euw_timelines_df = [feature_calc.calc_secondary_features(x) for x in euw_timelines_df]\n", "na_timelines_df = [feature_calc.calc_secondary_features(x) for x in na_timelines_df]\n", "kr_timelines_df = [feature_calc.calc_secondary_features(x) for x in kr_timelines_df]\n", "low_timelines_df = [feature_calc.calc_secondary_features(x) for x in low_timelines_df]\n", "pre2016_timelines_df = [feature_calc.calc_secondary_features(x) for x in pre2016_timelines_df]\n", "team_timelines_df = [feature_calc.calc_secondary_features(x) for x in team_timelines_df]\n", "euw_timelines_df = feature_calc.calc_second_diff(euw_timelines_df)\n", "na_timelines_df = feature_calc.calc_second_diff(na_timelines_df)\n", "kr_timelines_df = feature_calc.calc_second_diff(kr_timelines_df)\n", "low_timelines_df = feature_calc.calc_second_diff(low_timelines_df)\n", "pre2016_timelines_df = feature_calc.calc_second_diff(pre2016_timelines_df)\n", "team_timelines_df = feature_calc.calc_second_diff(team_timelines_df)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "These are the important features, as found in prior investigations." ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "collapsed": true }, "outputs": [], "source": [ "important_col = ['blue_inhibs', 'blue_barons', 'drag_diff', 'first_baron', 'first_inhib',\n", " 'gold_diff', 'gold_diff_diff', 'kill_diff', 'kill_diff_diff', 'red_barons',\n", " 'red_inhibs', 'tower_diff']\n", "timeline_end = 55\n", "time_indices = np.arange(5, timeline_end, 5)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Set up matplotlib so graphs are pretty." ] }, { "cell_type": "code", "execution_count": 84, "metadata": { "collapsed": false }, "outputs": [], "source": [ "import matplotlib as mpl\n", "mpl.rc('font', size=20)\n", "mpl.rc('lines', linewidth=2)\n", "mpl.rc('figure',figsize=[8, 6])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "## How different is each region?\n", "\n", "Korea is famed for its great players, and \"open mid\" philosophy. Are we able to see those attributes in our model? First, let's plot the distribution of game lengths." ] }, { "cell_type": "code", "execution_count": 29, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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sWNx+NUEPQxtgGsGgx9vd/Y64NuuAQQRjMD4CxgKTgd9HyU1ERES2FWWMQzvg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\ndx9Rok1/YBTQBVgA/M3dQyfgqcchBU8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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(1, figsize = [8, 6])\n", "euw_lengths =np.array( euw_timelines_df[0]['game_length'])\n", "na_lengths = np.array( na_timelines_df[0]['game_length'])\n", "kr_lengths = np.array( kr_timelines_df[0]['game_length'])\n", "plt.hist(euw_lengths, bins = range(0, 60), histtype='step', normed=True, label = 'EUW')\n", "plt.hist(na_lengths, bins = range(0, 60), histtype='step', normed=True, label = 'NA')\n", "plt.hist(kr_lengths, bins = range(0, 60), histtype='step', normed=True, label = 'KR')\n", "lol_plt.prettify_axes(ax)\n", "plt.xlabel('Game Length')\n", "ax.set_ylabel('Fraction of games')\n", "plt.legend(frameon=False, fontsize = 14);" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "NA and EUW games are of similar length. Korean games, however, are shorter, with more games ending before 20 minutes, and many more surrenders at twenty. The famed \"open mid\" attitude is indeed true.\n", "### Are regions similarly predictable?\n", "Given these differences, we can still ask, are the regions similarly predictable? First, I will create a scoring function to apply to each timepoint." ] }, { "cell_type": "code", "execution_count": 92, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# Since the previous post, I've found that these hyperparameters increase predictability, and reduce run time\n", "rfc = RandomForestClassifier(n_jobs = -1, n_estimators = 25, max_features = 'sqrt',\n", " max_depth=1, min_samples_leaf=10, min_samples_split=25)\n", "def cross_validate_df(cur_df, n_samples = 20000):\n", " sample_df = cur_df.sample(min(cur_df.shape[0], n_samples))\n", " return cross_validation.cross_val_score(rfc, sample_df[important_col], sample_df['winner'], cv=4, n_jobs = -1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we can apply the scoring function to each region, and plot the results." ] }, { "cell_type": "code", "execution_count": 32, "metadata": { "collapsed": false }, "outputs": [], "source": [ "kr_scores = list(map(cross_validate_df, kr_timelines_df))\n", "na_scores = list(map(cross_validate_df, na_timelines_df))\n", "euw_scores = list(map(cross_validate_df, euw_timelines_df))" ] }, { "cell_type": "code", "execution_count": 88, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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UKhqpTVWl1H7bMU8rpdo79lWIlMLPz6x/c+mSqRY8cWLMn+NB1iA+XfwpLQ/B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\nWZjrb6WswkKfEEDFnQkfnXcvw5f47Rwl3iJSTT/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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(1, figsize = [8, 6])\n", "cv = np.shape(euw_scores)[1]\n", "plt.errorbar(time_indices, np.mean(kr_scores, 1), np.std(kr_scores, 1) / np.sqrt(cv), label = 'KR', capsize = 0)\n", "plt.errorbar(time_indices, np.mean(na_scores, 1), np.std(na_scores, 1) / np.sqrt(cv), label = 'NA', capsize = 0)\n", "plt.errorbar(time_indices, np.mean(euw_scores, 1), np.std(euw_scores, 1) / np.sqrt(cv), label = 'EUW', capsize = 0)\n", "lol_plt.prettify_axes(plt.gca())\n", "plt.ylabel('Accuracy')\n", "plt.xlabel('Minutes in game')\n", "plt.xlim([0, 60])\n", "ax.set_ylim([0.6, 0.9])\n", "plt.legend(frameon=False, fontsize = 16);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Given the frequency of \"open mids,\" Korean games are easier to predict during the first twenty minutes. However, once all of the early surrenders are no longer predicted, each region behaves basically the same. We can try to confirm this by using forests trained on one region to predict the outcomes of a different region." ] }, { "cell_type": "code", "execution_count": 38, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def score_cross_region(train_df, test_df, n_samples = 20000):\n", " # train a random forest classifier on training data from one region, then score it on a different region\n", " train_sample_df = train_df.sample(min(train_df.shape[0], n_samples))\n", " rfc.fit(train_sample_df[important_col], train_sample_df['winner'])\n", " return rfc.score(test_df[important_col], test_df['winner'])" ] }, { "cell_type": "code", "execution_count": 39, "metadata": { "collapsed": false }, "outputs": [], "source": [ "na_eu_cross_scores = [score_cross_region(x, y) for x,y in zip(na_timelines_df, euw_timelines_df)]\n", "eu_na_cross_scores = [score_cross_region(x, y) for x,y in zip(euw_timelines_df, na_timelines_df)]\n", "eu_kr_cross_scores = [score_cross_region(x, y) for x,y in zip(euw_timelines_df, kr_timelines_df)]\n", "na_kr_cross_scores = [score_cross_region(x, y) for x,y in zip(na_timelines_df, kr_timelines_df)]" ] }, { "cell_type": "code", "execution_count": 77, "metadata": { "collapsed": false, "scrolled": true }, "outputs": [ { "data": { "image/png": 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FPXr0oGXLlljfn8HzBPr27cu8efOYMWMG/fv3T1Od6tWrA3D58mVq1KjxxDFk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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(1, figsize = [8, 6])\n", "plt.plot(time_indices, np.mean(na_scores, 1), label = 'NA -> NA')\n", "plt.plot(time_indices, eu_na_cross_scores, label = 'EU -> NA')\n", "plt.plot(time_indices, np.mean(kr_scores, 1), label = 'KR -> KR')\n", "plt.plot(time_indices, na_kr_cross_scores, label = 'NA -> KR')\n", "lol_plt.prettify_axes(plt.gca())\n", "plt.ylabel('Accuracy')\n", "plt.xlabel('Minutes in game')\n", "plt.xlim([0, 60])\n", "ax.set_ylim([0.6, 0.9])\n", "plt.legend(frameon=False, fontsize = 16);" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "Using EU data to predict NA does well, with a strange dip of 2-3% at 30 minutes. I have no idea what the difference there could be. Using NA to predict KR also does well, showing a higher probability at the pre-20 minute timepoints. This probably reflects that once the losing team goes \"open mid,\" the winning team then gains a large advantage that the model can use.\n", "\n", "## How does skill level impact predictability?\n", "Next I wanted to see how skill influences the predictability of games. One might assume that better players are able to exploit advantages, and make games more predictable. First, let's look at game lengths for low and high ELO games. I got low ELO games by scraping the games of Kaceytron (probably the funniest streamer out there), and the people she played against. High ELO games come from players in featured games." ] }, { "cell_type": "code", "execution_count": 73, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Low skill mean length: 37.6115551116, High skill mean length: 32.5614677361\n" ] }, { "data": { "image/png": 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Sb1KZ43AtsBYY6u4zMxSPiIiI5LFULlX8CHhUSYOIiEjxSiVxWAlsylQgIiIikv9SSRwm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\n0uDfA3d/IerpQjObDXxCkEy8XtOhGQ0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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(1, figsize = [8, 6])\n", "low_lengths =np.array( low_timelines_df[0]['game_length'])\n", "high_lengths = np.array( na_timelines_df[0]['game_length'])\n", "plt.hist(low_lengths, bins = range(0, 70), histtype='step', normed=True, label = 'low')\n", "plt.hist(high_lengths, bins = range(0, 70), histtype='step', normed=True,label = 'high')\n", "lol_plt.prettify_axes(plt.gca())\n", "plt.xlabel('Game Length')\n", "plt.ylabel('Fraction of Games')\n", "plt.ylim([0, 0.1])\n", "plt.legend(frameon=False, fontsize = 16);\n", "print('Low skill mean length: ' + str(low_lengths.mean() ) + ', High skill mean length: ' + str(high_lengths.mean()) )" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Low skilled players surrender less, and play longer games (~5 minutes longer). As someone who was played games from Bronze to Gold, this is likely due to less skilled players not knowing to take objectives after team fights, and generally not being able to press advantages.\n", "\n", "How does this effect predictability?" ] }, { "cell_type": "code", "execution_count": 52, "metadata": { "collapsed": false }, "outputs": [], "source": [ "low_scores = [cross_validate_df(x) for x in low_timelines_df]\n", "low_high_cross_scores = [score_cross_region(x, y) for x,y in zip(low_timelines_df, na_timelines_df)]" ] }, { "cell_type": "code", "execution_count": 94, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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9k9a/nqx1XpHhpCrJWHUMgVLKC5gGTACqAjuBDUqpJFeeUEqVAdYAftHlmwLZgfVJFH8O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\n6anp4QYmIiJJSwlBCDrwCnX4H7kn1ef+9EkAdNbIhCIiEiI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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(1, figsize = [8, 6])\n", "plt.errorbar(time_indices[:-1], np.mean(low_scores, 1)[:-1], np.std(low_scores, 1)[:-1] / np.sqrt(cv), label = 'Low skill', capsize = 0)\n", "plt.errorbar(time_indices[:-1], np.mean(na_scores, 1)[:-1], np.std(na_scores, 1)[:-1] / np.sqrt(cv), label = 'High skill', capsize = 0)\n", "plt.plot(time_indices[:-1], low_high_cross_scores[:-1], label = 'Low -> High')\n", "lol_plt.prettify_axes(plt.gca())\n", "plt.ylabel('Accuracy')\n", "plt.xlabel('Minutes in game')\n", "plt.xlim([0, 60])\n", "plt.ylim([0.6, 0.9])\n", "plt.legend(frameon=False, fontsize=16);" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "High skill games are slightly easier to predict than low-skill games, especially at 20-35 minutes. Is this due to better players or different game states? If we use low skill models to predict high skill games, we get a similar accuracy, so it is likely that high skill games simply have larger differences between teams at those timepoints.\n", "\n", "### Team ranked vs Solo queue\n", "\n", "Another way we can try to look at this is to plot solo queue games versus team ranked games. Theoretically, the coordination in team ranked games should be higher than Solo Queue games, and make things more predictable. I scraped Team Ranked games using my ELO Scraper notebook, which took games from Challenger Ranked Teams during the 2015 season. There are a lot fewer Team Ranked games, ~1,200 total." ] }, { "cell_type": "code", "execution_count": 72, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Solo mean length: 32.5614677361, Team mean length: 30.6936\n" ] }, { "data": { "image/png": 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IfKcMnHOHgFn+Y8IxARhqZsPM7HgzexTfjMJTAGZ2v5nNCuj/MpANTDGzE82s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\noaVcjPeSDjSz93LlPgf8Ee91aFtw7VVmtjCTfin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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(1, figsize = [8, 6])\n", "solo_lengths = np.array( na_timelines_df[0]['game_length'])\n", "team_lengths =np.array( team_timelines_df[0]['game_length'])\n", "plt.hist(solo_lengths, bins = range(0, 60), histtype='step', normed=True, label = 'Solo queue')\n", "plt.hist(team_lengths, bins = range(0, 60), histtype='step', normed=True,label = 'Team ranked')\n", "lol_plt.prettify_axes(plt.gca())\n", "plt.xlabel('Game Length')\n", "plt.ylabel('Fraction of Games')\n", "plt.ylim([0, 0.1])\n", "plt.legend(frameon=False, fontsize = 16)\n", "print('Solo mean length: ' + str(solo_lengths.mean() ) + ', Team mean length: ' + str(team_lengths.mean()) )" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Team ranked games average two minutes quicker than solo queue games.\n", "\n", "How predictable are they?" ] }, { "cell_type": "code", "execution_count": 65, "metadata": { "collapsed": true }, "outputs": [], "source": [ "team_scores = [cross_validate_df(x) for x in team_timelines_df]" ] }, { "cell_type": "code", "execution_count": 90, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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FC3P77bczZcqURNcuXryYJk2aUKRIEW677TY+//zzVJ/VSTlq9JdSTooyUfyx/w8mb5zM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\neU1ibER8QPooqavBzxhM6d2ijcAcSaMkjeHomhG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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.errorbar(time_indices[:-2], np.mean(na_scores[:-2], 1), np.std(low_scores[:-2], 1) / np.sqrt(cv), label = 'Solo queue', capsize = 0)\n", "plt.errorbar(time_indices[:-2], np.mean(team_scores[:-2], 1), np.std(na_scores[:-2], 1) / np.sqrt(cv), label = 'Team ranked', capsize = 0)\n", "lol_plt.prettify_axes(plt.gca())\n", "plt.ylabel('Accuracy')\n", "plt.xlabel('Minutes in game')\n", "plt.xlim([0, 60])\n", "plt.ylim([0.6, 0.9])\n", "plt.legend(frameon=False, fontsize=16);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "That's the biggest difference yet! And that's with many fewer games to train on. There's a 5% difference in predictability at 10 minutes. It seems that better teams get ahead early, and are better able at pressing that advantage to end the game quickly. It would be interesting to compare these results to professional games, which is something I plan to do. If you were to use these models for betting, you should use team ranked games, rather than solo queue!\n", "\n", "## Preseason 2016\n", "Finally, with the preseason for 2016 upon us, games appear to be snowballing more, and ending quickly. Is that feeling translated to the model?" ] }, { "cell_type": "code", "execution_count": 75, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "2106 mean length: 29.1938018333, 2015 mean length: 32.5614677361\n" ] }, { "data": { "image/png": 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zC95/YhjwE978hp+CXgujnqGIiIjEjTxHHMzsArwJkIOccxnBocCfnwUdqwh0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\noO2VHer9/hK/GTilFnd1iftk08+kDx/dHh6qMKY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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(1, figsize = [8, 6])\n", "pre_2016_lengths =np.array( pre2016_timelines_df[0]['game_length'])\n", "season_2015_lengths = np.array( na_timelines_df[0]['game_length'])\n", "plt.hist(pre_2016_lengths, bins = range(0, 60), histtype='step', normed=True, label = 'Pre 2016')\n", "plt.hist(season_2015_lengths, bins = range(0, 60), histtype='step', normed=True,label = 'Season 2015')\n", "lol_plt.prettify_axes(plt.gca())\n", "plt.xlabel('Game Length')\n", "plt.ylabel('Fraction of Games')\n", "plt.legend(frameon=False, fontsize=16);\n", "print('2106 mean length: ' + str(pre_2016_lengths.mean() ) + ', 2015 mean length: ' + str(season_2015_lengths.mean()) )" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Preseason 2016 games are averaging 3 minutes less than 2015 games. How about predictability?" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "pre_2016_scores = [cross_validate_df(x) for x in pre2016_timelines_df]\n", "season_2015_scores = [cross_validate_df(x) for x in na_timelines_df]" ] }, { "cell_type": "code", "execution_count": 91, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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XuAArVMg97ps7141wMybUBXysoYj0FpFtIhIlIqtE5LpzpG8rIstE5KiIHBCR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\nB5Vg+mzdZ+w5tsdtwlXJNuEyxmRNgX7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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.errorbar(time_indices[:-3], np.mean(pre_2016_scores[:-3], 1), np.std(pre_2016_scores[:-3], 1) / np.sqrt(4), label = 'Pre 2016', capsize=0)\n", "plt.errorbar(time_indices[:-3], np.mean(season_2015_scores[:-3], 1), np.std(season_2015_scores[:-3], 1) / np.sqrt(4), label = 'Season 2015', capsize=0)\n", "lol_plt.prettify_axes(plt.gca())\n", "plt.ylabel('Accuracy')\n", "plt.xlabel('Minutes in game')\n", "plt.xlim([0, 60])\n", "plt.ylim([0.6, 0.9])\n", "plt.legend(fontsize = 16,frameon=False);" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "Preseason 2016 is about 5% easier to predict 5-10 minutes into the game, reflecting the increased ability to snowball. Things converge around 20 minutes though, due to surrenders and teams simply losing. I would also not read too much into the 35 minute timepoint, as there are only a limited number of preseason games that the model has to train with.\n", "\n", "That's it for this update. In the future, I want to use this model to explore hyperparameters of random forests, and try out some other machine learning algorithms to see which works best." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "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": "3.4.3" } }, "nbformat": 4, "nbformat_minor": 0 }