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Created June 18, 2015 00:57
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gistfile1.txt
{
"metadata": {
"name": "",
"signature": "sha256:dc2c94954c4c2ad1c88d16c4ea2bd8768fc52cd73251f19a1f435cd3578dcb5e"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Regularized +/- (RAPM) in Python using scikit-learn"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"First thing we do is import matchup data. My nbawowy data is stored in a MongoDB collection which has a \"document\" (i.e. JSON object) for each \"stint\" in a game. A stint is defined as a series of possessions in between player substitutions. Every time a player (or more than one) is subbed into the game, a new stint is created. For this tutorial I'll be working with data from the current season (2014-15)."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import json # a built-in Python module for dealing with JSON data\n",
"\n",
"data = [] # create an empty array to hold all the stints\n",
"# open the file and read the data!\n",
"with open('/Users/evanzamir/ipython_notebooks/pymc_test/data/matchups-2015'\n",
" '-final.json') as units_file:\n",
" for j in units_file:\n",
" data.append(json.loads(j))"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 1
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"a = 2"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 2
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# \"pretty\" print the first stint, which in this case describes a matchup in a CHA-MIA game last season.\n",
"\n",
"from pprint import pprint\n",
"pprint(data[0])"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 2
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"You can see there's a ton of data even for one stint. The main things we care about are the players in the 'on' and 'off' arrays under each team, the possessions (.stats.poss) and the points scored during the stint ('.stats.pts')."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"To compute RAPM we'll be using a very popular machine learning toolkit in Python called scikit-learn (abbreviated sklearn). Within sklearn there are many different ML algorithms. RAPM uses a technique called Ridge Regression. But before we get to that, we will want to look at some \"helper\" functions that will be useful in transforming our stint data to a form that sklearn requires."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"First we will import a class called DictVectorizer which transforms a list of arrays into a list of Python dictionaries (\"dicts\" in Python or \"hashes\" or \"maps\" in other languages). In our stint objects there is an array containing the 5 players on the court for each team. When we do the regression, we will actually want to create a much larger array containing as many columns as there are players in the league (around 480 or so). *DictVectorizer* will help us do that quite easily as shown below."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# To demonstrate how DictVectorizer works...\n",
"# Create a small list of lists with \"fake\" units\n",
"\n",
"units = [['Stephen Curry','Klay Thompson','Harrison Barnes','Draymond Green','Andrew Bogut'],\n",
" ['Stephen Curry','Klay Thompson','Harrison Barnes','Draymond Green','Andrew Bogut'],\n",
" ['Shaun Livingston','Klay Thompson','Harrison Barnes','Draymond Green','Andrew Bogut'],\n",
" ['Shaun Livingston','Klay Thompson','Andre Iguodala','Draymond Green','Andrew Bogut'],\n",
" ['Leandro Barbosa','Shaun Livingston','Andre Iguodala','Harrison Barnes','Draymond Green']]\n",
"\n",
"from sklearn.feature_extraction import DictVectorizer\n",
"v = DictVectorizer(sparse=False)\n",
"list_dicts = []\n",
"\n",
"# For each unit we want to create a dict containing the players' names as keys and the value 1 as the value.\n",
"# Later the value will be +1 if the player is playing at home and -1 if he is away.\n",
"\n",
"for unit in units:\n",
" list_dicts.append({name: 1 for name in unit})\n",
"print(list_dicts)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"[{'Andrew Bogut': 1, 'Klay Thompson': 1, 'Draymond Green': 1, 'Harrison Barnes': 1, 'Stephen Curry': 1}, {'Andrew Bogut': 1, 'Klay Thompson': 1, 'Draymond Green': 1, 'Harrison Barnes': 1, 'Stephen Curry': 1}, {'Klay Thompson': 1, 'Andrew Bogut': 1, 'Shaun Livingston': 1, 'Draymond Green': 1, 'Harrison Barnes': 1}, {'Klay Thompson': 1, 'Andrew Bogut': 1, 'Shaun Livingston': 1, 'Draymond Green': 1, 'Andre Iguodala': 1}, {'Shaun Livingston': 1, 'Leandro Barbosa': 1, 'Harrison Barnes': 1, 'Andre Iguodala': 1, 'Draymond Green': 1}]\n"
]
}
],
"prompt_number": 3
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# This is where magic happens.\n",
"# The function fit_transform has turned our list of dicts into a list of arrays containing enough columns\n",
"# for all the players in this fake data set.\n",
"# The variable v, an instance of DictVectorizer, is able to keep track of all this bookkeeping for us.\n",
"# Basically, it's a really useful thing to have for what we're about to do and eliminates\n",
"# writing a metric ton of our own code.\n",
"\n",
"X = v.fit_transform(list_dicts)\n",
"print(X)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"[[ 0. 1. 1. 1. 1. 0. 0. 1.]\n",
" [ 0. 1. 1. 1. 1. 0. 0. 1.]\n",
" [ 0. 1. 1. 1. 1. 0. 1. 0.]\n",
" [ 1. 1. 1. 0. 1. 0. 1. 0.]\n",
" [ 1. 0. 1. 1. 0. 1. 1. 0.]]\n"
]
}
],
"prompt_number": 4
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# We can even take the inverse transform and get back the list of dicts!\n",
"\n",
"x = v.inverse_transform(X)\n",
"print(x)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"[{'Klay Thompson': 1.0, 'Andrew Bogut': 1.0, 'Draymond Green': 1.0, 'Harrison Barnes': 1.0, 'Stephen Curry': 1.0}, {'Klay Thompson': 1.0, 'Andrew Bogut': 1.0, 'Draymond Green': 1.0, 'Harrison Barnes': 1.0, 'Stephen Curry': 1.0}, {'Klay Thompson': 1.0, 'Shaun Livingston': 1.0, 'Andrew Bogut': 1.0, 'Draymond Green': 1.0, 'Harrison Barnes': 1.0}, {'Klay Thompson': 1.0, 'Shaun Livingston': 1.0, 'Andrew Bogut': 1.0, 'Draymond Green': 1.0, 'Andre Iguodala': 1.0}, {'Shaun Livingston': 1.0, 'Harrison Barnes': 1.0, 'Leandro Barbosa': 1.0, 'Draymond Green': 1.0, 'Andre Iguodala': 1.0}]\n"
]
}
],
"prompt_number": 5
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# And we can easily get the names of all the players in the data set!\n",
"# W00t\n",
"\n",
"print(v.get_feature_names())"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "['Andre Iguodala', 'Andrew Bogut', 'Draymond Green', 'Harrison Barnes', 'Klay Thompson', 'Leandro Barbosa', 'Shaun Livingston', 'Stephen Curry']\n",
"text": [
"['Andre Iguodala', 'Andrew Bogut', 'Draymond Green', 'Harrison Barnes', 'Klay Thompson', 'Leandro Barbosa', 'Shaun Livingston', 'Stephen Curry']\n"
]
}
],
"prompt_number": 13
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now we're going to iterate through our matchup **data** and create three variables: 1) **units** is a list of dicts of the home and away players for each stint with a +1/-1 indicating which side they are on; 2) **points** is a list containing the point differential (normalized to 100 possessions) for each stint; 3) **weights** is simply the number of possessions for each stint."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"units = []\n",
"points = []\n",
"weights = []\n",
"\n",
"for d in data:\n",
" home = d['home']\n",
" away = d['away']\n",
" home_poss = d[home]['stats']['poss']\n",
" away_poss = d[away]['stats']['poss']\n",
"\n",
" home_offense_unit = {\"{},offense\".format(name): 1 for name in d[home]['on']}\n",
" home_defense_unit = {\"{},defense\".format(name): 1 for name in d[home]['on']}\n",
" away_offense_unit = {\"{},offense\".format(name): 1 for name in d[away]['on']}\n",
" away_defense_unit = {\"{},defense\".format(name): 1 for name in d[away]['on']}\n",
"\n",
" home_stint = home_offense_unit.copy()\n",
" home_stint.update(away_defense_unit)\n",
" home_stint.update({'HCA': 1})\n",
" away_stint = away_offense_unit.copy()\n",
" away_stint.update(home_defense_unit)\n",
" away_stint.update({'HCA': -1})\n",
"\n",
" if home_poss >= 1: # to avoid some ill-conditioning we only use stints that have possessions >= 1\n",
" home_ortg = 100 * (d[home]['stats']['pts']) / home_poss\n",
" units.append(home_stint)\n",
" points.append(home_ortg)\n",
" weights.append(home_poss)\n",
"\n",
" if away_poss >= 1:\n",
" away_ortg = 100 * (d[away]['stats']['pts']) / away_poss\n",
" units.append(away_stint)\n",
" points.append(away_ortg)\n",
" weights.append(away_poss)\n",
"\n",
"print(len(units), len(points), len(weights))"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(72296, 72296, 72296)\n"
]
}
],
"prompt_number": 6
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Now we employ DictVectorizer to do its magic\n",
"from sklearn.feature_extraction import DictVectorizer\n",
"u = DictVectorizer(sparse=False)\n",
"u_mat = u.fit_transform(units)\n",
"print(u_mat) # a giant list of lists where each array contains five +1's, five -1's, and a whole mess of 0's\n",
"print(points[:25]) # just showing the first 25 stints\n",
"print(weights[:100]) # just showing the first 100 stints"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"[[ 0. 0. 0. ..., 0. 0. 0.]\n",
" [ 0. 0. 0. ..., 0. 0. 0.]\n",
" [ 0. 0. 0. ..., 0. 0. 0.]\n",
" ..., \n",
" [ 0. 0. 0. ..., 0. 0. 0.]\n",
" [ 0. 0. 0. ..., 0. 0. 0.]\n",
" [ 0. 0. 0. ..., 0. 0. 0.]]\n",
"[275, 100, 0, 90, 170, 200, 0, 100, 140, 120, 160, 200, 0, 100, 50, 233, 50, 0, 200, 200, 100, 0, 100, 60, 20]\n",
"[4, 4, 1, 10, 10, 3, 2, 1, 5, 5, 5, 5, 1, 2, 2, 3, 4, 1, 1, 1, 1, 2, 1, 5, 5, 7, 8, 1, 1, 1, 1, 1, 2, 2, 1, 1, 2, 2, 1, 1, 2, 2, 3, 3, 3, 4, 3, 3, 3, 3, 7, 6, 1, 1, 6, 6, 1, 1, 1, 2, 1, 5, 4, 1, 1, 1, 8, 9, 1, 1, 2, 1, 5, 6, 4, 5, 2, 1, 1, 2, 3, 3, 3, 4, 4, 3, 1, 2, 3, 3, 5, 4, 3, 3, 1, 2, 6, 5, 1, 1]\n"
]
}
],
"prompt_number": 7
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# The first 25 players alphabetically in the data set\n",
"from pprint import pprint\n",
"players = u.get_feature_names()\n",
"pprint(u.get_feature_names()[:25])"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"['A.J. Price,defense',\n",
" 'A.J. Price,offense',\n",
" 'Aaron Brooks,defense',\n",
" 'Aaron Brooks,offense',\n",
" 'Aaron Gordon,defense',\n",
" 'Aaron Gordon,offense',\n",
" 'Adreian Payne,defense',\n",
" 'Adreian Payne,offense',\n",
" 'Al Horford,defense',\n",
" 'Al Horford,offense',\n",
" 'Al Jefferson,defense',\n",
" 'Al Jefferson,offense',\n",
" 'Al-Farouq Aminu,defense',\n",
" 'Al-Farouq Aminu,offense',\n",
" 'Alan Anderson,defense',\n",
" 'Alan Anderson,offense',\n",
" 'Alec Burks,defense',\n",
" 'Alec Burks,offense',\n",
" 'Alex Kirk,defense',\n",
" 'Alex Kirk,offense',\n",
" 'Alex Len,defense',\n",
" 'Alex Len,offense',\n",
" 'Alexey Shved,defense',\n",
" 'Alexey Shved,offense',\n",
" 'Alexis Ajinca,defense']\n"
]
}
],
"prompt_number": 9
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# perform the inverse transform on one stint just to double check it makes sense\n",
"\n",
"pprint(u.inverse_transform(u_mat)[:1])"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"[{'Andre Iguodala,defense': 1.0,\n",
" 'Carlos Boozer,offense': 1.0,\n",
" 'Draymond Green,defense': 1.0,\n",
" 'HCA': 1.0,\n",
" 'Harrison Barnes,defense': 1.0,\n",
" 'Klay Thompson,defense': 1.0,\n",
" 'Robert Sacre,offense': 1.0,\n",
" 'Ronnie Price,offense': 1.0,\n",
" 'Stephen Curry,defense': 1.0,\n",
" 'Wayne Ellington,offense': 1.0,\n",
" 'Wesley Johnson,offense': 1.0}]\n"
]
}
],
"prompt_number": 10
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now the fun stuff begins! We import the **linear_model** class and use the function **RidgeCV** to perform ridge regression on our data set using five-fold cross validation. Briefly, the idea here is to pick the optimal value of *alpha* for regularizing the data (i.e. so it fits the data best)."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import numpy as np\n",
"from sklearn import linear_model\n",
"\n",
"clf = linear_model.RidgeCV(alphas=(np.array([0.01, 0.1, 1.0, 10, 100, 500, 750, 1000, 1500, 2000, 5000])), cv=5)\n",
"clf.fit(u_mat, points, sample_weight=weights)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 13,
"text": [
"RidgeCV(alphas=array([ 1.00000e-02, 1.00000e-01, 1.00000e+00, 1.00000e+01,\n",
" 1.00000e+02, 5.00000e+02, 7.50000e+02, 1.00000e+03,\n",
" 1.50000e+03, 2.00000e+03, 5.00000e+03]),\n",
" cv=5, fit_intercept=True, gcv_mode=None, normalize=False, scoring=None,\n",
" store_cv_values=False)"
]
}
],
"prompt_number": 13
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Here is the value of alpha that RidgeCV selected. We could probably add a few more values to test above too...\n",
"# but this is just a tutorial :)\n",
"\n",
"print(clf.alpha_)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"750.0\n"
]
}
],
"prompt_number": 14
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now we want to get the coefficients that RidgeCV found for our \"optimal\" solution. The coefficients for each player are contained in an attribute of the class called **coef_**. "
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"ratings = []\n",
"for player in players:\n",
" ratings.append((player, clf.coef_[players.index(player)]))\n",
"ratings.sort(key=lambda tup: tup[1], reverse=True) # sort by rating in descending order"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 15
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"And here are the ratings! Now, remember this is for one season of data. The ratings are obviously quite noisy. And that's why it is often not very useful to look at just one season of data. But this is enough to give you the basic idea of how it's done."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"for idx, rating in enumerate(ratings):\n",
" print(\"{},{},{}\".format(idx + 1, rating[0], rating[1]))"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"1,James Harden,offense,7.38697479911\n",
"2,Kyle Korver,offense,5.85487573511\n",
"3,LeBron James,offense,5.36099693388\n",
"4,Carmelo Anthony,offense,5.30841531408\n",
"5,Ty Lawson,offense,5.16697240343\n",
"6,Dirk Nowitzki,offense,5.14746637873\n",
"7,Draymond Green,offense,5.03424939767\n",
"8,Anthony Morrow,offense,5.01783439607\n",
"9,Lou Williams,offense,4.9226681932\n",
"10,Derrick Williams,defense,4.86095648867\n",
"11,Stephen Curry,offense,4.73777762545\n",
"12,Chris Paul,offense,4.61000345048\n",
"13,Tyreke Evans,offense,4.45570027837\n",
"14,George Hill,offense,4.28741286147\n",
"15,Doug McDermott,defense,4.2837490453\n",
"16,Russell Westbrook,offense,4.18133520419\n",
"17,Luol Deng,offense,4.17993627011\n",
"18,Aaron Brooks,offense,4.17879605781\n",
"19,DeAndre Jordan,offense,4.06731780006\n",
"20,Bojan Bogdanovic,defense,4.05450939019\n",
"21,Chandler Parsons,offense,4.01059989101\n",
"22,LaMarcus Aldridge,offense,4.00737258859\n",
"23,Anthony Davis,offense,3.95555393395\n",
"24,Terrence Ross,defense,3.90218415739\n",
"25,Shane Larkin,defense,3.89699694219\n",
"26,Bradley Beal,offense,3.83689474279\n",
"27,Brandon Davies,defense,3.62886078508\n",
"28,Adreian Payne,defense,3.54566246749\n",
"29,Timofey Mozgov,offense,3.54090738769\n",
"30,Ryan Anderson,offense,3.53309450562\n",
"31,Isaiah Thomas,offense,3.52564981982\n",
"32,Enes Kanter,defense,3.4870778136\n",
"33,Brandon Bass,defense,3.46003866659\n",
"34,Charlie Villanueva,defense,3.43178880586\n",
"35,Zach LaVine,defense,3.41987419221\n",
"36,Shawne Williams,defense,3.40283306948\n",
"37,Robert Covington,offense,3.39056114831\n",
"38,Rudy Gay,offense,3.36092971709\n",
"39,Monta Ellis,offense,3.34442863832\n",
"40,Dwight Howard,offense,3.33523092337\n",
"41,Enes Kanter,offense,3.3227084968\n",
"42,Kris Humphries,defense,3.3145767193\n",
"43,Anthony Bennett,defense,3.31271064601\n",
"44,Omri Casspi,defense,3.29990051344\n",
"45,Patrick Patterson,offense,3.29771034913\n",
"46,Brandon Rush,defense,3.2805611772\n",
"47,Jason Smith,defense,3.27368544674\n",
"48,Tony Parker,defense,3.20128185469\n",
"49,Damian Lillard,offense,3.16195844316\n",
"50,Marc Gasol,offense,3.10291802902\n",
"51,Mike Dunleavy,offense,3.06604543451\n",
"52,Jabari Parker,defense,2.95381806908\n",
"53,Nikola Vucevic,defense,2.8683564908\n",
"54,Klay Thompson,offense,2.84547786494\n",
"55,James Jones,defense,2.80109023225\n",
"56,Zach Randolph,offense,2.79486471605\n",
"57,Ben Gordon,defense,2.77318133597\n",
"58,Danny Green,offense,2.76741478132\n",
"59,Dennis Schroder,defense,2.76334255362\n",
"60,Gerald Green,offense,2.75044066619\n",
"61,Russell Westbrook,defense,2.72885074469\n",
"62,Jakarr Sampson,defense,2.72290568284\n",
"63,Shabazz Muhammad,defense,2.68711382824\n",
"64,Andre Drummond,offense,2.67636743128\n",
"65,Rudy Gay,defense,2.64792356052\n",
"66,Archie Goodwin,defense,2.63011893199\n",
"67,Markel Brown,defense,2.61575716121\n",
"68,Andrea Bargnani,defense,2.60931472335\n",
"69,Joe Johnson,defense,2.59302409747\n",
"70,Matt Bonner,offense,2.59269966872\n",
"71,Danny Granger,defense,2.58889182169\n",
"72,Jordan Clarkson,defense,2.58754950358\n",
"73,J.J. Barea,offense,2.57925612381\n",
"74,Kobe Bryant,defense,2.56519840002\n",
"75,Ian Clark,defense,2.56247507645\n",
"76,Ersan Ilyasova,defense,2.55314396533\n",
"77,Luke Babbitt,defense,2.53999267471\n",
"78,Jrue Holiday,offense,2.52907879352\n",
"79,Jeff Withey,defense,2.5149048475\n",
"80,Marcus Morris,offense,2.49547853903\n",
"81,Marreese Speights,offense,2.47685019677\n",
"82,Eric Bledsoe,offense,2.46406603653\n",
"83,Kenneth Faried,offense,2.4456055713\n",
"84,Leandro Barbosa,defense,2.42227560242\n",
"85,Jimmy Butler,offense,2.39724665335\n",
"86,Kawhi Leonard,offense,2.39596708216\n",
"87,Kevin Love,offense,2.36930728092\n",
"88,Chuck Hayes,offense,2.36124748017\n",
"89,Kyle Lowry,offense,2.35801226331\n",
"90,Tiago Splitter,offense,2.3489939041\n",
"91,Greivis Vasquez,defense,2.26173358307\n",
"92,Kyrie Irving,offense,2.23823350297\n",
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]
}
],
"prompt_number": 16
},
{
"cell_type": "code",
"collapsed": false,
"input": [],
"language": "python",
"metadata": {},
"outputs": []
}
],
"metadata": {}
}
]
}
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