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Created May 24, 2015 19:34
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gist.json
{
"cells": [
{
"cell_type": "markdown",
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"slide_type": "slide"
}
},
"source": [
"#Rugby Analytics\n",
"* Peadar Coyle \n",
"<img src='pydatalogo-generic.png'>\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
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},
"source": [
"#Contents: Probabilistic Programming applied to Rugby\n",
"* I'll discuss what probabilistic programming is, why should you care and how to use PyMC from Python to implement these methods. \n",
"* I'll be applying these methods to studying the problem of 'rugby sports analytics' particularly how to model the winning team in the recent Six Nations in Rugby. \n",
"* I will discuss the framework and how I was able to quickly and easily produce an innovative and powerful model as a non-expert.\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
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},
"source": [
"##Who am I?\n",
"* I'm a Data Analytics Professional based in Luxembourg\n",
"* I currently work for Vodafone\n",
"* My intellectual background is in Physics and Mathematics\n",
"* I've made open source contributions to Pandas and Probabilistic Programming and Bayesian Methods for Hackers. \n",
"* All opinions are my own!\n",
"<p>\n",
"\n",
"<table style=\"border-collapse: collapse; border-top-color: rgb(255, 255, 255); border-right-color: rgb(255, 255, 255); border-bottom-color: rgb(255, 255, 255); border-left-color: rgb(255, 255, 255); border-top-width: 1px; border-right-width: 1px; border-bottom-width: 1px; border-left-width: 1px; \" border=\"0\" bordercolor=\"#888\" cellspacing=\"0\" align=\"left\">\n",
" <tr>\n",
" <td>\n",
"<a href=\"mailto: peadarcoyle@gmail.com\"><svg width=\"40px\" height=\"40px\" viewBox=\"0 0 60 60\" version=\"1.1\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\" xmlns:sketch=\"http://www.bohemiancoding.com/sketch/ns\">\n",
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"</svg></a> \n",
"</td> \n",
"<td>\n",
"<a href=\"mailto: peadarcoyle@gmail.com\" target=\"_blank\">peadarcoyle@gmail.com</a> \n",
"</td> </tr><tr> <td>\n",
" \n",
"<a href=\"http://github.com/springcoil\"><svg width=\"40px\" height=\"40px\" viewBox=\"0 0 60 60\" version=\"1.1\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\" xmlns:sketch=\"http://www.bohemiancoding.com/sketch/ns\">\n",
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"\n",
"</td><td>\n",
"<a href=\"http://github.com/springcoil\" target=\"_blank\">http://github.com/springcoil</a> \n",
"\n",
"</td> </tr><tr> <td>\n",
"\n",
"<a href=\"https://www.linkedin.com/in/peadarcoyle\"><svg width=\"40px\" height=\"40px\" viewBox=\"0 0 60 60\" version=\"1.1\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\" xmlns:sketch=\"http://www.bohemiancoding.com/sketch/ns\">\n",
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"</svg></a> \n",
"</td> <td>\n",
"<a href=\"https://www.linkedin.com/in/peadarcoyle\" target=\"_blank\">https://www.linkedin.com/in/peadarcoyle</a> \n",
"\n",
"</td> </tr><tr> <td>\n",
"\n",
"<a href=\"http://twitter.com/springcoil\"><svg width=\"40px\" height=\"40px\" viewBox=\"0 0 60 60\" version=\"1.1\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\" xmlns:sketch=\"http://www.bohemiancoding.com/sketch/ns\">\n",
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"</svg></a>\n",
"</td> <td>\n",
"<a href=\"http://twitter.com/springcoil\" target=\"_blank\">@springcoil</a> \n",
"\n",
"</td> </tr>\n",
"</table>"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"#All Sports Commentary!\n",
"<img src=\"http://imgs.xkcd.com/comics/sports.png\" align=\"center\">\n",
"* Attribution: Xkcd"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"# How can statistics help with sports?\n",
"* Well fundamentally a Rugby game is a predictible event.\n",
"* How do we generate a model to predict the outcome of a tournament?\n",
"* How do we quantify our uncertainty in our model?\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"#What influenced me on this?\n",
"<img src=\"http://blog.quantopian.com/wp-content/uploads/2014/12/GraphicalModel.jpg\">\n",
"Attribution: Quantopian blog"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"#What's wrong with statistics\n",
"* Models should not be built for mathematical convenience (e.g. normality assumption), but to most accurately model the data.\n",
"\n",
"* Pre-specified models, like frequentist statistics, make many assumptions that are all to easily violated.\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"#\"The purpose of computation is insight, not numbers.\" -- Richard Hamming"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"# What is Bayesian Statistics?\n",
"* At the core: formula to update our beliefs after having observed data (Bayes formula)\n",
"* Implies that we have a prior belief about the world.\n",
"* Updated beliefs after observing data is called posterior.\n",
"* Beliefs are represented using random variables."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"###So what problem could I apply Bayesian models to?\n",
"* Rugby Analysis!\n",
"<img src=\"rugbyball.jpg\", width=\"50%\" height=\"50%\"/>\n",
"Attribution: http://www.sportsballshop.co.uk"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"#Bayesian Rugby\n",
" I came across the following blog post on http://danielweitzenfeld.github.io/passtheroc/blog/2014/10/28/bayes-premier-league/ \n",
"\n",
"\n",
"\n",
"* Based on the work of [Baio and Blangiardo](http://www.statistica.it/gianluca/Research/BaioBlangiardo.pdf)\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"* In this talk, I'm going to reproduce the first model described in the paper using pymc.\n",
"* Since I am a rugby fan I decide to apply the results of the paper Bayesian Football to the Six Nations.\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"<img src=\"http://upload.wikimedia.org/wikipedia/de/thumb/0/0b/Zalando_logo.svg/1024px-Zalando_logo.svg.png\">"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"## What they did?\n",
"Deriving our new measuring model and verifying that it works took some effort! But it was all worth it, because now we have:\n",
"\n",
"Automatic weight estimations for each Zalando article, which saves workers time\n",
"A reliable way to know the accuracy of our estimations\n",
"And most importantly: our warehouse workers can now focus on getting your fashion to you as quickly as possible. That’s isn’t just saving money–that’s priceless.\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"#So why Bayesians?\n",
"* Probabilistic Programming is a new paradigm.\n",
"* Attributions: My friend Thomas Wiecki influenced a lot of my thinking on this.\n",
"* I'm going to compare Blackbox Machine Learning with scikit-learn"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"<img src='https://raw.githubusercontent.com/twiecki/pymc3_talk/master/blackbox.png'>\n",
"\n",
"* Source: <a href='https://speakerdeck.com/ogrisel/trends-in-machine-learning'>Olivier Grisel's talk on ML</a>\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"# Limitations of Machine learning\n",
"* A big limitation of Machine Learning is that most of the models are black boxes.\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"\n",
"<img src='https://raw.githubusercontent.com/twiecki/pymc3_talk/master/openbox.png'>\n",
"\n",
"Source: <a href='https://speakerdeck.com/ogrisel/trends-in-machine-learning'>Olivier Grisel's talk on ML</a>"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"# Probabilistic Programming - what's the big deal?\n",
"* We are able to use data and our prior beliefs to generate a model. \n",
"* Generating a model is extremely powerful\n",
"* We can tell a story, which appeals to our understanding of stories. \n"
]
},
{
"cell_type": "code",
"execution_count": 253,
"metadata": {
"collapsed": false,
"slideshow": {
"slide_type": "skip"
}
},
"outputs": [],
"source": [
"import os\n",
"import math\n",
"import warnings\n",
"import numpy as np\n",
"import pandas as pd\n",
"import matplotlib.pyplot as plt\n",
"import pymc # I know folks are switching to \"as pm\" but I'm just not there yet\n",
"%matplotlib inline\n",
"import seaborn as sns\n",
"from IPython.core.pylabtools import figsize\n",
"import seaborn as sns\n",
"figsize(12, 12)"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"# Six Nations Rugby\n",
"* Rugby is a physical sport popular worldwide.\n",
"* Six Nations consists of Italy, Ireland, Scotland, England, France and Wales\n",
"* Game consists of scoring tries (similar to touch downs) or kicking the goal.\n",
"* Average player is something like 100kg and 1.82m tall.\n",
"* Paul O'Connell the Irish captain is Height: 6' 6\" (1.98 m) Weight: 243 lbs (110 kg)\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"#They compete for this!\n",
"* Significant this year because the World Cup occurs in 2015.\n",
"<img src=\"http://www.hostelrome.com/wp-content/uploads/2015/01/Rugby_Sei-Nazioni-Uomini.jpg\">\n",
"* Photo: Hostelrome"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"## Motivation\n",
"\n",
"\n",
"* Your estimate of the strength of a team depends on your estimates of the other strengths\n",
"* Ireland are a stronger team than Italy for example - but by how much?\n",
"* Source for Results 2014 are Wikipedia. \n",
"* I handcrafted these results\n",
"* Small data"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"<img src='smalldata.jpg'>"
]
},
{
"cell_type": "code",
"execution_count": 220,
"metadata": {
"collapsed": true,
"slideshow": {
"slide_type": "skip"
}
},
"outputs": [],
"source": [
"DATA_DIR = os.path.join(os.getcwd(), 'data/')"
]
},
{
"cell_type": "code",
"execution_count": 221,
"metadata": {
"collapsed": false,
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [
{
"data": {
"text/html": [
"<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>home_team</th>\n",
" <th>away_team</th>\n",
" <th>home_score</th>\n",
" <th>away_score</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
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" <tr>\n",
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" <td>11</td>\n",
" <td>52</td>\n",
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" <tr>\n",
" <th>13</th>\n",
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" <td>51</td>\n",
" <td>3</td>\n",
" </tr>\n",
" <tr>\n",
" <th>14</th>\n",
" <td>France</td>\n",
" <td>Ireland</td>\n",
" <td>20</td>\n",
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"text/plain": [
" home_team away_team home_score away_score\n",
"10 Scotland France 17 19\n",
"11 England Wales 29 18\n",
"12 Italy England 11 52\n",
"13 Wales Scotland 51 3\n",
"14 France Ireland 20 22"
]
},
"execution_count": 221,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"#The results_2014 is a handcrafted results table from Wikipedia\n",
"data_file = DATA_DIR + 'results_2014.csv'\n",
"df = pd.read_csv(data_file, sep=',')\n",
"df.tail()\n",
"\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 222,
"metadata": {
"collapsed": false,
"slideshow": {
"slide_type": "skip"
}
},
"outputs": [
{
"data": {
"text/html": [
"<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>team</th>\n",
" <th>i</th>\n",
" </tr>\n",
" </thead>\n",
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"</table>\n",
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"text/plain": [
" team i\n",
"0 Wales 0\n",
"1 France 1\n",
"2 Ireland 2\n",
"3 Scotland 3\n",
"4 Italy 4"
]
},
"execution_count": 222,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"teams = df.home_team.unique()\n",
"teams = pd.DataFrame(teams, columns=['team'])\n",
"teams['i'] = teams.index\n",
"teams.head()"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"* Now we need to do some merging and munging"
]
},
{
"cell_type": "code",
"execution_count": 223,
"metadata": {
"collapsed": false,
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [
{
"data": {
"text/html": [
"<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>home_team</th>\n",
" <th>away_team</th>\n",
" <th>home_score</th>\n",
" <th>away_score</th>\n",
" <th>i_home</th>\n",
" <th>i_away</th>\n",
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"text/plain": [
" home_team away_team home_score away_score i_home i_away\n",
"0 Wales Italy 23 15 0 4\n",
"1 France England 26 24 1 5\n",
"2 Ireland Scotland 28 6 2 3\n",
"3 Ireland Wales 26 3 2 0\n",
"4 Scotland England 0 20 3 5"
]
},
"execution_count": 223,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"df = pd.merge(df, teams, left_on='home_team', right_on='team', how='left')\n",
"df = df.rename(columns = {'i': 'i_home'}).drop('team', 1)\n",
"df = pd.merge(df, teams, left_on='away_team', right_on='team', how='left')\n",
"df = df.rename(columns = {'i': 'i_away'}).drop('team', 1)\n",
"df.head()"
]
},
{
"cell_type": "code",
"execution_count": 224,
"metadata": {
"collapsed": false,
"slideshow": {
"slide_type": "skip"
}
},
"outputs": [],
"source": [
"observed_home_goals = df.home_score.values\n",
"observed_away_goals = df.away_score.values\n",
"home_team = df.i_home.values\n",
"away_team = df.i_away.values\n",
"num_teams = len(df.i_home.drop_duplicates())\n",
"num_games = len(home_team)\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"Now we need to prepare the model for PyMC."
]
},
{
"cell_type": "code",
"execution_count": 225,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"g = df.groupby('i_away')\n",
"att_starting_points = np.log(g.away_score.mean())\n",
"g = df.groupby('i_home')\n",
"def_starting_points = -np.log(g.away_score.mean())"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"# What do we want to infer?\n",
"* We want to infer the latent paremeters (every team's strength) that are generating the data we observe (the scorelines). \n",
"* Moreover, we know that the scorelines are a noisy measurement of team strength, so ideally, we want a model that makes it easy to quantify our uncertainty about the underlying strengths.\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"# While my MCMC gently samples\n",
"* Often we don't know what the Bayesian Model is explicitly, so we have to 'estimate' the Bayesian Model'\n",
"* If we can't solve something, approximate it.\n",
"* Markov-Chain Monte Carlo (MCMC) instead draws samples from the posterior.\n",
"* Fortunately, this algorithm can be applied to almost any model.\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"# What do we want?\n",
"* We want to quantify our uncertainty\n",
"* We want to also use this to generate a model\n",
"* We want the answers as distributions *not* point estimates"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"## What assumptions do we know for our 'generative story'?\n",
"* We know that the Six Nations in Rugby only has 6 teams.\n",
"* We have data from last year!\n",
"* We also know that in sports scoring is modelled as a Poisson distribution\n",
"<img src=\"http://upload.wikimedia.org/wikipedia/commons/1/16/Poisson_pmf.svg\">\n",
"* Attribution: *Wikipedia*"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"#The model.\n",
"<p>The league is made up by a total of T= 6 teams, playing each other once \n",
"in a season. We indicate the number of points scored by the home and the away team in the g-th game of the season (15 games) as $y_{g1}$ and $y_{g2}$ respectively. </p>\n",
"<p>The vector of observed counts $\\mathbb{y} = (y_{g1}, y_{g2})$ is modelled as independent Poisson:\n",
"$y_{gi}| \\theta_{gj} \\tilde\\;\\; Poisson(\\theta_{gj})$\n",
"where the theta parameters represent the scoring intensity in the g-th game for the team playing at home (j=1) and away (j=2), respectively.</p>\n",
"\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"<p>We model these parameters according to a formulation that has been used widely in the statistical literature, assuming a log-linear random effect model:\n",
"$$log \\theta_{g1} = home + att_{h(g)} + def_{a(g)} $$\n",
"$$log \\theta_{g2} = att_{a(g)} + def_{h(g)}$$\n",
"the parameter home represents the advantage for the team hosting the game\n",
"and we assume that this effect is constant for all the teams and\n",
"throughout the season. \n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"* Key assumption home effect is an advantage in Sports\n",
"* We know these things empirically from our 'domain specific' knowledge\n",
"* Bayesian Models allow you to incorporate *beliefs* or *knowledge* into your model!\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "skip"
}
},
"source": [
"In addition, the scoring intensity is \n",
"determined jointly by the attack\n",
"and defense ability of the two teams involved, represented by the parameters att and def, respectively.\n",
"In line with the Bayesian approach, we have to specify some suitable prior distributions for all the \n",
"random parameters in our model. The variable $home$ \n",
"is modelled as a fixed effect, assuming a standard \n",
"flat prior distribution. We use the notation of describing the Normal distribution in terms of mean \n",
"and the precision. \n",
"$home \\tilde\\; Normal(0,0.0001)$</p>\n",
"<p>Conversely, for each t = 1, ..., T, the team-specific effects are modelled as exchangeable from a common distribution:\n",
"$att_t \\tilde\\; Normal(\\mu_{att}, \\tau_{att})$\n",
"and $def_t \\tilde\\; Normal(\\mu_{def}, \\tau_{def})$</p>\n",
"<p>Note that they're breaking out team strength into attacking and defending strength. \n",
"A negative defense parameter will sap the mojo from the opposing team&#39;s attacking parameter.</p>\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "skip"
}
},
"source": [
"<p>I made two tweaks to the model. It didn't make sense to me to have a $\\mu_{att}$ when we&#39;re enforcing the sum-to-zero constraint by subtracting the mean anyway. So I eliminated $\\mu_{att}$ and $\\mu_{def}$</p>\n",
"<p>Also because of the sum-to-zero constraint, \n",
"it seemed to me that we needed an intercept term in the log-linear model, capturing the average goals scored per game by the away team.\n",
"This we model with the following hyperprior.\n",
"$$intercept \\tilde\\; Normal(0, 0.001)$$</p>\n",
"\n",
"* The hyper-priors on the attack and defense parameters are also flat\n",
"* $\\mu_att \\tilde\\; Normal(0,0.001)$\n",
"* $\\mu_def \\tilde\\; Normal(0,0.001)$\n",
"* $\\tau_att \\tilde\\; \\Gamma(0.1,0.1)$\n",
"* $\\tau_def \\tilde\\; \\Gamma(0.1,0.1)$"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"###Digression: Why the flat priors were picked (our hyperpriors are flat)\n",
"* There are lots of different ways of picking priors - see the literature\n",
"* I learned from this that it didn't make any difference to the results picking a uniform prior versus a flat prior\n",
"\n",
"Often it simply doesn't matter much what prior you use. \n",
"\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"\n",
"###Definition: A prior distribution is non-informative if the prior is “flat” relative to the likelihood function.\n",
"\n",
"\n",
"* We are trying to have a reasonable model and let inference happen from the data set.\n",
"* ##Key takeaway - Often in Bayesian modelling it doesn't matter what your priors are. Let the data generate the story :) "
]
},
{
"cell_type": "code",
"execution_count": 226,
"metadata": {
"collapsed": false,
"slideshow": {
"slide_type": "slide"
}
},
"outputs": [],
"source": [
"#hyperpriors\n",
"home = pymc.Normal('home', 0, .0001, value=0)\n",
"tau_att = pymc.Gamma('tau_att', .1, .1, value=10)\n",
"tau_def = pymc.Gamma('tau_def', .1, .1, value=10)\n",
"intercept = pymc.Normal('intercept', 0, .0001, value=0)\n",
"#team-specific parameters\n",
"atts_star = pymc.Normal(\"atts_star\", \n",
" mu=0, \n",
" tau=tau_att, \n",
" size=num_teams, \n",
" value=att_starting_points.values)\n",
"defs_star = pymc.Normal(\"defs_star\", \n",
" mu=0, \n",
" tau=tau_def, \n",
" size=num_teams, \n",
" value=def_starting_points.values) \n",
"\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 227,
"metadata": {
"collapsed": true,
"slideshow": {
"slide_type": "skip"
}
},
"outputs": [],
"source": [
"# trick to code the sum to zero constraint\n",
"@pymc.deterministic\n",
"def atts(atts_star=atts_star):\n",
" atts = atts_star.copy()\n",
" atts = atts - np.mean(atts_star)\n",
" return atts\n",
"\n",
"@pymc.deterministic\n",
"def defs(defs_star=defs_star):\n",
" defs = defs_star.copy()\n",
" defs = defs - np.mean(defs_star)\n",
" return defs\n",
"\n",
"@pymc.deterministic\n",
"def home_theta(home_team=home_team, \n",
" away_team=away_team, \n",
" home=home, \n",
" atts=atts, \n",
" defs=defs, \n",
" intercept=intercept): \n",
" return np.exp(intercept + \n",
" home + \n",
" atts[home_team] + \n",
" defs[away_team])\n",
" \n",
"@pymc.deterministic\n",
"def away_theta(home_team=home_team, \n",
" away_team=away_team, \n",
" home=home, \n",
" atts=atts, \n",
" defs=defs, \n",
" intercept=intercept): \n",
" return np.exp(intercept + \n",
" atts[away_team] + \n",
" defs[home_team]) \n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"# Let us run the model!\n",
"* We specify the priors as Gamma distributions\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 228,
"metadata": {
"collapsed": false,
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" [-----------------100%-----------------] 200000 of 200000 complete in 73.6 sec"
]
}
],
"source": [
"home_points = pymc.Poisson('home_points', \n",
" mu=home_theta, \n",
" value=observed_home_goals, \n",
" observed=True)\n",
"away_points = pymc.Poisson('away_points', \n",
" mu=away_theta, \n",
" value=observed_away_goals, \n",
" observed=True)\n",
"\n",
"mcmc = pymc.MCMC([home, intercept, tau_att, tau_def, \n",
" home_theta, away_theta, \n",
" atts_star, defs_star, atts, defs, \n",
" home_points, away_points])\n",
"map_ = pymc.MAP( mcmc )\n",
"map_.fit()\n",
"\n",
"mcmc.sample(200000, 40000, 20)"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"#Diagnostics\n",
"Let's see if/how the model converged. \n",
"The home parameter looks good, and indicates that home field advantage amounts to goals per game at the intercept.\n",
"We can see that it converges just like the model for the Premier League in the other tutorial.\n",
"I wonder and this is left as a question if all field sports have models of this form that converge."
]
},
{
"cell_type": "code",
"execution_count": 229,
"metadata": {
"collapsed": false,
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Plotting home\n"
]
},
{
"data": {
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KREQ0zlWCaJyr9FPOlYiIKOcqQZRzlX5quRIRERFpIAVXIiIiIg2k4EpERJRz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\nUqTkSkRERCRFSq5EREREUvT/GG3i0xvhMyQAAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1138377f0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"pymc.Matplot.plot(home)"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"\n",
"* We can see in this analysis that home advantage gives about 0.55 points advantage.\n",
"* We also see not too much auto-correlation, so this looks quite good plot wise.\n",
"* We see here how *probabilistic programming* allows us to quantify our uncertainty about certain parameters.\n"
]
},
{
"cell_type": "code",
"execution_count": 230,
"metadata": {
"collapsed": false,
"slideshow": {
"slide_type": "slide"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Plotting atts_0\n",
"Plotting atts_1\n",
"Plotting atts_2\n",
"Plotting atts_3\n",
"Plotting atts_4\n",
"Plotting atts_5\n"
]
},
{
"data": {
"image/png": 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ZfDcBhwI9VHVVFudH7ZP0Y3WT8Ln5l7+4hwrg3DNPvgK7ZtLZmJRMLVBJZ+F5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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x114237860>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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MBlRb3L+8OBtEpERV406gE4EPcCNQ/6zhv0DDMIxaISIR4HpgG1y4jKxR1b+n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\nALXl3Lt8lwAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1111d3a58>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"pymc.Matplot.plot(atts)\n",
"# We can plot all of the parameters, just to see. "
]
},
{
"cell_type": "code",
"execution_count": 231,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"observed_season = DATA_DIR + 'table_2014.csv'\n",
"df_observed = pd.read_csv(observed_season)\n",
"df_observed.loc[df_observed.QR.isnull(), 'QR'] = ''\n",
"df_avg = pd.DataFrame({'avg_att': atts.stats()['mean'],\n",
" 'avg_def': defs.stats()['mean']}, \n",
" index=teams.team.values)\n"
]
},
{
"cell_type": "code",
"execution_count": 232,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"df_new = df_avg.merge(df_observed, left_index=True, right_on='team', how='left')\n",
"\n",
"#Bring in the new csv file\n",
"df_results = pd.read_csv('df_avg_data_edited.csv', sep=';')"
]
},
{
"cell_type": "code",
"execution_count": 233,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
"<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>avg_att</th>\n",
" <th>avg_def</th>\n",
" <th>points</th>\n",
" <th>team</th>\n",
" <th>position</th>\n",
" <th>QR</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>0.096729</td>\n",
" <td>0.150764</td>\n",
" <td>6</td>\n",
" <td>France</td>\n",
" <td>4</td>\n",
" <td>NaN</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td>0.179363</td>\n",
" <td>-0.560665</td>\n",
" <td>8</td>\n",
" <td>Ireland</td>\n",
" <td>1</td>\n",
" <td>winners</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3</th>\n",
" <td>-0.549843</td>\n",
" <td>0.289372</td>\n",
" <td>2</td>\n",
" <td>Scotland</td>\n",
" <td>5</td>\n",
" <td>NaN</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4</th>\n",
" <td>-0.251418</td>\n",
" <td>0.515101</td>\n",
" <td>0</td>\n",
" <td>Italy</td>\n",
" <td>6</td>\n",
" <td>wooden_spoon</td>\n",
" </tr>\n",
" <tr>\n",
" <th>5</th>\n",
" <td>0.399824</td>\n",
" <td>-0.255811</td>\n",
" <td>8</td>\n",
" <td>England</td>\n",
" <td>2</td>\n",
" <td>triple_crown</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" avg_att avg_def points team position QR\n",
"1 0.096729 0.150764 6 France 4 NaN\n",
"2 0.179363 -0.560665 8 Ireland 1 winners\n",
"3 -0.549843 0.289372 2 Scotland 5 NaN\n",
"4 -0.251418 0.515101 0 Italy 6 wooden_spoon\n",
"5 0.399824 -0.255811 8 England 2 triple_crown"
]
},
"execution_count": 233,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"df_results.tail()"
]
},
{
"cell_type": "code",
"execution_count": 254,
"metadata": {
"collapsed": false,
"slideshow": {
"slide_type": "skip"
}
},
"outputs": [],
"source": [
"\n",
"def fig3():\n",
" fig, ax = plt.subplots(figsize=(12,12))\n",
" for outcome in ['winners', 'wooden_spoon', 'triple_crown', 'NaN']:\n",
" ax.plot(df_results.avg_att[df_results.QR == outcome], \n",
" df_results.avg_def[df_results.QR == outcome], 'o', label=outcome)\n",
" for label, x, y in zip(df_results.team.values, df_results.avg_att.values, df_results.avg_def.values):\n",
" ax.annotate(label, xy=(x,y), xytext = (-5,5), textcoords = 'offset points')\n",
" ax.set_title('Attack vs Defense avg effect: 13-14 Six Nations')\n",
" ax.set_xlabel('Avg attack effect')\n",
" ax.set_ylabel('Avg defense effect')\n",
" ax.legend()"
]
},
{
"cell_type": "code",
"execution_count": 255,
"metadata": {
"collapsed": false,
"slideshow": {
"slide_type": "slide"
}
},
"outputs": [
{
"data": {
"image/png": 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lw44kSZKkKhl2JEmSJFXJsCNJkiSpSoYdSZIkSVUy7EiSJEmqkmFHkiRJUpUM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\ndgAAgCH9fzWnMNzGnbo5AAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1143c65f8>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig3()"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"#Simulating a season\n",
"We would like to now simulate a season. Just to see what happens. "
]
},
{
"cell_type": "code",
"execution_count": 235,
"metadata": {
"collapsed": true,
"slideshow": {
"slide_type": "skip"
}
},
"outputs": [],
"source": [
"def simulate_season():\n",
" \"\"\"\n",
" Simulate a season once, using one random draw from the mcmc chain. \n",
" \"\"\"\n",
" num_samples = atts.trace().shape[0]\n",
" draw = np.random.randint(0, num_samples)\n",
" atts_draw = pd.DataFrame({'att': atts.trace()[draw, :],})\n",
" defs_draw = pd.DataFrame({'def': defs.trace()[draw, :],})\n",
" home_draw = home.trace()[draw]\n",
" intercept_draw = intercept.trace()[draw]\n",
" season = df.copy()\n",
" season = pd.merge(season, atts_draw, left_on='i_home', right_index=True)\n",
" season = pd.merge(season, defs_draw, left_on='i_home', right_index=True)\n",
" season = season.rename(columns = {'att': 'att_home', 'def': 'def_home'})\n",
" season = pd.merge(season, atts_draw, left_on='i_away', right_index=True)\n",
" season = pd.merge(season, defs_draw, left_on='i_away', right_index=True)\n",
" season = season.rename(columns = {'att': 'att_away', 'def': 'def_away'})\n",
" season['home'] = home_draw\n",
" season['intercept'] = intercept_draw\n",
" season['home_theta'] = season.apply(lambda x: math.exp(x['intercept'] + \n",
" x['home'] + \n",
" x['att_home'] + \n",
" x['def_away']), axis=1)\n",
" season['away_theta'] = season.apply(lambda x: math.exp(x['intercept'] + \n",
" x['att_away'] + \n",
" x['def_home']), axis=1)\n",
" season['home_goals'] = season.apply(lambda x: np.random.poisson(x['home_theta']), axis=1)\n",
" season['away_goals'] = season.apply(lambda x: np.random.poisson(x['away_theta']), axis=1)\n",
" season['home_outcome'] = season.apply(lambda x: 'win' if x['home_goals'] > x['away_goals'] else \n",
" 'loss' if x['home_goals'] < x['away_goals'] else 'draw', axis=1)\n",
" season['away_outcome'] = season.apply(lambda x: 'win' if x['home_goals'] < x['away_goals'] else \n",
" 'loss' if x['home_goals'] > x['away_goals'] else 'draw', axis=1)\n",
" season = season.join(pd.get_dummies(season.home_outcome, prefix='home'))\n",
" season = season.join(pd.get_dummies(season.away_outcome, prefix='away'))\n",
" return season\n",
"\n",
"\n",
"def create_season_table(season):\n",
" \"\"\"\n",
" Using a season dataframe output by simulate_season(), create a summary dataframe with wins, losses, goals for, etc.\n",
" \n",
" \"\"\"\n",
" g = season.groupby('i_home') \n",
" home = pd.DataFrame({'home_goals': g.home_goals.sum(),\n",
" 'home_goals_against': g.away_goals.sum(),\n",
" 'home_wins': g.home_win.sum(),\n",
" 'home_losses': g.home_loss.sum()\n",
" })\n",
" g = season.groupby('i_away') \n",
" away = pd.DataFrame({'away_goals': g.away_goals.sum(),\n",
" 'away_goals_against': g.home_goals.sum(),\n",
" 'away_wins': g.away_win.sum(),\n",
" 'away_losses': g.away_loss.sum()\n",
" })\n",
" df = home.join(away)\n",
" df['wins'] = df.home_wins + df.away_wins\n",
" df['losses'] = df.home_losses + df.away_losses\n",
" df['points'] = df.wins * 2\n",
" df['gf'] = df.home_goals + df.away_goals\n",
" df['ga'] = df.home_goals_against + df.away_goals_against\n",
" df['gd'] = df.gf - df.ga\n",
" df = pd.merge(teams, df, left_on='i', right_index=True)\n",
" df = df.sort_index(by='points', ascending=False)\n",
" df = df.reset_index()\n",
" df['position'] = df.index + 1\n",
" df['champion'] = (df.position == 1).astype(int)\n",
" df['relegated'] = (df.position > 5).astype(int)\n",
" return df \n",
" \n",
"def simulate_seasons(n=100):\n",
" dfs = []\n",
" for i in range(n):\n",
" s = simulate_season()\n",
" t = create_season_table(s)\n",
" t['iteration'] = i\n",
" dfs.append(t)\n",
" return pd.concat(dfs, ignore_index=True)"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"# Simulation\n",
"* We are going to simulate 1000 seasons\n"
]
},
{
"cell_type": "code",
"execution_count": 236,
"metadata": {
"collapsed": false,
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [],
"source": [
"simuls = simulate_seasons(1000)"
]
},
{
"cell_type": "code",
"execution_count": 237,
"metadata": {
"collapsed": false,
"slideshow": {
"slide_type": "skip"
}
},
"outputs": [],
"source": [
"def fig1():\n",
" ax = simuls.points[simuls.team == 'Ireland'].hist()\n",
" median = simuls.points[simuls.team == 'Ireland'].median()\n",
" ax.set_title('Ireland: 2015 points, 1000 simulations')\n",
" ax.plot([median, median], ax.get_ylim())\n",
" plt.annotate('Median: %s' % median, xy=(median + 1, ax.get_ylim()[1]-10))"
]
},
{
"cell_type": "code",
"execution_count": 238,
"metadata": {
"collapsed": false,
"slideshow": {
"slide_type": "slide"
}
},
"outputs": [
{
"data": {
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m4mb+ZcCBwF7A0sxclZkrgduA3TZSzZIkbfKG6uLeFtgReBnl6PnrlKPmPvcA04CpwN0D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\nAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x109a0bfd0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig1()"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"* So what have we learned so far, we've got 1000 simulations of Ireland and their median points in the table is 8.\n",
"* In Rugby you get 2 points per win, and there are 5 games per year. So this model predicted that Ireland would win most of the time 4 games.\n"
]
},
{
"cell_type": "code",
"execution_count": 239,
"metadata": {
"collapsed": false,
"slideshow": {
"slide_type": "skip"
}
},
"outputs": [],
"source": [
"def fig2():\n",
" ax = simuls.gf[simuls.team == 'Ireland'].hist(figsize=(7,5))\n",
" median = simuls.gf[simuls.team == 'Ireland'].median()\n",
" ax.set_title('Ireland: 2015 scores for, 1000 simulations')\n",
" ax.plot([median, median], ax.get_ylim())\n",
" plt.annotate('Median: %s' % median, xy=(median + 1, ax.get_ylim()[1]-10))"
]
},
{
"cell_type": "code",
"execution_count": 240,
"metadata": {
"collapsed": false,
"slideshow": {
"slide_type": "slide"
}
},
"outputs": [
{
"data": {
"image/png": 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"text/plain": [
"<matplotlib.figure.Figure at 0x1143b3048>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig2()"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"#What happened in reality?\n",
"* Well Ireland actually scored 119 points, so the model over predicted this!\n",
"* We call this 'shrinkage' in the literature. \n",
"* All models are wrong, but some are useful"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"# What are the predictions of the model?\n",
"* So let us look at the winning team on average.\n",
"* We do a simulation and we'll assign probability of 'winning' to the team\n",
"* We used the MCMC to do this.\n"
]
},
{
"cell_type": "code",
"execution_count": 241,
"metadata": {
"collapsed": true,
"slideshow": {
"slide_type": "skip"
}
},
"outputs": [],
"source": [
"g = simuls.groupby('team')\n",
"df_champs = pd.DataFrame({'percent_champs': g.champion.mean()})\n",
"df_champs = df_champs.sort_index(by='percent_champs')\n",
"df_champs = df_champs[df_champs.percent_champs > .05]\n",
"df_champs = df_champs.reset_index()"
]
},
{
"cell_type": "code",
"execution_count": 242,
"metadata": {
"collapsed": false,
"slideshow": {
"slide_type": "slide"
}
},
"outputs": [
{
"data": {
"image/png": 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"text/plain": [
"<matplotlib.figure.Figure at 0x11081dfd0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"\n",
"fig, ax = plt.subplots(figsize=(8,6))\n",
"ax.barh(df_champs.index.values, df_champs.percent_champs.values)\n",
"\n",
"for i, row in df_champs.iterrows():\n",
" label = \"{0:.1f}%\".format(100 * row['percent_champs'])\n",
" ax.annotate(label, xy=(row['percent_champs'], i), xytext = (3, 10), textcoords = 'offset points')\n",
"ax.set_ylabel('Team')\n",
"ax.set_title('% of Simulated Seasons In Which Team Finished Winners')\n",
"_= ax.set_yticks(df_champs.index + .5)\n",
"_= ax.set_yticklabels(df_champs['team'].values)"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"Unfortunately it seems that in most of the Universes England come top of the Six Nations. And as an Irish man this is firm proof that I put Mathematical rigour before patriotism :)\n",
"This is a reasonable result, and I hope it proved a nice example of Bayesian models in Rugby Analytics."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"# What actually happened\n",
"We need to investigate like 'scientists' what actually happened.\n"
]
},
{
"cell_type": "code",
"execution_count": 243,
"metadata": {
"collapsed": false,
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [
{
"data": {
"text/html": [
"<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>Rank</th>\n",
" <th>Team</th>\n",
" <th>Games</th>\n",
" <th>Wins</th>\n",
" <th>Draws</th>\n",
" <th>Losses</th>\n",
" <th>Points_For</th>\n",
" <th>Points_Against</th>\n",
" <th>Points</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td>1</td>\n",
" <td>Ireland</td>\n",
" <td>5</td>\n",
" <td>4</td>\n",
" <td>0</td>\n",
" <td>1</td>\n",
" <td>119</td>\n",
" <td>56</td>\n",
" <td>8</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>2</td>\n",
" <td>England</td>\n",
" <td>5</td>\n",
" <td>4</td>\n",
" <td>0</td>\n",
" <td>1</td>\n",
" <td>157</td>\n",
" <td>100</td>\n",
" <td>8</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td>3</td>\n",
" <td>Wales</td>\n",
" <td>5</td>\n",
" <td>4</td>\n",
" <td>0</td>\n",
" <td>1</td>\n",
" <td>146</td>\n",
" <td>93</td>\n",
" <td>8</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3</th>\n",
" <td>4</td>\n",
" <td>France</td>\n",
" <td>5</td>\n",
" <td>2</td>\n",
" <td>0</td>\n",
" <td>3</td>\n",
" <td>103</td>\n",
" <td>101</td>\n",
" <td>4</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4</th>\n",
" <td>5</td>\n",
" <td>Italy</td>\n",
" <td>5</td>\n",
" <td>1</td>\n",
" <td>0</td>\n",
" <td>4</td>\n",
" <td>62</td>\n",
" <td>182</td>\n",
" <td>2</td>\n",
" </tr>\n",
" <tr>\n",
" <th>5</th>\n",
" <td>6</td>\n",
" <td>Scotland</td>\n",
" <td>5</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>5</td>\n",
" <td>73</td>\n",
" <td>128</td>\n",
" <td>0</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" Rank Team Games Wins Draws Losses Points_For Points_Against \\\n",
"0 1 Ireland 5 4 0 1 119 56 \n",
"1 2 England 5 4 0 1 157 100 \n",
"2 3 Wales 5 4 0 1 146 93 \n",
"3 4 France 5 2 0 3 103 101 \n",
"4 5 Italy 5 1 0 4 62 182 \n",
"5 6 Scotland 5 0 0 5 73 128 \n",
"\n",
" Points \n",
"0 8 \n",
"1 8 \n",
"2 8 \n",
"3 4 \n",
"4 2 \n",
"5 0 "
]
},
"execution_count": 243,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"pd.read_csv('data/results_2015.csv', sep='\\t', header=0, \n",
" names =['Rank','Team','Games','Wins','Draws',\n",
" 'Losses','Points_For','Points_Against','Points'])"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"##Ireland won the Six Nations!\n",
"* The model incorrectly predicted that England would come out on top.\n",
"* Ireland actually won by points difference of 6 points. \n",
"* It really came down to the wire!"
]
},
{
"cell_type": "code",
"execution_count": 244,
"metadata": {
"collapsed": false,
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [
{
"data": {
"image/jpeg": 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QelplqCwzliDCFuA7S4vrqPlMRJzjK10/lCWkHHL011mnozxAJkbrmez+drfi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\n",
"text/plain": [
"<IPython.core.display.Image object>"
]
},
"execution_count": 244,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"from IPython.display import Image\n",
"Image(filename='onedoesnotsimply.jpg') "
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"#Conclusion\n",
"* 'All models are wrong, some are useful'\n",
"* Model correctly predicts that Ireland would win 4 games\n",
"* Model incorrectly predicted that England would come out on top\n",
"* In reality it was very close\n",
"* Recommendation: Don't use this model to bet on the Six Nations next years"
]
},
{
"cell_type": "markdown",
"metadata": {
"collapsed": true,
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"* [Thomas Wiecki Blog on all things Bayesian](https://twiecki.github.io)\n",
"* Twitter: [@springcoil](https://twitter.com/springcoil)\n",
"* [Probilistic Programming for Hackers](http://camdavidsonpilon.github.io/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers/) -- IPython Notebook book on Bayesian stats using PyMC2\n",
"\n",
"* [Doing Bayesian Data Analysis](http://www.indiana.edu/~kruschke/DoingBayesianDataAnalysis/) -- Great book by Kruschke.\n",
"* [Get PyMC3 alpha](https://github.com/pymc-devs/pymc/tree/pymc3)\n",
"* [Zalando Example](http://dataconomy.com/how-zalando-used-bayesian-statistics-to-save-loads-of-money/)"
]
},
{
"cell_type": "code",
"execution_count": 245,
"metadata": {
"collapsed": false,
"slideshow": {
"slide_type": "slide"
}
},
"outputs": [
{
"data": {
"image/jpeg": 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YE96VdknkU8oVm4rHL5qQ+hxIL+IyOUv/APygx8Gf9mLV/wDylq44Gde/TMKrx8PcR4sq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\nHa3IJ9sG6WojKhWXZ1lLZZCFdct9x0urcW6tQAKlKUTrpCU//9k=\n",
"text/plain": [
"<IPython.core.display.Image object>"
]
},
"execution_count": 245,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"from IPython.display import Image\n",
"Image(filename='the-most-interesting-man-in-the-world-meme-generator-i-don-t-give-many-talks-but-when-i-do-i-do-q-a-e38222 copy.jpg') "
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"TODO: Include some pedagogical points about Bayesian models. How do you pick your prior"
]
}
],
"metadata": {
"celltoolbar": "Slideshow",
"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
}
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