world_cup02.ipynb

{
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The World Cup Problem: Germany v. Argentina\n",
    "-------------------------------------------\n",
    "\n",
    "Copyright 2016 Allen Downey\n",
    "\n",
    "MIT License: https://opensource.org/licenses/MIT\n",
    "\n",
    "This notebook contains a solution to the following problem:\n",
    "\n",
    "> In the final match of the 2014 FIFA World Cup, Germany defeated Argentina 1-0.  How much evidence \n",
    "> does this victory provide that Germany had the better team?  What is the probability that Germany\n",
    "> would win a rematch?\n",
    "\n",
    "Scoring in games like soccer and hockey can be modeled by a Poisson process, which assumes that each team, against a given opponent, will score goals at some goal-scoring rate, $\\lambda$, and that this rate does not vary; in other words, the probability of scoring a goal is about the same at any point during the game.\n",
    "\n",
    "Based on this modeling decision, we can answer the questions by\n",
    "\n",
    "1. Defining a prior distribution for each team's goal-scoring rate against the other,\n",
    "2. Updating the prior based on the outcome of the game,\n",
    "3. Using the posterior distributions to compute the probability that Germany's goal-scoring rate is higher.\n",
    "4. Generating a predictive distribution for the number of goals each team would score in a rematch.\n",
    "\n",
    "My solution uses the ThinkBayes2 framework, which is described in [Think Bayes](http://thinkbayes.com), and summarized in [this notebook](http://nbviewer.ipython.org/github/AllenDowney/ThinkBayes2/blob/master/code/framework.ipynb).\n",
    "\n",
    "I'll start with Step 2.\n",
    "\n",
    "### Step 2: Updating\n",
    "\n",
    "If goal-scoring is a Poisson process, the distribution of goals per game is Poisson with parameter $\\lambda$.  To compute the distribution of $\\lambda$ we can define a new class that inherits from `thinkbayes2.Suite` and provides an appropriate `Likelihood` function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# first a little house-keeping\n",
    "from __future__ import print_function, division\n",
    "\n",
    "% matplotlib inline\n",
    "\n",
    "import numpy as np\n",
    "import thinkplot\n",
    "import thinkbayes2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "class Soccer2(thinkbayes2.Suite):\n",
    "    \"\"\"Represents hypotheses about goal-scoring rates.\"\"\"\n",
    "\n",
    "    def Likelihood(self, data, hypo):\n",
    "        \"\"\"Computes the likelihood of the data under the hypothesis.\n",
    "\n",
    "        hypo: goal rate in goals per game\n",
    "        data: interarrival time in minutes\n",
    "        \"\"\"\n",
    "        # FILL THIS IN!\n",
    "        return 1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`Likelihood` computes the likelihood of `data` given `hypo`, where `data` is an observed number of goals, and `hypo` is a hypothetical goal-scoring rate in goals per game.  We can compute the likelihood of the data by evaluating the Poisson probability mass function (PMF).\n",
    "\n",
    "Now we can get back to Step 1.\n",
    "\n",
    "### Step 1: Constructing the prior\n",
    "\n",
    "Before the game starts, what should we believe about each team's goal scoring rate against each other?  We could use previous tournament results to construct the priors, but to keep things simple, I'll just use the average goal-scoring rate from all matches in the tournament, which was 2.67 goals per game (total for both teams).\n",
    "\n",
    "To construct the prior, I use a gamma distribution with a mean of 1.34 goals per game."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.3103599490022562"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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Zfclr8yqw1cw2A48CX/Ve3gN4y8xKgCXA6/WFfKKgz7qJN+26uuGb5Wu2se/QcR+rERH5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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f9b6835c510>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from thinkbayes2 import MakeGammaPmf\n",
    "\n",
    "xs = np.linspace(0, 8, 101)\n",
    "pmf = MakeGammaPmf(xs, 1.3)\n",
    "thinkplot.Pdf(pmf)\n",
    "thinkplot.Config(xlabel='Goals per game')\n",
    "pmf.Mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "suite = Soccer2(pmf)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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3ZbNj39FKSiulwsnkyZO54YYbaNmyJU2bNvW97rjjDqZOnUpxcfEJ+zz33HMcPnyY5s2b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\n0iShlFIqIE0SSimlAtIkoZRSKqD/B1Dv6uLRcfuZAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f9b37101450>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "germany = suite.Copy(label='Germany')\n",
    "argentina = suite.Copy(label='Argentina')\n",
    "thinkplot.Pdf(germany)\n",
    "thinkplot.Pdf(argentina)\n",
    "thinkplot.Config(xlabel='goal-scoring rate', ylabel='probability')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "According to this prior, the goal-scoring rates are always greater than zero, with the most likely value (a priori) near 0.5.  Goal scoring rates greater than 5 are considered unlikely.\n",
    "\n",
    "### Step 2: Comparing posteriors\n",
    "\n",
    "The next step is to compute the posteriors for the two teams:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "posterior mean Germany 1.310359949\n",
      "posterior mean Argentina 1.310359949\n"
     ]
    }
   ],
   "source": [
    "germany = suite.Copy(label='Germany')\n",
    "argentina = suite.Copy(label='Argentina')\n",
    "germany.Update(1)\n",
    "argentina.Update(0)\n",
    "\n",
    "print('posterior mean Germany', germany.Mean())\n",
    "print('posterior mean Argentina', argentina.Mean())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`Update` invokes the likelihood function for each hypothetical value of $\\lambda$ and updates the distribution accordingly.\n",
    "\n",
    "Since both teams scored fewer goals than the prior mean (1.4), we expect both posterior means to be lower.  Germany's posterior mean is 1.2; Argentina's is 0.7.  We can plot the posteriors:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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KhVawbTNvALcbY9oaY9oCd+C94ynsOLkmAXCXX21ize5jeqeTUiqkgk0SxcaY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\n0iShlFIqIE0SSimlAtIkoZRSKqD/B1Dv6uLRcfuZAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f9b6ecd6a10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "thinkplot.Pdf(germany)\n",
    "thinkplot.Pdf(argentina)\n",
    "thinkplot.Config(xlabel='goal-scoring rate', ylabel='probability')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To answer the first question, \"How much evidence does this victory provide that Germany had the better team?\", we can compute the posterior probability that Germany had a higher goal-scoring rate:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "posterior prob Germany > Argentina 0.485133146448\n"
     ]
    }
   ],
   "source": [
    "post_prob = germany.ProbGreater(argentina)\n",
    "print('posterior prob Germany > Argentina', post_prob)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Based on the prior distributions, we would have said that Germany had a 50% chance of having the better team, or 1:1 odds.  Based on the posteriors, we would say that Germany has a 70% chance.  We can use the ratio of the prior and posterior odds to compute the Bayes factor, which measures the strength of the evidence."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "posterior odds Germany > Argentina 0.942249715827\n",
      "Bayes factor 0.942249715827\n"
     ]
    }
   ],
   "source": [
    "prior_odds = 1\n",
    "post_odds = post_prob / (1 - post_prob)\n",
    "print('posterior odds Germany > Argentina', post_odds)   \n",
    "k = post_odds / prior_odds\n",
    "print('Bayes factor', k)   "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The Bayes factor is 2.4, which is generally considered weak evidence.\n",
    "\n",
    "Now on to Step 4."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Step 4\n",
    "\n",
    "**Exercise:**  Write a few lines of code to \n",
    "\n",
    "1. Choose a random value of `lam` from the posterior distribution of each time.\n",
    "\n",
    "2. Choose a random number of goals for each team, conditioned on the value of `lam` you chose.\n",
    "\n",
    "3. Run that \"simulation\" many times and accumulate the distribution of wins, losses, and ties.\n",
    "\n",
    "Use the results to estimate the probability that Germany would win a rematch."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Solution goes here"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Instead of running simulations, you could compute the posterior predictive distributions explicitly.\n",
    "\n",
    "`PredictiveDist` takes the posterior distribution of $\\lambda$ and a duration (in units of games).\n",
    "\n",
    "It loops through the hypotheses in `suite`, computes the predictive distribution of goals for each hypothesis, and assembles a \"meta-Pmf\" which is a Pmf that maps from each predictive distribution to its probability.\n",
    "\n",
    "Finally, it uses `MakeMixture` to compute the mixture of the distributions.  Here's what the predictive distributions look like."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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A88CFEdEevsQuBoYDPSLixGLH0xxJy4HhEfFhsWMphKT/BJ6NiDslfQnoFhEb\nihxWQZLvu1XAYRGxsrEybkl8XtEf4mupiJgDtIt/UHUi4n8j4tVkeyOwmBJ/DiYi/phsdiE3nlfy\nf2FJ6g+cANxW7FhaQLST7yZJPYAjI+JOgIj4a3tJEIn/A7yVliCgnfyHaGN+iK+NSdoT+BrwYnEj\naVrSbbMA+F/gyYhoD4/Y3gBcRjtIaHkCeFLSfEmTih1MMwYB6yXdmXTfTJPUtdhBtcA3gSbn+3CS\nsKJKupoeAKYkLYqSFRFbIuIgoD9wmKShxY6pKZL+HliXtNhE+3lQ9YiIOJhcC+i7SXdqqfoScDBw\nSxLzH4ErihtSYSTtAJwI/Lqpck4Sn7caGJC33z85Zq0s6b99APiviHi42PEUKulOeAYYXexYmnEE\ncGLSx38fcLSku4scU7MiYm3y/gdgBrku4FK1ClgZES8l+w+QSxrtwfHAy8nvOZWTxOfVPwAoqTO5\nh/jaw10h7ekvxTp3AG9ExI3FDqQ5kvpI6plsdwX+DijZQXaAiPiXiBgQEXuR+//46YiYUOy4miKp\nW9K6RNKXgWOB14sbVbqIWAeslLR3cugY4I0ihtQSp9NMVxN4ZbrPaY8P8Un6b6AC2EXSu8A1dQNp\npUrSEcCZwKKknz+Af4mIx4sbWap+wF3J3SBlwP0R8WiRY9oe9QVmJFPtfAm4NyJmFTmm5lwI3Jt0\n3ywneSC4lEnqRm7Q+tvNlvUtsGZmlsbdTWZmlspJwszMUjlJmJlZKicJMzNL5SRhZmapnCTMzCyV\nk4R1eJI+Sd77SfpVM2WnSNqxhdc/StIjzZR5WlJnSTdkPdV0IfGY1XGSsO1S8tBboQJy00FExNhm\nyl4EdNuGkFIfSEqe4K6NiE+BQ4GX0sq2Ij8gZQVxkrB2JZkuZbGkeyS9IelXdX/ZS3pb0o8lvQT8\no6S9JD2WzCb6bN3UCZL2lPRCsrDNDxtce1GyXSbpp8kCQ69K+q6kC4DdgWckPZWUOza51kuS7k+e\nZK1buGpxEsspTfw8TwMLgf2VWzRqf2C+pM/NC6XcMr+Lk5/nxrrWgKRekmYkP88Lkg5Ijh+a7L8s\naY6krzRyzaPyFqB5OZkKw+wzEeGXX+3mBQwEtgAjk/3bgUuS7beB7+WV/R9gcLI9Angq2X4YODPZ\nPh/YkHfthcn2ecCv+GxWgp2T9+VAr2R7F+BZoGuy/8/A1eTWm3gX2Cs5fj8ws4mf6VLgZOBI4Ccp\nZequOSAVeF32AAACi0lEQVTZ/++6awI3Ad9Pto8GFiTb3YGyZPsY4IFk+6i8ujOBw5PtbnXl/fKr\n7uWWhLVH70bE3GT7HiB/Kun7oX5yuL8Ffp3MDTWV3LxAkJsddXqy/V8pn3EMMDUi6rqiPkqO50+k\nOBIYCjyffMYEconmq8DyiFieF2NThpNrTQxL3hvzVXKLw7yb7OdPzDaq7ueIiGeA3skkeTsDDySt\noxuSWBt6HrghaSX1iogtzcRqHYwn+LPtQX7/+qbkvQz4MHJz/DdWvq7OF5k5V8CsiDhzq4PSsEKu\nK+kcoBIYTC4JDAT+V9LoiBif8nkt8UNyM7+eImkguenNtxIRP5H0W+DvySW7YyNiaQs/x7ZjbklY\nezQg7w6gM4DnGhaIiE+AtyX9Y90xSXXrfz9PbppkyM1E25gngcnKrWeNpF7J8Q1Aj2R7LnCEpMFJ\nmW5Jv/8SYKCkQUm502lERNxObirsp5Nktiwi9ktJEG8CgyTVrXXyzbxzzwHfSmKoANZHbgGnnny2\nFkqjM5NK2isifhcR15GbJv+rjf42rMNykrD26E1yK5a9Qa5L5RfJ8YZ37JwJnJMMPL9ObhUuyN2h\n9F1Jr5GbArwxt5FbxnZh0pVU90X/S+BxSU9FxHpyX773Jdd6AdgnIv4CTAYeTQau1zXxs3wdmKPc\nWtQr0gpFxJ/JjZ88IWk+uWT1cXK6ChiexPBvwMTk+HXAjyW9TPq/9YvqBueBT4HHmojVOiBPFW7t\nStJt8tuIOKDYsbQ1SV+OiE3J9i3A0mgHCzZZ++aWhLVHHfUvm0nJ7aq/I9flNbXYAdn2zy0JMzNL\n5ZaEmZmlcpIwM7NUThJmZpbKScLMzFI5SZiZWSonCTMzS/X/ARf6VqPK/VB6AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f9b36c91d50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def PredictiveDist(suite, duration=1, label='pred'):\n",
    "    \"\"\"Computes the distribution of goals scored in a game.\n",
    "\n",
    "    returns: new Pmf (mixture of Poissons)\n",
    "    \"\"\"\n",
    "    metapmf = thinkbayes2.Pmf()\n",
    "    for lam, prob in suite.Items():\n",
    "        pred = thinkbayes2.MakePoissonPmf(lam * duration, 15)\n",
    "        metapmf[pred] = prob\n",
    "\n",
    "    mix = thinkbayes2.MakeMixture(metapmf, label=label)\n",
    "    return mix\n",
    "\n",
    "germany_pred = PredictiveDist(germany, label='germany')\n",
    "argentina_pred = PredictiveDist(argentina, label='argentina')\n",
    "\n",
    "thinkplot.Hist(germany_pred, width=0.45, align='right')\n",
    "thinkplot.Hist(argentina_pred, width=0.45, align='left')\n",
    "thinkplot.Config(xlabel='predicted # goals', ylabel='probability', xlim=[-0.5, 7])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Using the predictive distributions, we can compute probabilities for the outcomes of a rematch."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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A88CFEdEevsQuBoYDPSLixGLH0xxJy4HhEfFhsWMphKT/BJ6NiDslfQnoFhEb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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f9b36cd8e90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "thinkplot.Hist(germany_pred, width=0.45, align='right')\n",
    "thinkplot.Hist(argentina_pred, width=0.45, align='left')\n",
    "thinkplot.Config(xlabel='predicted # goals', ylabel='probability', xlim=[-0.5, 7])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "posterior prob Germany wins rematch 0.367755251824\n",
      "posterior prob Argentina wins rematch 0.367755251824\n",
      "posterior prob tie 0.264489496352\n"
     ]
    }
   ],
   "source": [
    "win = germany_pred.ProbGreater(argentina_pred)\n",
    "lose = germany_pred.ProbLess(argentina_pred)\n",
    "tie = 1 - (win + lose)\n",
    "\n",
    "print('posterior prob Germany wins rematch', win)\n",
    "print('posterior prob Argentina wins rematch', lose)\n",
    "print('posterior prob tie', tie)"
   ]
  },
  {
   "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": "3.6.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}