{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "### July 14th Riddler Classic: SquishyBall Playoff Strategy \n", "***\n", "\n", "The July 14th Riddler Classic from [FiveThirtyEight](https://fivethirtyeight.com/features/can-you-eat-more-pizza-than-your-siblings/) is as follows: \n", "\n", "> Congratulations! The Acme Axegrinders, which you own, are the regular season champions of the National Squishyball League (NSL). Your team will now play a championship series against the Boondocks Barbarians, which had the second-best regular season record. You feel good about Acme’s chances in the series because Acme won exactly 60 percent of the hundreds of games it played against Boondocks this season. (The NSL has an incredibly long regular season.) The NSL has two special rules for the playoffs:\n", "\n", "> 1. The owner of the top-seeded team (i.e., you) gets to select the length of the championship series in advance of the first game, so you could decide to play a single game, a best two out of three series, a three out of five series, etc., all the way up to a 50 out of 99 series $~~~~~~~~~~~~~~~~~~~$.\n", "\n", "> 2. The owner of the winning team gets \\$1 million minus \\$10,000 for each of the victories required to win the series, regardless of how many games the series lasts in total. Thus, if the top-seeded team’s owner selects a single-game championship, the winning owner will collect \\$990,000. If he or she selects a 4 out of 7 series, the winning team’s owner will collect \\$960,000. The owner of the losing team gets nothing.\n", "\n", "> Since Acme has a 60 percent chance of winning any individual game against Boondocks, Rule 1 encourages you to opt for a very long series to improve Acme’s chances of winning the series. But Rule 2 means that a long series will mean less winnings for you if Acme does take the series.\n", "\n", "> How long a series should you select in order to maximize your expected winnings? And how much money do you expect to win?\n", "\n", "First, let's state our assumptions. \n", "\n", "1. We assume that we're playing from the perspective of Acme.\n", "2. Motivated by the last sentence in Rule 2, we assume that _losing_ the series to the Boondocks does not cost us anything. That is, there is no negative payoff if we win, say, 3 games in a 7 game series but lose the series overall. \n", "\n", "Some notation: Let $N$ be the number of games required to win a particular series. Then an $N$-win series is the first to $N$ out of a possible $2N-1$ games. \n", "\n", "Our strategy will be to compute the **expected payoff** of each $N$-win series for $N=1,2, \\ldots 50$ and choose the value of $N$ with the largest expected payoff. \n", "\n", "Before jumping into fun probability-by-hand computations, let's see if we can get an idea of the optimal series length using Monte Carlo simulation. The following code estimates the expected payoff for each series length by simulating 5 Million independent series and averaging the realized payoffs. " ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def series_sim(N, M):\n", " # We draw M samples from Bin(2N-1, p) to simulate the number of wins in a \n", " # 2N-1 length series where the probability of and individual win is p=0.6 \n", " wins = np.random.binomial(2*N-1, 0.6, M)\n", " \n", " # We win the series if wins >= N and return N as the number of wins\n", " # We lose the series if wins < N and return 0 as the number of wins \n", " return map(lambda w: N if w >= N else 0, wins)\n", "\n", "def payoff_sim(N, M):\n", " # We simulate M samples of an N-win series and compute the expected payoff\n", " expected_payoff = np.sum(map(lambda w: 1000000 - 10000*w if w > 0 else 0.0, series_sim(N, M))) / M \n", " return expected_payoff \n", "\n", "def tournaments_sim(M=10000):\n", " # Run the simulation with M independent samples and compute expected \n", " # payoffs for series of lengths N=1, 2, ..., 50\n", " payoffs = np.array([payoff_sim(N, M) for N in xrange(1,51)])\n", " return payoffs" ] }, { "cell_type": "code", "execution_count": 53, "metadata": {}, "outputs": [ { "data": { "image/png": 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Ktgd4LIb6un9XfwnRlO7fZUVFpC34hn1rV7tt49uuHdF9+9G+S1fad+rc4DQ5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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "mc_payoffs = tournaments_sim(M=5000000)\n", "plot_tournaments(mc_payoffs = mc_payoffs)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "According to the simulation the series with the greatest expected payoff corresponds to $N=13$, meaning that the series is **first to 13 out of 25** games. \n", "\n", "Let's see if we can work out the exact expectation and confirm our simulation results. \n", "\n", "In general, the probability of winning the series on the $K^\\textrm{th}$ game (where $K \\geq N)$ is equal to the probability that we have won $N-1$ out of the first $K-1$ games and then win the $K^\\textrm{th}$ game to win the series. Let $P(K,N)$ be the probability that we win the $N$-win series on the $K^\\textrm{th}$ game.\n", "\n", "The probability that we randomly generate any particular $K-1$ length series with exactly $N-1$ wins is \n", "\n", "$\n", "(0.6)^{N-1}(0.4)^{K-N}\n", "$\n", "\n", "Since there are ${{K-1}\\choose{N-1}}$ ways that we can generate exactly $N-1$ wins, the probability of winning exactly $N-1$ of $K-1$ games is \n", "\n", "$\n", "{{K-1}\\choose{N-1}} (0.6)^{N-1}(0.4)^{K-N}\n", "$\n", "\n", "Finally, multiplying by the probability that we win the $K^\\textrm{th}$ game gives \n", "\n", "$P(K,N) = {{K-1}\\choose{N-1}} (0.6)^{N-1}(0.4)^{K-N} \\times (0.6) = {{K-1}\\choose{N-1}} (0.6)^{N}(0.4)^{K-N}$\n", "\n", "Now we simply sum up the weighted payoffs for ending the series on games $K=N, \\ldots, 2N-1$. We have \n", "\n", "$$\n", "\\mathbb{E}[\\texttt{PayOff}] = \\sum_{K=N}^{2N-1} P(K,N)\\left[$1,000,000 + N\\times-$10,000\\right]\n", "$$\n", "\n", "Notice that despite the fact that $P(K,N)$ is not a distribution, this is a valid expectation since the probabilities for events not accounted for (e.g. losing the series on the $K^\\textrm{th}$ game) are associated with payoffs of zero. \n", "\n", "The following code computes the expected payoff for each $N$-win series for $N=1, 2, \\ldots, 50$. " ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": true }, "outputs": [], "source": [ "from scipy.special import binom \n", "\n", "def P(K, N):\n", " # Function to compute the probability of winning an N-win \n", " # series on the Kth game \n", " assert(K >= N)\n", " return binom(K-1, N-1) * (0.6)**N * (0.4)**(K-N)\n", "\n", "def expected_payoff(N):\n", " # Function to compute he expected payoff of winning an \n", " # N-win series. \n", " return np.sum([P(K, N)*(1e6 - N*1e4) for K in xrange(N,2*N)])\n", "\n", "def tournaments_expected():\n", " # Function to compute expected payoff over series requiring \n", " # 1, 2, ..., N wins\n", " return [expected_payoff(N) for N in xrange(1,51)]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Running the code and plotting the results gives " ] }, { "cell_type": "code", "execution_count": 52, "metadata": {}, "outputs": [ { "data": { "image/png": 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gQ4cO3HrrHXzwwbvVx/H1tXL11dfx5ZefsXnzRt5//5M652rbth2zZr3Na6+9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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "expected_payoffs = tournaments_expected()\n", "plot_tournaments(expected_payoffs = expected_payoffs)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It appears that our analytic computation of the expected payoff agrees well with our simulated results. We therefore conclude that the optimal choice of playoff series length is **first to 13 of 25 games**. The corresponding element of the $\\texttt{expected_payoffs}$ vector is the maximum expected payoff. " ] }, { "cell_type": "code", "execution_count": 56, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "maximum expected payoff = 736222.040991\n" ] } ], "source": [ "print \"maximum expected payoff = \", np.max(expected_payoffs)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "From this we see that the expected payoff in choosing to play a best of 25 series is approximately ${\\bf \\$736,222}$. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As a sanity check, it's nice to overlay the analytic results with the simulated results. We have " ] }, { "cell_type": "code", "execution_count": 51, "metadata": {}, "outputs": [ { "data": { "image/png": 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22puAKQt5t27d+eqrFRgMJ8xBjKWy6riRtaXArC3PZLntqad6EBsbw7p1a/j2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5XX/pmHukbziV+1cOYR45j52iPYvGE965Yvo3XVCjIdnaSrq6ifMo0J02dQWVtX6NI1QtlsS5Ik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\nSZIkSZLyzGZbkiRJk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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_tournaments(mc_payoffs = mc_payoffs, expected_payoffs = expected_payoffs)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If you squint you can see a few points where the simulated results disagree slightly with the analytic results, owing to sampling error in the Monte Carlo simulation. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "



\n", "



\n", "\n", "### Helper Functions\n", "***" ] }, { "cell_type": "code", "execution_count": 55, "metadata": {}, "outputs": [], "source": [ "import numpy as np \n", "import matplotlib.pyplot as plt\n", "import seaborn as sns\n", "%matplotlib inline\n", "\n", "mycolors = {\"blue\": \"steelblue\", \"red\": \"#a76c6e\", \"green\": \"#6a9373\"}\n", "\n", "def plot_tournaments(mc_payoffs=None, expected_payoffs=None):\n", " \n", " if (mc_payoffs is None) and (expected_payoffs is None): \n", " print \"You need to give me some data, Dude.\"\n", " return\n", " \n", " fig = plt.figure(figsize=(16,8))\n", " ax = fig.add_subplot(111)\n", " \n", " \n", " if mc_payoffs is not None:\n", " best_mc = np.argmax(mc_payoffs) + 1 \n", " mc_report = \"Best simulated series is \" + str(best_mc) + \" out of \" + str(2*best_mc-1)\n", " markersize = 11 if expected_payoffs is not None else 8 \n", " plt.plot([ii+1 for ii in xrange(50)], mc_payoffs, color=mycolors[\"red\"], marker=\"o\", markersize=markersize, label=mc_report)\n", " plt.plot([best_mc, best_mc], [450000,749000], color=mycolors[\"red\"], linestyle=\"-\", alpha=0.5)\n", " extratick = [best_mc]\n", "\n", " \n", " if expected_payoffs:\n", " best_expected = np.argmax(expected_payoffs) + 1 \n", " expected_report = \"Best analytic series is \" + str(best_expected) + \" out of \" + str(2*best_expected-1)\n", " plt.plot([ii+1 for ii in xrange(50)], expected_payoffs, color=mycolors[\"blue\"], marker=\"o\", label=expected_report)\n", " plt.plot([best_expected, best_expected], [450000,749000], color=mycolors[\"blue\"], linestyle=\"-\", alpha=0.5)\n", " extratick = [best_expected]\n", " \n", " plt.xticks(list(plt.xticks()[0]) + extratick)\n", " \n", " plt.xlim([0, 51])\n", "\n", " plt.legend(loc=\"upper right\", prop={'size':16})\n", " \n", " plt.xlabel(\"Wins Required\", fontsize=16)\n", " plt.ylabel(\"Expected Payoff\", fontsize=16)\n", " plt.tick_params(axis='both', which='major', labelsize=16)\n", " plt.tick_params(axis='both', which='minor', labelsize=16)\n", " " ] }, { "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": "3.6.1" } }, "nbformat": 4, "nbformat_minor": 1 }