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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"<div align=\"right\">Peter Norvig<br>March 2019</div>\n",
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"\n",
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"# Dice Baseball\n",
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"\n",
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"The [March 22, 2019 Riddler](https://fivethirtyeight.com/features/can-you-turn-americas-pastime-into-a-game-of-yahtzee/) asks us to simulate baseball using probabilities from a 19th century dice game. The simulation is pretty straightforward. (Note that I chose not to implement a strike as an event, but rather to count the probability of getting 3 strikes in a row, and calling that an event.)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 1,
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"metadata": {},
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"outputs": [],
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"source": [
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"%matplotlib inline\n",
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"import matplotlib.pyplot as plt\n",
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"from collections import Counter\n",
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"from statistics import mean\n",
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"import random"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 2,
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"metadata": {},
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"outputs": [],
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"source": [
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"def inning(events='2111111EEBBOOooooooofffffD334', strikes=7*'s', verbose=False):\n",
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" \"Play a random inning and return number of runs scored.\"\n",
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" assert len(events) + len(strikes) == 6 * 6\n",
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" K = (len(strikes) / len(strikes+events)) ** 3 # The probability of a strikeout\n",
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" events = events.replace('E', '1') # An error is the same as a single\n",
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" outs = runs = 0\n",
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" runners = [] # A list of runners; [1, 2, 3] means bases loaded\n",
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" while True:\n",
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" x = 'K' if random.random() <= K else random.choice(events)\n",
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" if verbose: \n",
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" print('{} outs; {} runs; runners on {}; result is {}'\n",
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" .format(outs, runs, runners, x))\n",
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" if x in '1234': # single, double, triple, homer\n",
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" runners = [r + int(x) + (r == 2) for r in runners + [0]]\n",
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" elif x == 'B': # base on balls\n",
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" runners = [(r+1 if r==1 or r-1 in runners else r) for r in runners] + [1]\n",
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" elif x in 'KOofD': # srikeout, foul out, out at first, fly out, double play\n",
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" outs += 1\n",
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" if x == 'D' and runners: # double play\n",
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" runners.remove(min(runners))\n",
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" outs += 1\n",
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" elif x == 'o': # out at first (other runners advance)\n",
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" runners = [r+1 for r in runners]\n",
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" elif x == 'f' and 3 in runners: # fly out; runner on 3rd scores\n",
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" runs += 1\n",
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" runners.remove(3)\n",
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" else:\n",
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" raise ValueError('unknown events: ' + x)\n",
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" if outs >= 3:\n",
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" return runs\n",
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" else: # See if anybody scored\n",
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" runs += sum(r >= 4 for r in runners)\n",
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" runners = [r for r in runners if r < 4]"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"Let's peek at some random innings:"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 3,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"0 outs; 0 runs; runners on []; result is o\n",
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"1 outs; 0 runs; runners on []; result is o\n",
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"2 outs; 0 runs; runners on []; result is 1\n",
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"2 outs; 0 runs; runners on [1]; result is 1\n",
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"2 outs; 0 runs; runners on [2, 1]; result is O\n"
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]
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},
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{
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"data": {
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"text/plain": [
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"0"
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]
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},
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"execution_count": 3,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"inning(verbose=True)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 4,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"0 outs; 0 runs; runners on []; result is 3\n",
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"0 outs; 0 runs; runners on [3]; result is f\n",
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"1 outs; 1 runs; runners on []; result is 1\n",
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"1 outs; 1 runs; runners on [1]; result is o\n",
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"2 outs; 1 runs; runners on [2]; result is 1\n",
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"2 outs; 2 runs; runners on [1]; result is 1\n",
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"2 outs; 2 runs; runners on [2, 1]; result is K\n"
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]
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},
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{
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"data": {
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"text/plain": [
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"2"
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]
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},
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"execution_count": 4,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"inning(verbose=True)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 5,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"0 outs; 0 runs; runners on []; result is o\n",
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"1 outs; 0 runs; runners on []; result is 3\n",
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"1 outs; 0 runs; runners on [3]; result is D\n"
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]
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},
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{
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"data": {
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"text/plain": [
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"0"
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]
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},
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"execution_count": 5,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"inning(verbose=True)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"That looks good.\n",
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"\n",
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"Now, simulate a million innings, use them to simulate a million games, and show a histogram of runs scored per team per game:"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 6,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"CPU times: user 20.7 s, sys: 73.7 ms, total: 20.8 s\n",
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"Wall time: 20.9 s\n"
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]
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}
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],
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"source": [
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"%%time\n",
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"N = 1000000\n",
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"innings = [inning() for _ in range(N)]\n",
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"games = [sum(random.choice(innings) for i in range(9)) for g in range(N)]"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 7,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"(15.106058, 15.10542)"
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]
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},
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"execution_count": 7,
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"metadata": {},
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"output_type": "execute_result"
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},
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|
{
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"data": {
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|
"image/png": 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truncated
|
||||||
|
"text/plain": [
|
||||||
|
"<Figure size 432x288 with 1 Axes>"
|
||||||
|
]
|
||||||
|
},
|
||||||
|
"metadata": {
|
||||||
|
"needs_background": "light"
|
||||||
|
},
|
||||||
|
"output_type": "display_data"
|
||||||
|
}
|
||||||
|
],
|
||||||
|
"source": [
|
||||||
|
"plt.hist(games, ec='black', bins=max(games)-min(games)+1)\n",
|
||||||
|
"mean(games), mean(innings) * 9"
|
||||||
|
]
|
||||||
|
}
|
||||||
|
],
|
||||||
|
"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": "3.5.3"
|
||||||
|
}
|
||||||
|
},
|
||||||
|
"nbformat": 4,
|
||||||
|
"nbformat_minor": 2
|
||||||
|
}
|
||||||
Reference in new issue
Block a user