\n",
"\n",
"# Dice Baseball\n",
"\n",
"The [538 Riddler for March 22, 2019](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 called *Our National Ball Game*:\n",
"\n",
" 1,1: double 2,2: strike 3,3: out at 1st 4,4: fly out\n",
" 1,2: single 2,3: strike 3,4: out at 1st 4,5: fly out\n",
" 1,3: single 2,4: strike 3,5: out at 1st 4,6: fly out\n",
" 1,4: single 2,5: strike 3,6: out at 1st 5,5: double play\n",
" 1,5: base on error 2,6: foul out 5,6: triple\n",
" 1,6: base on balls 6,6: home run\n",
"\n",
"\n",
"The rules left some things unspecified; the following are my current choices (in an early version I made different choices that resulted in slightly more runs):\n",
"\n",
"* On a* b*-base hit, runners advance* b* bases, except that a runner on second scores on a 1-base hit.\n",
"* On an \"out at first\", all runners advance one base.\n",
"* A double play only applies if there is a runner on first; in that case other runners advance.\n",
"* On a fly out, a runner on third scores; other runners do not advance.\n",
"* On an error all runners advance one base. \n",
"* On a base on balls, only forced runners advance.\n",
"\n",
"I also made some choices about the implementation:\n",
"\n",
"- Exactly one outcome happens to each batter. We call that an *event*.\n",
"- I'll represent events with the following one letter codes:\n",
" - `K`, `O`, `o`, `f`, `D`: strikeout, foul out, out at first, fly out, double play\n",
" - `1`, `2`, `3`, `4`: single, double, triple, home run\n",
" - `E`, `B`: error, base on balls\n",
"- Note the \"strike\" dice roll is not an event; it is only part of an event. From the probability of a \"strike\" dice roll, I compute the probability of three strikes in a row, and call that a strikeout event. Sice there are 7 dice rolls giving \"strike\", the probability of a strike is 7/36, and the probability of a strikeout is (7/36)**3.\n",
"- Note that a die roll such as `1,1` is a 1/36 event, whereas `1,2` is a 2/36 event, because it also represents (2, 1).\n",
"- I'll keep track of runners with a list of occupied bases; `runners = [1, 2]` means runners on first and second.\n",
"- A runner who advances to base 4 or higher has scored a run (unless there are already 3 outs).\n",
"- The function `inning` simulates a half inning and returns the number of runs scored.\n",
"- I want to be able to test `inning` by feeding it specific events, and I also want to generate random innings. So I'll make the interface be that I pass in an *iterable* of events. The function `event_stream` generates an endless stream of randomly sampled events.\n",
"- Note that it is consider good Pythonic style to automatically convert Booleans to integers, so for a runner on second (`r = 2`) when the event is a single (`e = '1'`), the expression `r + int(e) + (r == 2)` evaluates to `2 + 1 + 1` or `4`, meaning the runner on second scores.\n",
"- I'll play 1 million innings and store the resulting scores in `innings`.\n",
"- To simulate a game I just sample 9 elements of `innings` and sum them.\n",
"\n",
"# The Code"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"%matplotlib inline\n",
"import matplotlib.pyplot as plt\n",
"import random"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"def event_stream(events='2111111EEBBOOooooooofffffD334', strike=7/36):\n",
" \"An iterator of random events. Defaults from `Our National Ball Game`.\"\n",
" while True:\n",
" yield 'K' if (random.random() < strike ** 3) else random.choice(events)\n",
" \n",
"def inning(events=event_stream(), verbose=False) -> int:\n",
" \"Simulate a half inning based on events, and return number of runs scored.\"\n",
" outs = runs = 0 # Inning starts with no outs and no runs,\n",
" runners = [] # ... and with nobody on base\n",
" for e in events:\n",
" if verbose: print(f'{outs} outs, {runs} runs, event: {e}, runners: {runners}')\n",
" # What happens to the batter?\n",
" if e in 'KOofD': outs += 1 # Batter is out\n",
" elif e in '1234EB': runners.append(0) # Batter becomes a runner\n",
" # What happens to the runners?\n",
" if e == 'D' and 1 in runners: # double play: runner on 1st out, others advance\n",
" outs += 1\n",
" runners = [r + 1 for r in runners if r != 1]\n",
" elif e in 'oE': # out at first or error: runners advance\n",
" runners = [r + 1 for r in runners]\n",
" elif e == 'f' and 3 in runners and outs < 3: # fly out: runner on 3rd scores\n",
" runners.remove(3)\n",
" runs += 1\n",
" elif e in '1234': # single, double, triple, homer\n",
" runners = [r + int(e) + (r == 2) for r in runners]\n",
" elif e == 'B': # base on balls: forced runners advance \n",
" runners = [r + forced(runners, r) for r in runners]\n",
" # See if inning is over, and if not, whether anyone scored\n",
" if outs >= 3:\n",
" return runs\n",
" runs += sum(r >= 4 for r in runners)\n",
" runners = [r for r in runners if r < 4]\n",
" \n",
"def forced(runners, r) -> bool: return all(b in runners for b in range(r))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Testing\n",
"\n",
"Let's peek at some random innings:"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"0 outs, 0 runs, event: E, runners: []\n",
"0 outs, 0 runs, event: 4, runners: [1]\n",
"0 outs, 2 runs, event: E, runners: []\n",
"0 outs, 2 runs, event: 1, runners: [1]\n",
"0 outs, 2 runs, event: f, runners: [2, 1]\n",
"1 outs, 2 runs, event: B, runners: [2, 1]\n",
"1 outs, 2 runs, event: 1, runners: [3, 2, 1]\n",
"1 outs, 4 runs, event: E, runners: [2, 1]\n",
"1 outs, 4 runs, event: o, runners: [3, 2, 1]\n",
"2 outs, 5 runs, event: o, runners: [3, 2]\n"
]
},
{
"data": {
"text/plain": [
"5"
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"inning(verbose=True)"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"0 outs, 0 runs, event: 1, runners: []\n",
"0 outs, 0 runs, event: B, runners: [1]\n",
"0 outs, 0 runs, event: O, runners: [2, 1]\n",
"1 outs, 0 runs, event: 1, runners: [2, 1]\n",
"1 outs, 1 runs, event: 3, runners: [2, 1]\n",
"1 outs, 3 runs, event: 1, runners: [3]\n",
"1 outs, 4 runs, event: f, runners: [1]\n",
"2 outs, 4 runs, event: o, runners: [1]\n"
]
},
{
"data": {
"text/plain": [
"4"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"inning(verbose=True)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"And we can feed in any events we want to test the code:"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"0 outs, 0 runs, event: 2, runners: []\n",
"0 outs, 0 runs, event: E, runners: [2]\n",
"0 outs, 0 runs, event: B, runners: [3, 1]\n",
"0 outs, 0 runs, event: B, runners: [3, 2, 1]\n",
"0 outs, 1 runs, event: 1, runners: [3, 2, 1]\n",
"0 outs, 3 runs, event: D, runners: [2, 1]\n",
"2 outs, 3 runs, event: B, runners: [3]\n",
"2 outs, 3 runs, event: 1, runners: [3, 1]\n",
"2 outs, 4 runs, event: 2, runners: [2, 1]\n",
"2 outs, 5 runs, event: f, runners: [3, 2]\n"
]
},
{
"data": {
"text/plain": [
"5"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"inning('2EBB1DB12f', verbose=True)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"That looks good.\n",
"\n",
"# Simulating\n",
"\n",
"Now, simulate a million innings, and then sample from them to simulate a million nine-inning games (for one team):"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [],
"source": [
"N = 1000000\n",
"innings = [inning() for _ in range(N)]\n",
"games = [sum(random.sample(innings, 9)) for _ in range(N)]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's see histograms:"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"def hist(nums, title): \n",
" \"Plot a histogram.\"\n",
" plt.hist(nums, ec='black', bins=max(nums)-min(nums)+1, align='left')\n",
" plt.title(f'{title} Mean: {sum(nums)/len(nums):.3f}, Min: {min(nums)}, Max: {max(nums)}')\n",
" \n",
"hist(innings, 'Runs per inning:')"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"hist(games, 'Runs per game:')"
]
}
],
"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": "3.7.2"
}
},
"nbformat": 4,
"nbformat_minor": 2
}