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@@ -8,17 +8,18 @@
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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. There were some choices to make that were left unspecified in the rules; these are my choices (your choices may differ):\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. There were some choices to make that were left unspecified in the rules; the following are my current choices (in an early version I made different choices that resulted in slightly more runs):\n",
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"\n",
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"* On a `b`-base hit, runners advance `b` bases, except that a runner on second scores on a 1-base hit.\n",
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"* On an \"out at first\", all runners advance one base.\n",
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"* On a double play, the runner on first is out if there is one, otherwise a runner on second, otherwise a runner on third, otherwise it is only a single out.\n",
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"* A double play only applies if there is a runner on first; in that case other runners advance.\n",
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"* On a fly out, a runner on third scores; other runners do not advance.\n",
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"* On an error all runners advance one base. (*Note: in an earlier version, I treated an error as a single, meaning that a runner would score from second on an error, which seems wrong. Under that interpretation, teams score about 0.05 runs more per game.*)\n",
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"* On an error all runners advance one base. \n",
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"* On a base on balls, only forced runners advance.\n",
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"\n",
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"I also made some choices about the implementation:\n",
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"- I wanted to have one event per batter, so I don't allow \"strike\" as an event. Rather I compute the probability of a strikeout event (i.e. getting three \"strike\" dice rolls in a row before getting another event) as `(7/36)**3`, and check for that.\n",
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"- Note that a die roll such as (1, 1) is a 1/36 event, whereas (1, 2) is a 2/36 event, because it is also (2, 1).\n",
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"- 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",
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"- I'll represent events with the following one letter codes:\n",
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" - `K`, `O`, `o`, `f`, `D`: strikeout, foul out, out at first, fly out, double play\n",
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" - `1`, `2`, `3`, `4`: single, double, triple, home run\n",
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@@ -56,29 +57,29 @@
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" while True:\n",
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" x = 'K' if random.random() <= PK else random.choice(events)\n",
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" if verbose: print(f'outs: {outs}, runs: {runs}, runners: {runners}, event: {x}')\n",
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" if x in 'KOofD': # batter is out: strikeout, 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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" if x in 'KODof': # strikeout, foul out, double play, out at first, fly out, \n",
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" outs += 1 # Batter is out\n",
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" if x == 'D' and 1 in runners: # double play\n",
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" outs += 1\n",
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" runners = [r + 1 for r in runners if r != 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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" runners = [r + 1 for r in runners]\n",
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" elif x == 'f' and 3 in runners and outs < 3: # fly out; runner on 3rd scores\n",
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" runners.remove(3)\n",
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" runs += 1\n",
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" else: # batter reaches base safely\n",
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" runners.append(0)\n",
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" if x in '1234': # single, double, triple, homer\n",
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" else: \n",
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" runners.append(0) # Batter becomes a runner\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]\n",
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" elif x == 'E': # error\n",
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" elif x == 'E': # error\n",
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" runners = [r + 1 for r in runners]\n",
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" elif x == 'B': # base on balls\n",
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" elif x == 'B': # base on balls\n",
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" runners = [r + all(b in runners for b in range(r)) for r in runners]\n",
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" # See if inning is over, and if not, whether anyone scored\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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" 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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@@ -97,20 +98,19 @@
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"outs: 0, runs: 0, runners: [], event: 4\n",
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"outs: 0, runs: 1, runners: [], event: E\n",
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"outs: 0, runs: 1, runners: [1], event: 1\n",
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"outs: 0, runs: 1, runners: [2, 1], event: 4\n",
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"outs: 0, runs: 4, runners: [], event: 3\n",
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"outs: 0, runs: 4, runners: [3], event: o\n",
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"outs: 1, runs: 5, runners: [], event: o\n",
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"outs: 2, runs: 5, runners: [], event: f\n"
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"outs: 0, runs: 0, runners: [], event: O\n",
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"outs: 1, runs: 0, runners: [], event: 1\n",
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"outs: 1, runs: 0, runners: [1], event: o\n",
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"outs: 2, runs: 0, runners: [2], event: B\n",
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"outs: 2, runs: 0, runners: [2, 1], event: 3\n",
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"outs: 2, runs: 2, runners: [3], event: E\n",
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"outs: 2, runs: 3, runners: [1], event: f\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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"5"
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"3"
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]
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},
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"execution_count": 3,
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@@ -131,12 +131,12 @@
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"outs: 0, runs: 0, runners: [], event: o\n",
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"outs: 1, runs: 0, runners: [], event: D\n",
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"outs: 2, runs: 0, runners: [], event: 1\n",
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"outs: 2, runs: 0, runners: [1], event: E\n",
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"outs: 2, runs: 0, runners: [2, 1], event: 3\n",
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"outs: 2, runs: 2, runners: [3], event: o\n"
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"outs: 0, runs: 0, runners: [], event: 3\n",
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"outs: 0, runs: 0, runners: [3], event: 1\n",
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"outs: 0, runs: 1, runners: [1], event: 2\n",
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"outs: 0, runs: 1, runners: [3, 2], event: D\n",
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"outs: 1, runs: 1, runners: [3, 2], event: f\n",
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"outs: 2, runs: 2, runners: [2], event: o\n"
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]
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},
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{
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@@ -163,20 +163,25 @@
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"outs: 0, runs: 0, runners: [], event: f\n",
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"outs: 1, runs: 0, runners: [], event: 1\n",
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"outs: 1, runs: 0, runners: [1], event: B\n",
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"outs: 1, runs: 0, runners: [2, 1], event: B\n",
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"outs: 1, runs: 0, runners: [3, 2, 1], event: 1\n",
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"outs: 1, runs: 2, runners: [2, 1], event: 3\n",
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"outs: 1, runs: 4, runners: [3], event: o\n",
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"outs: 2, runs: 5, runners: [], event: K\n"
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"outs: 0, runs: 0, runners: [], event: 4\n",
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"outs: 0, runs: 1, runners: [], event: 1\n",
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"outs: 0, runs: 1, runners: [1], event: B\n",
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"outs: 0, runs: 1, runners: [2, 1], event: 1\n",
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"outs: 0, runs: 2, runners: [2, 1], event: f\n",
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"outs: 1, runs: 2, runners: [2, 1], event: 2\n",
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"outs: 1, runs: 3, runners: [3, 2], event: 3\n",
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"outs: 1, runs: 5, runners: [3], event: B\n",
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"outs: 1, runs: 5, runners: [3, 1], event: B\n",
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"outs: 1, runs: 5, runners: [3, 2, 1], event: 1\n",
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"outs: 1, runs: 7, runners: [2, 1], event: 1\n",
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"outs: 1, runs: 8, runners: [2, 1], event: o\n",
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"outs: 2, runs: 8, runners: [3, 2], event: 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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"5"
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"8"
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]
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},
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"execution_count": 5,
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@@ -223,7 +228,7 @@
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{
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"data": {
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"text/plain": [
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"14.959092"
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"14.457532"
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]
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},
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"execution_count": 7,
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@@ -232,7 +237,7 @@
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},
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{
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"data": {
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"image/png": 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truncated
|
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"text/plain": [
|
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"<Figure size 432x288 with 1 Axes>"
|
||||
]
|
||||
|
||||
Reference in new issue
Block a user