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Peter Norvig 2018-04-15 15:50:33 -07:00 committed by GitHub
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@ -54,7 +54,7 @@
{ {
"data": { "data": {
"text/plain": [ "text/plain": [
"0.61119" "0.61163"
] ]
}, },
"execution_count": 2, "execution_count": 2,
@ -84,7 +84,7 @@
"text": [ "text": [
"0 point differential = 50% win game\n", "0 point differential = 50% win game\n",
"1 point differential = 54% win game\n", "1 point differential = 54% win game\n",
"2 point differential = 57% win game\n", "2 point differential = 58% win game\n",
"3 point differential = 61% win game\n", "3 point differential = 61% win game\n",
"4 point differential = 65% win game\n", "4 point differential = 65% win game\n",
"5 point differential = 68% win game\n", "5 point differential = 68% win game\n",
@ -146,16 +146,16 @@
"name": "stdout", "name": "stdout",
"output_type": "stream", "output_type": "stream",
"text": [ "text": [
"0 point differential = 50% win game = 49% win series\n", "0 point differential = 50% win game = 50% win series\n",
"1 point differential = 54% win game = 58% win series\n", "1 point differential = 54% win game = 58% win series\n",
"2 point differential = 57% win game = 66% win series\n", "2 point differential = 57% win game = 66% win series\n",
"3 point differential = 61% win game = 73% win series\n", "3 point differential = 61% win game = 73% win series\n",
"4 point differential = 65% win game = 80% win series\n", "4 point differential = 65% win game = 80% win series\n",
"5 point differential = 68% win game = 85% win series\n", "5 point differential = 68% win game = 85% win series\n",
"6 point differential = 71% win game = 89% win series\n", "6 point differential = 72% win game = 89% win series\n",
"7 point differential = 75% win game = 93% win series\n", "7 point differential = 75% win game = 93% win series\n",
"8 point differential = 78% win game = 95% win series\n", "8 point differential = 78% win game = 95% win series\n",
"9 point differential = 80% win game = 97% win series\n" "9 point differential = 81% win game = 97% win series\n"
] ]
} }
], ],
@ -330,7 +330,7 @@
"Rockets vs Wolves 89%; through here: 89%\n", "Rockets vs Wolves 89%; through here: 89%\n",
"Rockets vs Jazz 78%; through here: 69%\n", "Rockets vs Jazz 78%; through here: 69%\n",
"Rockets vs Warriors 69%; through here: 48%\n", "Rockets vs Warriors 69%; through here: 48%\n",
"Rockets vs Raptors 57%; through here: 27%\n" "Rockets vs Raptors 58%; through here: 28%\n"
] ]
} }
], ],
@ -351,9 +351,9 @@
"name": "stdout", "name": "stdout",
"output_type": "stream", "output_type": "stream",
"text": [ "text": [
"Warriors vs Spurs 73%; through here: 73%\n", "Warriors vs Spurs 72%; through here: 72%\n",
"Warriors vs Blazers 74%; through here: 54%\n", "Warriors vs Blazers 74%; through here: 54%\n",
"Warriors vs Rockets 31%; through here: 17%\n", "Warriors vs Rockets 31%; through here: 16%\n",
"Warriors vs Raptors 38%; through here: 6%\n" "Warriors vs Raptors 38%; through here: 6%\n"
] ]
} }
@ -374,13 +374,27 @@
"\n", "\n",
"# Series Length\n", "# Series Length\n",
"\n", "\n",
"Given a team's game win percentage, how many games should we expect a series to run? That is, with a game win percentage of 60%, how likely is it to sweep all 4 games? To go to 7 games? Here's a chart:" "Given a team's game win percentage, how many games should we expect a series to run? That is, with a game win percentage of 60%, how likely is it to sweep all 4 games? To go to 7 games? Here's a chart of the probability of each possible series outcome, based on the win percentage of the first team:"
] ]
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 12, "execution_count": 12,
"metadata": {}, "metadata": {},
"outputs": [],
"source": [
"import collections\n",
"\n",
"class MCounter(collections.Counter):\n",
" \"A multipliable Counter: you can say `2 * MCounter(stuff)`.\"\n",
" def __mul__(self, p): return MCounter({k: p * self[k] for k in self})\n",
" __rmul__ = __mul__"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [ "outputs": [
{ {
"name": "stdout", "name": "stdout",
@ -401,11 +415,9 @@
} }
], ],
"source": [ "source": [
"from collections import Counter\n", "def series_results(p, W=0, L=0) -> MCounter:\n",
"\n",
"def series_results(p, W=0, L=0):\n",
" \"\"\"Return {(win, loss): probability} for all possible outcomes of the series.\"\"\"\n", " \"\"\"Return {(win, loss): probability} for all possible outcomes of the series.\"\"\"\n",
" return MCounter([(W, L)] if W == 4 or L == 4 else\n", " return MCounter([(W, L)] if W == 4 or L == 4 else\n",
" (p * series_results(p, W + 1, L) + \n", " (p * series_results(p, W + 1, L) + \n",
" (1 - p) * series_results(p, W, L + 1)))\n", " (1 - p) * series_results(p, W, L + 1)))\n",
" \n", " \n",
@ -417,12 +429,7 @@
" for (W, L) in outcomes:\n", " for (W, L) in outcomes:\n",
" results = [series_results(p)[W, L] for p in pcts]\n", " results = [series_results(p)[W, L] for p in pcts]\n",
" print('{}-{} | {}'.format(W, L, ' '.join(map(pct, results))))\n", " print('{}-{} | {}'.format(W, L, ' '.join(map(pct, results))))\n",
" \n", "\n",
"class MCounter(Counter):\n",
" \"A multipliable Counter.\"\n",
" def __mul__(self, p): return MCounter({k: p * self[k] for k in self})\n",
" __rmul__ = __mul__\n",
" \n",
"series_results_table()" "series_results_table()"
] ]
}, },
@ -430,9 +437,9 @@
"cell_type": "markdown", "cell_type": "markdown",
"metadata": {}, "metadata": {},
"source": [ "source": [
"So we see that our 60% team has a 13% chance of sweeping, and 13+21+21 = 55% chance of winning in 6 games or less.\n", "So we see that our 60% team has a 13% chance of sweeping (4-0), and 13+21+21 = 55% chance of winning in 6 games or less.\n",
"\n", "\n",
"**Note:** I think `Counter` should support multiplication. If `C` is a `Counter`, then shouldn't `C + C` be the same as `2 * C`?" "**Note:** I had to define `MCounter` because `collectionsCounter` does not support multiplication. I think it should: if `C` is a `Counter`, then shouldn't `C + C` be the same as `2 * C`?"
] ]
}, },
{ {
@ -461,7 +468,7 @@
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@ -487,7 +494,7 @@
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