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Peter Norvig
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{
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"data": {
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"text/plain": [
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"0.61119"
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"0.61163"
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]
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},
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"execution_count": 2,
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@ -84,7 +84,7 @@
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"text": [
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"0 point differential = 50% win game\n",
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"1 point differential = 54% win game\n",
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"2 point differential = 57% win game\n",
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"2 point differential = 58% win game\n",
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"3 point differential = 61% win game\n",
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"4 point differential = 65% win game\n",
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"5 point differential = 68% win game\n",
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@ -146,16 +146,16 @@
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"0 point differential = 50% win game = 49% win series\n",
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"0 point differential = 50% win game = 50% win series\n",
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"1 point differential = 54% win game = 58% win series\n",
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"2 point differential = 57% win game = 66% win series\n",
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"3 point differential = 61% win game = 73% win series\n",
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"4 point differential = 65% win game = 80% win series\n",
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"5 point differential = 68% win game = 85% win series\n",
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"6 point differential = 71% win game = 89% win series\n",
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"6 point differential = 72% win game = 89% win series\n",
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"7 point differential = 75% win game = 93% win series\n",
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"8 point differential = 78% win game = 95% win series\n",
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"9 point differential = 80% win game = 97% win series\n"
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"9 point differential = 81% win game = 97% win series\n"
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]
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}
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],
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@ -330,7 +330,7 @@
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"Rockets vs Wolves 89%; through here: 89%\n",
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"Rockets vs Jazz 78%; through here: 69%\n",
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"Rockets vs Warriors 69%; through here: 48%\n",
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"Rockets vs Raptors 57%; through here: 27%\n"
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"Rockets vs Raptors 58%; through here: 28%\n"
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]
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}
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],
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@ -351,9 +351,9 @@
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"Warriors vs Spurs 73%; through here: 73%\n",
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"Warriors vs Spurs 72%; through here: 72%\n",
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"Warriors vs Blazers 74%; through here: 54%\n",
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"Warriors vs Rockets 31%; through here: 17%\n",
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"Warriors vs Rockets 31%; through here: 16%\n",
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"Warriors vs Raptors 38%; through here: 6%\n"
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]
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}
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@ -374,13 +374,27 @@
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"\n",
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"# Series Length\n",
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"\n",
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"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:"
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"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:"
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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": 12,
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"metadata": {},
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"outputs": [],
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"source": [
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"import collections\n",
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"\n",
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"class MCounter(collections.Counter):\n",
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" \"A multipliable Counter: you can say `2 * MCounter(stuff)`.\"\n",
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" def __mul__(self, p): return MCounter({k: p * self[k] for k in self})\n",
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" __rmul__ = __mul__"
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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": 13,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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@ -401,9 +415,7 @@
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}
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],
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"source": [
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"from collections import Counter\n",
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"\n",
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"def series_results(p, W=0, L=0):\n",
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"def series_results(p, W=0, L=0) -> MCounter:\n",
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" \"\"\"Return {(win, loss): probability} for all possible outcomes of the series.\"\"\"\n",
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" return MCounter([(W, L)] if W == 4 or L == 4 else\n",
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" (p * series_results(p, W + 1, L) + \n",
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@ -417,12 +429,7 @@
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" for (W, L) in outcomes:\n",
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" results = [series_results(p)[W, L] for p in pcts]\n",
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" print('{}-{} | {}'.format(W, L, ' '.join(map(pct, results))))\n",
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" \n",
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"class MCounter(Counter):\n",
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" \"A multipliable Counter.\"\n",
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" def __mul__(self, p): return MCounter({k: p * self[k] for k in self})\n",
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" __rmul__ = __mul__\n",
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" \n",
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"\n",
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"series_results_table()"
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]
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},
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@ -430,9 +437,9 @@
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"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",
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"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",
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"\n",
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"**Note:** I think `Counter` should support multiplication. If `C` is a `Counter`, then shouldn't `C + C` be the same as `2 * C`?"
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"**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`?"
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]
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},
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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": 13,
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"execution_count": 14,
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"metadata": {
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"scrolled": true
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},
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@ -487,7 +494,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 14,
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"execution_count": 15,
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"metadata": {},
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"outputs": [
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{
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@ -511,7 +518,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 15,
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"execution_count": 16,
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"metadata": {},
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"outputs": [
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{
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@ -555,7 +562,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 16,
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"execution_count": 17,
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"metadata": {},
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"outputs": [
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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": 17,
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"execution_count": 18,
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"metadata": {},
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"outputs": [
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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": 18,
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"execution_count": 19,
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"metadata": {},
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"outputs": [
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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": 19,
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"execution_count": 20,
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"metadata": {},
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"outputs": [
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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": 20,
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"execution_count": 21,
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"metadata": {},
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"outputs": [
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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": 21,
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"execution_count": 22,
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"metadata": {},
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"outputs": [
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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": 22,
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"execution_count": 23,
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"metadata": {},
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"outputs": [
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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": 23,
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"execution_count": 24,
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"metadata": {},
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"outputs": [
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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": 24,
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"execution_count": 25,
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"metadata": {},
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"outputs": [
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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": 25,
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"execution_count": 26,
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"metadata": {},
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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": 26,
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"execution_count": 27,
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"metadata": {},
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"outputs": [
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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": 27,
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"execution_count": 28,
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"metadata": {},
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"outputs": [
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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": 28,
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"execution_count": 29,
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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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"0.967480202675441"
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"0.966301733"
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]
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},
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"execution_count": 28,
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"execution_count": 29,
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"metadata": {},
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"output_type": "execute_result"
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}
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