Match-Statistics.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Leela Zerozeug"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import sys\n",
    "import os\n",
    "import math\n",
    "\n",
    "import numpy as np\n",
    "import scipy.stats as stats\n",
    "\n",
    "import sqlite3\n",
    "\n",
    "from PIL import Image\n",
    "from IPython import display\n",
    "import matplotlib.pyplot as pyplot\n",
    "%matplotlib inline\n",
    "\n",
    "%load_ext autoreload\n",
    "%autoreload 2\n",
    "\n",
    "from src import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Leela Zero Training Match Database\n",
    "db_path = 'data/leela-zero.db'\n",
    "\n",
    "# Confidence Level for Hypothesis Tests\n",
    "alpha = 0.01"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Resignation Rate\n",
    "\n",
    "While scrutinising the *Leela Zero* web pages, I noticed what seemed like an alarmingly high resignation rate. How large, exactly?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "191383 of 200044 games (95.6705%) ended with resignation.\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "with sqlite3.connect(db_path) as sql:\n",
    "    count_games = sql.execute(\"SELECT COUNT(*) FROM Game\").fetchone()[0]\n",
    "    count_resignations = sql.execute(\"SELECT COUNT(*) FROM Game WHERE resign=1\").fetchone()[0]\n",
    "    \n",
    "print(\"{0} of {1} games ({2:.4%}) ended with resignation.\".format(count_resignations, count_games, (count_resignations / count_games)))\n",
    "\n",
    "pyplot.figure()\n",
    "pyplot.pie([count_resignations, count_games - count_resignations],\n",
    "           labels = ['resigned', 'scored'], colors = ['xkcd:fawn', 'xkcd:kiwi'], explode = (0.01, 0),\n",
    "           autopct = '%1.1f%%', shadow=False, startangle=70)\n",
    "pyplot.axis('equal')\n",
    "pyplot.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Well. I wonder why so many match games end prematurely. These games are played *without* Dirichlet noise."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Fairness Tests\n",
    "\n",
    "Here is a routine to test fairness using a *coin-toss* model in which various trials are modelled as *independent* Bernoulli trials."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def test_fairness(trials, p, successes, alpha, silent=False):\n",
    "    mu = trials * p\n",
    "    sigma = math.sqrt(trials * p * (1.0 - p))\n",
    "    delta = abs(mu - successes)\n",
    "    p_binomial = 2.0 * stats.binom.cdf(mu - delta, trials, p) if (delta > 0) else 1.0\n",
    "    p_normal = 2.0 * (1.0 - stats.norm.cdf((delta - 0.5) / sigma)) if (delta > 0) else 1.0\n",
    "    reject = (p_binomial < alpha)\n",
    "    \n",
    "    if not silent:\n",
    "        print(\"Expected number of successes after {0} Bernoulli trials (p = {1:.1%}): {2}\".format(trials, p, mu))\n",
    "        print(\"Observed successes after {0} Bernoulli trials: {1}\".format(trials, successes))\n",
    "        print(\"Probability of observing ≤ {0} or ≥ {1} successes: {2:.4%}    (binomial distribution)\".format((mu - delta), (mu + delta), p_binomial))\n",
    "        print(\"Probability of observing ≤ {0} or ≥ {1} successes: {2:.4%}    (normal approximation)\".format((mu - delta), (mu + delta), p_normal))\n",
    "        if reject:\n",
    "            print(\"At an α = {0} confidence level, we REJECT the null hypothesis that p = {1}.\".format(alpha, p))\n",
    "        else:\n",
    "            print(\"At an α = {0} confidence level, we have insufficient evidence to reject the null hypothesis that p = {1}.\".format(alpha, p))\n",
    "            \n",
    "    return reject"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As a sanity check, let's apply the test to the scraped data in the simplest way imaginable. It is immediately apparent that the *nigiri* procedure is, at least, unbiased.\n",
    "\n",
    "<span style=\"color: red;\">(For all following tests, unless otherwise stated, it is assumed that *nigiri* is fair and that the stronger and weaker networks get equal opportunities to play as both colours within the scope of a match.)</span>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "In 99895 of 200044 games (49.9365%), the challenger took black.\n",
      "\n",
      "Expected number of successes after 200044 Bernoulli trials (p = 50.0%): 100022.0\n",
      "Observed successes after 200044 Bernoulli trials: 99895\n",
      "Probability of observing ≤ 99895.0 or ≥ 100149.0 successes: 57.1623%    (binomial distribution)\n",
      "Probability of observing ≤ 99895.0 or ≥ 100149.0 successes: 57.1623%    (normal approximation)\n",
      "At an α = 0.01 confidence level, we have insufficient evidence to reject the null hypothesis that p = 0.5.\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "with sqlite3.connect(db_path) as sql:\n",
    "    count_games = sql.execute(\"SELECT COUNT(*) FROM Game\").fetchone()[0]\n",
    "    count_challenger_as_black = sql.execute(\"SELECT COUNT(*) FROM Game\"\n",
    "                                            \" JOIN Match ON Game.match_id = Match.id\"\n",
    "                                            \" WHERE Game.black = Match.challenger\").fetchone()[0]\n",
    "    \n",
    "print(\"In {0} of {1} games ({2:.4%}), the challenger took black.\".format(count_challenger_as_black, count_games, (count_challenger_as_black / count_games)))\n",
    "print()\n",
    "\n",
    "test_fairness(count_games, 0.5, count_challenger_as_black, alpha)\n",
    "\n",
    "pyplot.figure()\n",
    "pyplot.pie([count_challenger_as_black, count_games - count_challenger_as_black],\n",
    "           labels = ['black', 'white'], colors = ['lightcoral', 'lightskyblue'], explode = (0.01, 0),\n",
    "           autopct = '%1.4f%%', shadow=False, startangle=70)\n",
    "pyplot.axis('equal')\n",
    "pyplot.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, let's test the assumption that *komi*, alone, makes the game of *Go* fair. Let's be naïeve and consider only global totals, weighting game results equally, regardless of the match in which they were played or the network that played them."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Black won 88362 games; white won 111682.\n",
      "\n",
      "Expected number of successes after 200044 Bernoulli trials (p = 50.0%): 100022.0\n",
      "Observed successes after 200044 Bernoulli trials: 88362\n",
      "Probability of observing ≤ 88362.0 or ≥ 111682.0 successes: 0.0000%    (binomial distribution)\n",
      "Probability of observing ≤ 88362.0 or ≥ 111682.0 successes: 0.0000%    (normal approximation)\n",
      "At an α = 0.01 confidence level, we REJECT the null hypothesis that p = 0.5.\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "with sqlite3.connect(db_path) as sql:\n",
    "    (black_victories, white_victories) = sql.execute(\"SELECT SUM(case [victor] when 1 then 1 else 0 end) as [black], SUM(case [victor] when 2 then 1 else 0 end) as [white] FROM Game\").fetchone()\n",
    "    \n",
    "print(\"Black won {0} games; white won {1}.\".format(black_victories, white_victories))\n",
    "print()\n",
    "\n",
    "test_fairness((black_victories + white_victories), 0.5, black_victories, alpha)\n",
    "\n",
    "pyplot.figure()\n",
    "pyplot.pie([black_victories, white_victories],\n",
    "           labels = ['black', 'white'], colors = ['lightcoral', 'lightskyblue'], explode = (0.01, 0),\n",
    "           autopct = '%1.4f%%', shadow=False, startangle=70)\n",
    "pyplot.axis('equal')\n",
    "pyplot.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "That's interesting: white appears to be favoured and the margin appears to be statistically significant. Taken by itself, this result could be enough to conclude that *Leela Zero* prefers white although it gives no indication of *why* this might be the case. The model used and the data-selection criteria are extremely naïeve, however -- we need to go deeper!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Fairness Tests: Matches\n",
    "\n",
    "Let's restrict the query to the thirty most recent, completed matches -- about 30% of the available data -- and also repeat the hypothesis test for each match, independently."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def present_match_black_white_win_rate(query, title, history = 30):\n",
    "    match_count = 0\n",
    "    match_black_victories = []\n",
    "    match_white_victories = []\n",
    "    match_dates = []\n",
    "    match_rejects = []\n",
    "    total_black_victories = 0\n",
    "    total_white_victories = 0\n",
    "    black_rejects = 0\n",
    "    white_rejects = 0\n",
    "\n",
    "    with sqlite3.connect(db_path) as sql:\n",
    "        cursor = sql.execute(query + \" LIMIT ?\", [history])\n",
    "\n",
    "        for r in cursor:\n",
    "            (match_id, start_date, black_victories, white_victories) = r\n",
    "            total_black_victories += black_victories\n",
    "            total_white_victories += white_victories\n",
    "\n",
    "            reject = test_fairness((black_victories + white_victories), 0.5, black_victories, alpha, silent=True)\n",
    "            if (reject) and (black_victories > white_victories):\n",
    "                black_rejects = black_rejects + 1\n",
    "            elif (reject) and (white_victories > black_victories):\n",
    "                white_rejects = white_rejects + 1\n",
    "\n",
    "            match_count = match_count + 1\n",
    "            match_black_victories.append(black_victories)\n",
    "            match_white_victories.append(white_victories)\n",
    "            match_dates.append(start_date)\n",
    "            match_rejects.append((max(black_victories, white_victories) + 10) if reject else None)\n",
    "\n",
    "    print(\"Black won {0} games; white won {1}.\".format(total_black_victories, total_white_victories))\n",
    "    print()\n",
    "\n",
    "    test_fairness((total_black_victories + total_white_victories), 0.5, total_black_victories, alpha)\n",
    "\n",
    "    pyplot.figure()\n",
    "    pyplot.pie([total_black_victories, total_white_victories],\n",
    "               labels = ['black', 'white'], colors = ['lightcoral', 'lightskyblue'], explode = (0.01, 0),\n",
    "               autopct = '%1.4f%%', shadow=False, startangle=70)\n",
    "    pyplot.axis('equal')\n",
    "    pyplot.show()\n",
    "\n",
    "    match_index = np.arange(match_count)\n",
    "\n",
    "    pyplot.figure(figsize=(12, 6))\n",
    "    pyplot.bar(match_index, match_black_victories, 0.4, color='lightcoral', label='black')\n",
    "    pyplot.bar(match_index + 0.4, match_white_victories, 0.4, color='lightskyblue', label='white')\n",
    "    pyplot.scatter(match_index + 0.2, match_rejects, marker='x', color='red')\n",
    "\n",
    "    pyplot.suptitle('Black-White Win-Rates')\n",
    "    pyplot.title(title.format(history))\n",
    "    pyplot.ylabel('victories')\n",
    "    pyplot.xticks(match_index + 0.2, match_dates, rotation=90)\n",
    "    pyplot.legend(bbox_to_anchor=(1.11, 1.0), loc='upper right', borderaxespad=0)\n",
    "    pyplot.show()\n",
    "\n",
    "    print()\n",
    "    print(\"Data from {0} of {1} recent matches proved sufficient to reject the null hypothesis at α = {2}.\".format(sum(r is not None for r in match_rejects), len(match_rejects), alpha))\n",
    "    print(\"{0} of these matches favoured black; {1} of these favoured white.\".format(black_rejects, white_rejects))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Black won 4881 games; white won 5376.\n",
      "\n",
      "Expected number of successes after 10257 Bernoulli trials (p = 50.0%): 5128.5\n",
      "Observed successes after 10257 Bernoulli trials: 4881\n",
      "Probability of observing ≤ 4881.0 or ≥ 5376.0 successes: 0.0001%    (binomial distribution)\n",
      "Probability of observing ≤ 4881.0 or ≥ 5376.0 successes: 0.0001%    (normal approximation)\n",
      "At an α = 0.01 confidence level, we REJECT the null hypothesis that p = 0.5.\n"
     ]
    },
    {
     "data": {
      "image/png": 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z+tKlNC0r498nnVRzENCDdHZFbvSJxpMZHzMRFXIu9Mv0CSJHHcV7l17KOxdfzL+GD6dfp06MO9HdEuOxd9/lmK5daearvfPXVFayYaN7ceyV69bx2pIldGvblh2bNaNi/Xo++fZbAP776ad0bfvTca2Pv/2WNZWV9P7FL2puG9C5My8tWsSaykrWVFby0qJFDOjceYvXevajjxhx4IF8n0zSxBgM7pSJB30UC4aXk4X/PrKVJkB32yGKgaYssi+nb/jpCxdycd++W9wWX7aMCW+8wdihQ/nwm2+4+MknMcaQSqX4U9++7FV9CtztwSBnTp2KMYYdmzXjn5tNV0x75x1O3G8/jPlpJfFOLVpweb9+HDFuHABX9O/PTi1a1Hz9xlmzuKxfP4wxDOjcmfHz53NoLMbvemY0Y5MrWiqdWz2ovh6lNJ6uqZdFCcfxAQm0naPXpIDOsWD4acCTk9tF4N5QwKeL+GZIUxbZ1ROVsRfNjQXDbVAZ51LdR5mlwVTI2aUrg3iTDubl3j7ReHI72yEKnQo5u+o+9UFs2fC1v/10tBVqrpWjAUnGVMjZpUL2niem9x/VBy2VzgdNW2RIhZxdXW0HkK1oqXT+qJAzpELOkoTjlAF72s4hW/j2scNOn0sWdt6TBlEhZ0iFnD17AE1th5AtPLS8zR5aKp0/neu/i2yLCjl7NH/sPTq7Ir92isaTGpRkQIWcPSpkb/koFgyvIAs770ladrEdoJCpkLNHhewtk4DT0VLpfGtnO0Ah014W2bOz7QBSI4W7d8UM20FKkAo5AxohZ8/Wl98QW16OBcNtgdqvcSW5pELOgAo5e1TI3qFzj+1RIWdAhZw9KmRvWL+szR6PoKXStqiQM6BCzh4Vsjc88fhhpx+Klkrb0t52gEKmQs4eFbI3aLrCLo2QM6BCzh4Vsn3fPnbY6a8Ax9sOUsJa1H8XqYsKOQsSjmOAHWznEB5c3maPE9BSaZt03ncGVMjZ0QL9IHqBlkrbp/dBBlTI2bHJdgDh9VgwvBLoW+89JZdUyBlQIWeBPxKpRKVs2xXANagQbNO/fwZUyNnzve0AJeypWDBcAYywHUTYaDtAIVMhZ48K2Y4q4ErgZjQ684L1tgMUMhVy9qyzHaBE3RsLhvcAjrQdRAAVcka021v2qJDz7/v1vmYR4BnbQaSGCjkDGiFnj6Ys8u/Wfw++5Ghgf9tBpMYG2wEKmUbI2aMRcn59s7Bjj9uBuO0gsoVvbAcoZBohZ893tgOUmGvmHDDoXGA320FkC4ttByhkGiFnz5e2A5SQj6f2P3sa8KHtILIVFXIGNELOnkW2A5SQMSv97cJAK9tBZCsq5AxohJw9KuT8mBcLhhcAU2wHkVotsR2gkGmEnD2f2g5QIi4HbgB8toPIVjaiqbuMqJCzRyPk3HssFgwngZNsB5FafRkK+KpshyhkKuQs8Ucia9EpP7m0EQjhLpEWb9L8cYZUyNmlaYvcGR8LhrsB/WwHkTqpkDOkQs4uTVvkxndrm7e6BojaDiLbpELOkAo5uz6xHaBI3TJ54O+PB/a2HUS2aYHtAIVOp71l1xu2AxShFfO79bsTeMt2EKnXPNsBCp1GyNn1CpCyHaLIXP1mt76jgV1tB5Ft+jIU8GnKIkMq5CzyRyIrgQ9s5ygiH0wc+IfHcc899qwbh3ThtpMD/OPUntxx2iEAPH1riL//Zj9uP7kHky4dTuXaNXU+flNVFf8Y0Yt7/zis5rZXHryTm4N7M6ZHU9at/rbm9vdmPs7tJ/eoea3P43NrvvbmExO5Zeg+3DJ0H958YiIAG3/YwIQLj+O2k7ozb+pdNfd95K+j+fKDrO7LpNFxFmjKIvteRnOd2RJa17zlX4AdbAepz7l3P8/2O+1c8/dfHTKAY/5wLWXl5Txz+xhmTriRwRfdUOtj504Zyy6d9mL9d2trbuvYvQ979zuWcecO3OK+nXsfyd79j8cYw/KP3mZKaCSXPLKQ7xOreHHcdfx+8jyMMYw97RD26X88n8VfZre9A5w19nHuGNmbPiefz/KP3iKV2kSHvQLZ/CdQIWeBRsjZN7f+u0gDzIkFwx8A59gO0hhd+wykrNwd7+yx/8Ekvl5W6/0SXy3lwznP0GvYqC1u77BXgJ06dNzq/tu12AFj3CtV/VD5PT9eteqjec/R5eABtPC3pnmrnehy8AA+fOVZysp9JDesZ1PVT5e6e/7Oqxk4OpKF73ILKuQsUCFn38u2AxSJy3FPc/P8b3HGGCZceCxjRx7M/Onjt/r6G/+5l26HHlPrY5+85VIGX3QDpknD34rvvvQYf//Nftx30VBOjNwDQMXXX+Jvv3vNfVq1242Kr7/kVwcfxXcrV3DnmYfR77eX8t6sJ+iwdw9ate2Q5ne5TT8Ab2bzCUuV53/YC40/ElmUcJwVQHvbWQrYw7FguBwYVu89PeD8f8+kVdsOfLfqa/41ejBtO3aj00GHA/Df8TfQpLyc7seO3Opx789+iu1b78Ju+/Tg0zdmNfj19j1yGPseOYzP3pzD87GrOeeuGZDa+liyMYay8nJOvX4SAFXJJBMuHMKZtz3Ck3+7nMSKxQSOO519+h/fyO+8RjwU8OlKIVmgEXJuaNqi8ZLAGApoifSPo80dWu/CvkcMZcm7rwPuQbb35zzNKddOrJlm2NwXb73C+7Oe5MYhXZgy5nQ+feO/PHTVbxv8up0OOpxVSz9l3epvadVuNxIrltZ8reKrZbRsu+WJKa8+fBc9jj+dxW+/SrnPx4joA/x3fO3z2mnSdEWWqJBzY7btAAXsrlgw3B3oYztIQ/xQuY4N69bWfP7xqy/QrvO+fDj3WWbfewtn3vYITZu3qPWxg/5wHWNmfMaVT33MiBsms2fPIzjluvu2+XrfLv6EVPVoeNn7caqSP9BixzZ07XM0H7/6ApUVq6msWM3Hr75A1z5H1zyusmI1H8x5mh7HnUFy/fcY0wSMYeOGrFyTVNN0WaIpi9x4ArjddogCVLGq5c7XAXNsB2mo71Z+xaRL3c3nNlVtpPugU+l22DHcHNybquQGJoweDMAv9j+YE676JxXffMn0a87nd2Mf3+bzzp1yB7Pv+xvfrVzB7accRLe+gzjxL3fz7kuP8r8nJ1NW7qN8u+aMiN6PMYYW/tYceU6YO04/FIAjz72KFv7WNc/34rjrOOKcMRhj6NLnaOZNvYvbTw5w8PDzMv0nqARmZPok4jKpWuaeJHMJx1kAHGg7R4G5KhYMJ4A7bAeRBnskFPCdaDtEsdAIOXceRYWcjmUzDxx8D7DQdhBJy1TbAYqJ5pBz51HbAQrMX97/ZeCPwC62g0iDVQJP2g5RTFTIOeKPRN5GV0VuqIX/GnTJs8AltoNIWp4JBXzrbIcoJirk3HrAdoACceUPTZs5QO2nI4hXaboiy1TIuaVCrt9LsWD4C+As20EkLZquyAEVcg75I5FPgNdt5/CwFHAFcCNQZjmLpEfTFTmgQs69e20H8LAHY8FwS2CI7SCSNk1X5IAKOffuA1bbDuFBGzY2KQsDN9kOImlbCWx7ZYs0igo5x/yRyDrgHts5POif9xx35SFAL9tBJG33hAK+StshipEKOT/GAhvrvVfpWL105443AtfZDiJp2wj803aIYqVCzgN/JLIUeNh2Dg+54YlDR44E9rQdRNL2aCjgW1r/3aQxVMj5c6vtAB7xxTO9h98L/Nl2EGmUjDfNMsZ8V8ft5xtjzqz+/CxjTFZ30S8EKuQ88Ucir6N9kgH+7/P2XS8F2tgOIml7ORTw5exnOJVK3ZVKpSZW//UsQIUsOVXqo+QF44ZcMRO4yHYQaZQG7WZvjLnCGPPH6s9vNca8VP35AGPM5OrPrzPGvGWMedUY0676tquNMZcZY4YDPYH7jTELjDHNjTEHGWNmGWPeNMY8a4zZta7XL2Qq5Px6FFhkO4RFl1eVlf8VaGY7iKTtrVDA93QD7zsbOLz6857ADsYYH9AXd6/r7YFXU6nUgdX3PXfzB6dSqWnAG8BpqVSqO+6BxLHA8FQqdRAwgSI9IKxCziN/JLIJCNvOYclzsWD4G+AM20GkUaJp3PdN4CBjTEtgA+4lnnrilvQc3IuiPrnZfTvW83zdgP2A540xC3CPP+y+7YcUJhVynvkjkanAK7Zz5Nkm3CXSN6GfuUL0NmmcJZRKpZLA58DvcH/W5wBHAJ2B94Fk6qcrY1RR/77sBng3lUp1r/7YP5VKHV3PYwqS3hx2XIK7j0OpmBwLhncBivJNVAL+GAr4qtJ8zGzgsuo/5wDnAwtSDb9E0VqgZfXnHwJtjTF9AIwxPmPMvmnmKQgqZAv8kchrwEO2c+TJ+o1Nyv+MlkgXqodDAd+sRjxuDrArMC+VSn0FrCe9ayXeC9xVPUVRBgwHbjTGvAUsAA5tRCbP0zX1LEk4TkfgA2A7u0ly7qZYMLwQmFjvPcVrKoG9QgHfYttBSoVGyJb4I5HPKf4rU69ctGu3W4BrbQeRRrlRZZxfKmS7rgO+sR0ih659rteJZwF72A4iaVuMppnyToVskT8SqQCusp0jRz599LAzplC6p/kVusu0o1v+qZAt80ci9wDP2c6RA1etaPOLK4AdbQeRtM0MBXzaDMsCFbI3jKK4NrF//e4hV7wKXGg7iKRtI1rabo0K2QP8kcgyiqu8rthUVn4dxX8GSTH6Syjge9t2iFKlQvYIfyQyheI4N/mpWDC8FhhhO4ik7UXcC86KJSpkb7kA+NJ2iAxUAVcCN+Mud5XC8Q1wRijg22Q7SClTIXuIPxJZBZxtO0cG7o0Fw7/E3bdACkcK+G0o4FtuO0ipUyF7jD8SmQHcZTtHI3y/3tcsgn7lLUS3hgK+Z2yHEBWyV10MzLcdIk23/nvwJcfgbpMoheNNYIztEOJSIXuQPxJZDwwFCuVikt8s7NjjduAa20EkLWuBU0MB3w+2g4hLhexR/khkBXA8sM52lga4Zs4Bg84FdrMdRNIyOhTwfWI7hPxEhexh/khkAe4VNry8Jd/HU/ufPQ337AopHH8NBXz32w4hW1Ihe5w/EnkU95I1XjVmpb9dGGhlO4g02D2hgO8vtkPI1lTIBcAfiVwPTLadoxbzYsHwAtyrQUhheBwYbTuE1E6FXDjOwXvX4rsc99LwPttBpEFewT2Il+7lmCRPVMgFwh+JbACGAK/bzlLtsVgwnAROsh1EGuQ94DhtqeltKuQC4o9E1gADsX+O8kYghLtEWrxvKTAoFPAV046CRUmFXGD8kUgCt5RftRhjfCwY7gb0s5hBGmY1bhkvsR1E6qdCLkDVVxo5Bphn4eW/W9u81TVoiXQhWA0MDgV879oOIg2jQi5Qm5Vyvg/03TJ54O+DwF55fl1Jzwqgfyjge812EGk4FXIB80cia3FL+eU8veSK+d363QlcnafXk8b5HDg8FPC9YzuIpEeFXOD8kch3wGDc80tz7eo3u/W9AGifh9eSxnkX6Ksl0YVJhVwEqkv5BNxzgnPlg4kD//A4cFkOX0My8xJwWCjgW2Y7iDSOSaW8vE2CpCvhOCOAfwHNs/zUw2LB8CC0Ks+rJgLnhAK+pO0g0ngq5CKUcJyewGNkb/e1ObFg+FxgIVCepeeU7LkmFPBFbIeQzGnKogj5I5E3gF5Ato6wXwZEURl7zUpgqMq4eKiQi5Q/ElkO/BqYlOFTPRwLhn3AsIxDSTbNAg4MBXz5OJgreaJCLmL+SGS9PxI5EzgLSDTiKZK4l/fREmnvqAIiwJE6eFd8NIdcIhKOszswHve85YYaGwuGZwHTcpNK0rQUGBkK+ObYDiK5oUIuMQnHOQ/4G7BDPXet+Nrfvtv0/qNmA11yn0zq8R9gVCjgW2U7iOSOCrkEJRynEzABd465LlfFguEKYGxeQkldKoErQgHfHbaDSO5pDrkE+SORz4AjgYtw3/A/t2zmgYPvAXSZH7umAnupjEuHRsglrnq0fCNbbjR/diwY3hO4yk6qkvc28MdQwDfLdhDJLxWyAJBwnL7ArUCzfw26ZNAPTZt9BLSwHKvUrAL+D7hbl1kqTZqyEAD8kcjLQG/gmB+aNjsPlXE+VQH/BLqEAr47VcalSyNk2Uo0njTACMABfmU5TrF7CfiTtsplqkcuAAAB4UlEQVQUUCHLNkTjyXJgFO7BvWztiyGwCXgUuCUU8Nm8FJd4jApZ6hWNJ7cDTgZ+jzutIY3zPfBv4NZQwLfIdhjxHhWypCUaT/YCLgROAZpZjlMovgLuAO7Uwg7ZFhWyNEo0nmwDnAOMBn5pOY5XfQD8HZgYCvg22A4j3qdCloxE48kmwHG4o+aj0Jk7X+Mu6Lhf88OSLhWyZE00ntwFGAIEgYHA9nYT5c1q4AlgCvBCKODbaDmPFCgVsuRENJ5sBgwAjq/+6GA3UdYtxb0qy2PALJWwZIMKWXKu+rzmg3CLeTBwINDUaqj0fQTMq/54BVgYCvj05pGsUiFL3kXjSR+wH9Bjs48D8M7qwHXAfH4q4HmhgG+l3UhSClTI4gnReLIM6MZPBb0vsDvughR/Dl6yAlhcy8e7wDtaviw2qJDF86Lx5A64xdweaFP90br6YwfcvSA2Vn9U/ezPHz9fCyyhunhDAV9jLmklklMqZBERjyj1c0ZFRDxDhSwi4hEqZBERj1Ahi4h4hApZRMQjVMgiIh6hQhYR8QgVsoiIR6iQRUQ8QoUsIuIRKmQREY9QIYuIeIQKWUTEI1TIIiIeoUIWEfEIFbKIiEeokEVEPEKFLCLiESpkERGPUCGLiHjE/wO9GPQ6lNig4wAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Data from 3 of 30 recent matches proved sufficient to reject the null hypothesis at α = 0.01.\n",
      "0 of these matches favoured black; 3 of these favoured white.\n"
     ]
    }
   ],
   "source": [
    "query = \"\"\"\n",
    "SELECT Game.match_id, Match.start_date, SUM(case [victor] when 1 then 1 else 0 end) as [black], SUM(case [victor] when 2 then 1 else 0 end) as [white]\n",
    " FROM Game\n",
    " JOIN Match ON Game.match_id = Match.id\n",
    " WHERE Match.result is not null\n",
    " GROUP BY Game.match_id, Match.start_date\n",
    " ORDER BY Match.start_date DESC\n",
    "\"\"\"\n",
    "present_match_black_white_win_rate(query, '(last {0} matches)')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Black won 5440 games; white won 6562.\n",
      "\n",
      "Expected number of successes after 12002 Bernoulli trials (p = 50.0%): 6001.0\n",
      "Observed successes after 12002 Bernoulli trials: 5440\n",
      "Probability of observing ≤ 5440.0 or ≥ 6562.0 successes: 0.0000%    (binomial distribution)\n",
      "Probability of observing ≤ 5440.0 or ≥ 6562.0 successes: 0.0000%    (normal approximation)\n",
      "At an α = 0.01 confidence level, we REJECT the null hypothesis that p = 0.5.\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Data from 6 of 30 recent matches proved sufficient to reject the null hypothesis at α = 0.01.\n",
      "0 of these matches favoured black; 6 of these favoured white.\n"
     ]
    }
   ],
   "source": [
    "query = \"\"\"\n",
    "SELECT Game.match_id, start_date, SUM(case Game.victor when 1 then 1 else 0 end) as [black], SUM(case Game.victor when 2 then 1 else 0 end) as [white]\n",
    " FROM Game\n",
    " JOIN Match ON Match.id = Game.match_id\n",
    " JOIN Network challenger ON challenger.id = Match.challenger\n",
    " WHERE challenger.promoted\n",
    " GROUP BY Game.match_id\n",
    " ORDER BY start_date DESC\n",
    "\"\"\"\n",
    "present_match_black_white_win_rate(query, '(last {0} matches that resulted in promotion)')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Fairness Tests: Networks\n",
    "\n",
    "Do individual networks have a predilection for white? Let's take a look at the data. We must turn to [Fischer's Exact Test](https://en.wikipedia.org/wiki/Fisher's_exact_test) and ask a new question: does *Leela Zero* win more, as white, than she does as black?\n",
    "\n",
    "The *null hypothesis* becomes the following: the win-rate of a network is not significantly higher when *Leela Zero* plays as white."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "def present_network_black_white_win_rate(query, title, history = 30):\n",
    "    network_count = 0\n",
    "    network_black_victories = []\n",
    "    network_white_victories = []\n",
    "    network_hashes = []\n",
    "    network_rejects = []\n",
    "\n",
    "    with sqlite3.connect(db_path) as sql:\n",
    "        cursor = sql.execute(query + \" LIMIT ?\", [history])\n",
    "\n",
    "        for r in cursor:\n",
    "            (network_id, upload_date, black_games, black_victories, white_games, white_victories) = r\n",
    "            \n",
    "            contingency = [[black_victories, white_victories],\n",
    "                           [black_games - black_victories, white_games - white_victories]]\n",
    "            (_, p) = stats.fisher_exact(contingency, alternative='less')\n",
    "            reject = (p < alpha)\n",
    "\n",
    "            network_count = network_count + 1\n",
    "            network_black_victories.append(black_victories)\n",
    "            network_white_victories.append(white_victories)\n",
    "            network_hashes.append(network_id[0:8])\n",
    "            network_rejects.append((max(black_victories, white_victories) + 50) if reject else None)\n",
    "\n",
    "    domain = np.arange(network_count)\n",
    "\n",
    "    pyplot.figure(figsize=(12, 6))\n",
    "    pyplot.bar(domain, network_black_victories, 0.4, color='lightcoral', label='black')\n",
    "    pyplot.bar(domain + 0.4, network_white_victories, 0.4, color='lightskyblue', label='white')\n",
    "    pyplot.scatter(domain + 0.2, network_rejects, marker='x', color='red')\n",
    "\n",
    "    pyplot.suptitle('Black-White Win-Rates')\n",
    "    pyplot.title(title.format(history))\n",
    "    pyplot.ylabel('victories')\n",
    "    pyplot.xticks(domain + 0.2, network_hashes, rotation=90)\n",
    "    pyplot.legend(bbox_to_anchor=(1.11, 1.0), loc='upper right', borderaxespad=0)\n",
    "    pyplot.show()\n",
    "\n",
    "    print()\n",
    "    print(\"Data from {0} of {1} networks proved sufficient to reject the null hypothesis at α = {2}.\".format(sum(r is not None for r in network_rejects), len(network_rejects), alpha))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's look at the most recent promoted networks and, for intrigues sake, the most recent failed challengers."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Data from 25 of 30 networks proved sufficient to reject the null hypothesis at α = 0.01.\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Data from 3 of 30 networks proved sufficient to reject the null hypothesis at α = 0.01.\n"
     ]
    }
   ],
   "source": [
    "query = \"\"\"\n",
    "SELECT Network.id, Network.upload_date,\n",
    " SUM(case when Network.id = Game.black then 1 else 0 end) as black_games,\n",
    " SUM(case when victor = 1 and Network.id = Game.black then 1 else 0 end) as black_victories,\n",
    " SUM(case when Network.id = Game.white then 1 else 0 end) as white_games,\n",
    " SUM(case when victor = 2 and Network.id = Game.white then 1 else 0 end) as white_victories\n",
    " FROM Network\n",
    " JOIN Game on Game.black = Network.id OR Game.white = Network.id\n",
    " WHERE Network.promoted={0}\n",
    " GROUP BY Network.id\n",
    " ORDER BY Network.upload_date DESC\n",
    "\"\"\"\n",
    "\n",
    "present_network_black_white_win_rate(query.format(1), '(last {0} promoted networks)')\n",
    "present_network_black_white_win_rate(query.format(0), '(last {0} failed challengers)')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Fairness Tests: Self-Play Games"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "def present_self_play_black_white_win_rate(query, title, history = 30):\n",
    "    data_count = 0\n",
    "    data_black_victories = []\n",
    "    data_white_victories = []\n",
    "    data_ticks = []\n",
    "    data_rejects = []\n",
    "    total_black_victories = 0\n",
    "    total_white_victories = 0\n",
    "\n",
    "    with sqlite3.connect(db_path) as sql:\n",
    "        cursor = sql.execute(query + \" LIMIT ?\", [history])\n",
    "\n",
    "        for r in cursor:\n",
    "            (id, upload_date, black_victories, white_victories) = r\n",
    "            total_black_victories += black_victories\n",
    "            total_white_victories += white_victories\n",
    "\n",
    "            reject = test_fairness((black_victories + white_victories), 0.5, black_victories, alpha, silent=True)\n",
    "\n",
    "            data_count = data_count + 1\n",
    "            data_black_victories.append(black_victories)\n",
    "            data_white_victories.append(white_victories)\n",
    "            data_ticks.append(id[0:8])\n",
    "            data_rejects.append((max(black_victories, white_victories) + 400) if reject else None)\n",
    "\n",
    "    print(\"Black won {0} games; white won {1}.\".format(total_black_victories, total_white_victories))\n",
    "    print()\n",
    "\n",
    "    test_fairness((total_black_victories + total_white_victories), 0.5, total_black_victories, alpha)\n",
    "\n",
    "    pyplot.figure()\n",
    "    pyplot.pie([total_black_victories, total_white_victories],\n",
    "               labels = ['black', 'white'], colors = ['lightcoral', 'lightskyblue'], explode = (0.01, 0),\n",
    "               autopct = '%1.4f%%', shadow=False, startangle=70)\n",
    "    pyplot.axis('equal')\n",
    "    pyplot.show()\n",
    "\n",
    "    data_index = np.arange(data_count)\n",
    "\n",
    "    pyplot.figure(figsize=(12, 6))\n",
    "    pyplot.bar(data_index, data_black_victories, 0.4, color='lightcoral', label='black')\n",
    "    pyplot.bar(data_index + 0.4, data_white_victories, 0.4, color='lightskyblue', label='white')\n",
    "    pyplot.scatter(data_index + 0.2, data_rejects, marker='x', color='red')\n",
    "\n",
    "    pyplot.suptitle('Black-White Win-Rates')\n",
    "    pyplot.title(title.format(history))\n",
    "    pyplot.ylabel('victories')\n",
    "    pyplot.xticks(data_index + 0.2, data_ticks, rotation=90)\n",
    "    pyplot.legend(bbox_to_anchor=(1.11, 1.0), loc='upper right', borderaxespad=0)\n",
    "    pyplot.show()\n",
    "\n",
    "    print()\n",
    "    print(\"Self-Play Data from {0} of {1} networks proved sufficient to reject the null hypothesis at α = {2}.\".format(sum(r is not None for r in data_rejects), len(data_rejects), alpha))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Black won 66780 games; white won 75160.\n",
      "\n",
      "Expected number of successes after 141940 Bernoulli trials (p = 50.0%): 70970.0\n",
      "Observed successes after 141940 Bernoulli trials: 66780\n",
      "Probability of observing ≤ 66780.0 or ≥ 75160.0 successes: 0.0000%    (binomial distribution)\n",
      "Probability of observing ≤ 66780.0 or ≥ 75160.0 successes: 0.0000%    (normal approximation)\n",
      "At an α = 0.01 confidence level, we REJECT the null hypothesis that p = 0.5.\n"
     ]
    },
    {
     "data": {
      "image/png": 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y8N9B+PADHzvkEGKHeDMf786YwX0ffMCAY73Dql+YOpXDd9yRRqF1X1V3cLt23PjmmyxctgyAsd98Q+zgg9mkrIyz9tgDgO9++YWThg7l1TO9bZq3aNqU92bOZP+2bRk3Ywbbt2gBQO8OHXj44485tmNHJsyeTbONNlqrkN+bOZMtmzalXYsWLE2lKDKG4qIilqZS6f4VZMITwHO2Q+Shg+OJVKNoOLTcdpBcp0L2X9rTFbUZMWUKl3XvvtbHEnPmMGjCBO496ig2KSvjqh49OGjAAACuPuAANinb8GtYdx95JNFRo1i1ejWNSkq4+0jvmv/D2rdn9PTphO+5h7JQiPuP+n1xluu63D5uHI8d713hd0bXrpxTfSncHX37+vkl++G/lZGKJkBH20HyUBnQjbVPcpcG0CGnPks6zjRgR9s5pIYLKyMV7YDLbQfJUxdFw6H7bYfIdRoh+yjpOM1QGQdRKlnW/FngU9tB8pi24/SBXtzw1y62A8g6vTb0kAu6oqXSmRT4C9BzgQrZXyrkYNJS6czrGE+kdKp6mlTI/trVdgCpYeGY3SNvAUfbDpLnGgPrvg5T6kyF7C+NkIPnmelbdzwSLZXOBk1bpEmF7C8VcvAMRtMV2aIX9tKkQvZJ0nGaAtvYziFr+bYyUjETb7GOZJ5GyGlSIfun5gYRYtsQ4K/o+zxbVMhp0jeqf1TIwaOrK7KrdTyRCvRm2EGnQvaPrnENlo8qIxVN0ZUv2dbSdoBcpkL2TwvbAWQtGh3boUJOg5ZO+2dT2wFkjZULm2zyDPCZ7SAFSIWcBo2Q/aMRcnC89tTB53dD00g2qJDToEL2j0bIwfEEcLrtEAVKhZwGFbJ/NEIOhl9e2/O4t9FSaVtUyGlQIftHI+RgeOa7LXaM4O2tINmnQk6DCtk/KuRg0FJpu1TIaVAh+yDpOI2AjWznEL6pjFT8DzjQdpACpkJOgwrZHzoHKxiGADpV2q5GtgPkMl2H7I9AHrFcgIYAL9gOUeBW2w6QyzSS8EF5LLYajZJte6EyUtESLZW2TYWcBo2Q/ZMCtLGKHctXFRVfDjxpO4iokNOhEbJ/NG1hz20P972mB7CP7SCiQk6HRsj+USHb8d3YLn3uBz61HUQAWGE7QC7TCNk/KmQ7Lp+2Teco0Mp2EAFgie0AuUwjZP+okLPvjcpIxZfAMNtBZA0VchpUyP5ZbjtAgUkB/YAH0PdxkKiQ06ApC/98bztAgbm7MlKxG9DTdhBZiwo5DRpZ+GeW7QAFZO4n2+/5b2CC7SBSw8+2A+QyjZD9M9t2gAJy9QcdD+kHtLEdRGr41naAXKYRsn80Qs6O9yojFR8Cj9gOIus0w3aAXKYRsn9UyJlXBVwE3IV21wsqFXIaVMj+0ZRF5j1UGanYGuhrO4is04JoOJS0HSKXacrCPxohZ9bPM1vtcCPwnu0gsl4aHadJI2T//AistB0ij/UfudcJZwE72A4i66UX9NKkQvZJeSzmohFCpkwc2PvykUCF7SCyQfr+T5MK2V8TbQfIQy5w0cpQo9uBJrbDyAZphJwmFbK/xtsOkIcer4xUNAZOsB1EaqURcpr0op6/VMj+Si5ssml/4HXbQaROPrMdINdphOyvBN61suKPG546+LwTgI62g0itvomGQ3Nth8h1KmQflcdiS4GptnPkialP9jxvGHCD7SBSJ+/aDpAPNGXhv/HAbrZD5IGLF2286c1Aue0gtbm1T3s2arIxRUXFFBWXcNGTH/HanVG+fPcViktK2bTN9hx3wyM0btq8xn3fH3ov458fiOu67HHMWXQ/tR8AYx68kfHPD6LJJi0BOOyim9ipe2+WLJzP0KtPYvbUCex+5OkcFb17zWN9+vozvDUwzurVVezUvTe9L40D8MHT9/PxiIcp32IbTrtjOCWhUmYm3mfK2Bfoe8W//fprUCH7QCNk/2keOX3PVEYqlgF/sx2krs55aDT9np7ARU9+BMAOex/MJc9M5pJnJtFym/a8PejWGvf54espjH9+IBcM/oB+T0/ky3df4+f/TV/z+f1O7Ue/pyfQ7+kJ7NS9NwChjRpx6Pk3cMRlaz/ekoXzee3uaznrode5bPgnLF7wI1//dywA458fRL9hk2jdoTPTP3gD13UZ+/DNHHyOr1cRqpB9oEL2nwo5PUtWhDa6CrgXMLbDNNSO+xxKcYn3C+g2nfYi+eOcGrf5acaXtOm0F6WNyyguKaFt1/2ZOvbFDT5uaeMmbBfej5LSRmt9fMGcGbTcpj0bb7IZADvs2ZMpY59f8/nVq1Kkli+jqCRE4tUhdOjei8bNNkn3y/zNvGg4NL32m0ltVMj++xRYZDtEDrt5UO8rDge62Q5SV8YYBl14BPeeshcfj6i5Cd2EFx+jw76H1/h4q3a7MmPSuyxZOJ+Vy5Yy7b1RJOf9viXKh8MqufuE3Rl+wzksW/TLBjO0bNOOn2ZO45fvZ1K1ahWfv/0SyR+81fz7n3YZD/ytO0t++YntuuzLpJeHsPfx56X5Va9Fo2OfGNd1bWfIO0nHGQ4caztHDvr6lb1P6j5r8+2nAC1th6mrRT99T7PNWvPrgh8ZeH5vIlffRduu+wPw1iO3MPuLifz19mcxpuaAf/wLj/LRM5WUNt6YzbffmdBGjel75e0snj+PJs1bgjGMfiDG4p9/4LgbHl5zv4kvDWb25xPXmkP+4p1XGDvwFowpYtvO+7Bgzrec9p/haz3fmIduonWHzmAMiVeGUN6qDUdcfhtFRWmNzS6JhkP3pPMA4tEIOTNesx0gR106a/PtryOHyhig2WatAdh4083Z9aCjmDXVm7Wa+PJgvnj3NU785+B1ljHAHkefycVDP+YfA8dS1mwTWmzjbdXRtEUrioqLKSoqYs+/nMXsqbXPhO18QF8uHPw+Fzz+LpttuyMt26y97cein75n9tSJ7HJghLceuYWT40MpKS3lm4/HpvPlg0bIvlEhZ8ZIvCW/UnevVkYqZgO+/i6daSuXLWHFksVr3p/+0RhatduVae+/zrjHbuf0u56jtHHZeu//64IfAVg4939MfesFuvQ6EYBFP/1+Se/UsS/Sqt2utWb57bGWLfqFj559kG7H/H2tz49+4AYOuyAGQGrFMjAGY4pILV9aj6+4hkV403TiA132lgHlsdjcpONMArrazpIjVgCXAI8BxXaj1M+v8+fxxBXHA7C6ahVdep1Eh/0O59+RnalKrWDQ+d7VEW067cUx/e9n0U/fM+LG8zjz3pcAePLKE1manE9RSYjINfeseaFt5N3XMverTzAYNmm9LUf3f2DNc97apz0rliyiKrWSz99+ib8/8Cqttt+Fl/99OT985XVjz3P7s9m2O665z/dfJgBovVMYgG5HncndJ4Qpb9WGg/9xXTp/Ba9GwyEthvKJ5pAzJOk4/YF/2s6RI26ujFR8DgyxHUTq7choOPSK7RD5QlMWmTPCdoAcMevdTofdDfi2QkGyZj7aZ8RXKuQMKY/FvgS+sJ0jB1wxpW23K4EtbQeRehseDYdStkPkExVyZg2v/SYFbWxlpOJT4FLbQaRBhtoOkG9UyJn1OLraYn1WARcD9wAhy1mk/mahy918p0LOoPJY7BvgDds5Auq+ykhFB+Aw20GkQZ6OhkMabPhMhZx5D9R+k4Iz7/Ntu9wC3GE7iDSYpisyQIWcea8C/7MdImCi73Q+4gJgO9tBpEG+iIZDk22HyEcq5Awrj8WqgAG2cwTIhw/1ufod4BrbQaTBBtsOkK9UyNnxCKDLg2A1cNHq4pI7gEa13VgCaQnwkO0Q+UqFnAXlsdg84Plab5j/HqmMVGwGHG07iDTYoGg4tOG9QKXBVMjZU+gv7i2Y13zL64G7a72lBFUVcJftEPlMhZwl5bHYOxT2aSLXPdfjzL8BHWwHkQZ7PhoOfWs7RD5TIWdXf9sBLJk8sNflLwJpbSsm1t3ix4MYY35dz8fPM8acXv3+GcaY1n48Xy5RIWdReSw2GnjLdg4LLlpZ2ug2YGPbQaTBXomGQ5My+QSu6z7ouu5vV3CcAaiQJeMKbZQ8pDJSUQScYjuIpMWp6w2NMVcbY/pVv3+nMWZs9fsHG2OGVL//L2PMJ8aYj4wxrao/doMx5kpjzHF4Zyo+aYyZbIxpbIzpaox5xxgz0RjzujEmLzejUiFnWXks9iFQKPvHLv61UdMo3gnSkrtei4ZDE+px+3HA/tXvdwM2NsaEgO54+180AT5yXbdz9W3P+eOdXdcdDkwATnVdtwvevif3Ase5rtsVGAT8K42vJ7B0Yogd/YE+5PAx93V04xOHXXwM0Nl2EGkwF7ihnveZCHQ1xjTFOw1mEl4x7w/0A1by+6BkInBoLY/XAegIjK4+m7AYmLvBe+QojZAtKI/FPgWG2c6RYV8+c8BZQ4AbbQeRtAyKhkP1ujrIdd0UMBM4E/gAb1R8ENAOb4/wlPv7UUVV1D4wNMBU13W7VL91cl03LzelUiHbcx3er2L5qt/88lY3AZvYDiINNp+GL3EfB1xZ/d938Q6vnezW/cy4xUDT6venAZsZY/YBMMaEjDG1n/qag1TIlpTHYl+TvxfZP1cZqfgF+Hutt5QguzYaDs1v4H3fxTsF5kPXdecBy6nf/smPAQ8aYybjTVEcB9xqjPkEmAzs28BcgaZDTi1KOk5j4DO8X+XyxbJVRcU7P9z3mmHAXrbDSIP9F9hHex5nl0bIFpXHYsv40yvMeSD+cN9reqIyzmVVwPkq4+xTIVtWHou9hbcbXD6Y8UbXYx4E4raDSFoqo+FQwnaIQqRCDoYrge9th/DBZd9stXMFsLntINJgPwD/ZztEoVIhB0B5LJYEzredI02jKiMV3wAX2g4iabkqGg4lbYcoVCrkgCiPxV4CnrGdo4FWApfgrabSYqPc9VI0HBpiO0QhUyEHy8XAj7ZDNMCdlZGKMHCg7SDSYDOAv9kOUehUyAFSHov9CJxAbi0YmTNhx/3uAG63HUQabAVwQjQcWmg7SKFTIQdM9Ub2uXQA6FXjdzrgUmBr20Gkwa6o5+ZBkiFaGBJQScd5CjjJdo5ajKuMVJwNTAFKbYeRBhkWDYeC/n1WMDRCDq7fii6oqvDmvO9CZZyrpuF9n0lAqJADqjwWWwIcAwT1EqTKykjFtsARtoNIgywDjouGQ+s8TknsUCEHWPUGRKfh7UkbJD/N2KL9TcCdtoNIg10QDYeC/BtYQVIhB1x5LPYyELOd40+uHbXn8eeSX5siFZI7ouHQY7ZDSE16US9HJB3nLrzFF7aNH9Dn6uOqiku+AMpsh5F6GxgNhzRvHFAaIeeOy/DOErPJBS6qKi75DyrjXPQscK7tELJ+KuQcUR6LuXhbddpcXv1oZaSiKd5m4ZJbRgKnRsOh1baDyPqpkHNIeSy2Gvgrdk6tXrhg4xb9gXssPLek513g2Gg4lLIdRDZMhZxjymOxFHA88FaWnzo2rOc/TgF2yfLzSnomAX2j4dAy20GkdnpRL0clHWdjYDSwdxae7rPHD7u419JGTb8AmmXh+cQfXwI9ouHQT7aDSN1ohJyjymOxX4HDgTFZeLqLljZqegsq41wyHThUZZxbVMg5rDwWW4S3Uu7xDD7N05WRihTeAhXJDR8D+0XDodm2g0j9aMoiTyQd50bgOp8fdsnyUKOdHu19+YvA7j4/tmTGa3hbaS6xHUTqTyPkPFEei12Pt1GMn3sp//PR3pf3QWWcKx4FjlIZ5y6NkPNM0nF64S0A2DjNh/rq+f1O6/FDizZTgRbpJ5MMcoH/i4ZDN9sOIunRCDnPlMdio4AewNw0H+qSH1q0uQGVcdAtwbvGWGWcB1TIeag8FksAYeCNBj7ES5WRinlomW3QzQK6R8Oh520HEX+okPNUeSw2D+gFXAXUZ4XW8lVFxZcB96HvjyB7GegWDYcm2w4i/tEccgFIOk5X4CmgfR1uflNlpGI6MDizqaSBlgCXRcOhh20HEf9pBFQAymOxiXhXStR2vfJ3b3fufS9wW+ZTSQN8BHRWGecvjZALTNJxTgEqWfequ+MqIxX7AFdkN5XUYhVwI3BzNByqsh1GMkeFXICSjrMdcD9rn4c3pjJS0Q/4BAhZiCXrNg34azQcmmA7iGSa+zlZAAACeElEQVSepiwKUHksNrM8FusDHAvMxnvRrx/e1poq42BwgQeA3VXGhUMj5AJXvWvcgZWRilJghO08AsDbwJXRcGii7SCSXSpkASCeSLUC/gn8Hf3mZMuXwNXRcOhl20HEDhWyrCWeSHUG7gB62s5SQH7EO1n8kWg45OdeJJJjVMiyTvFEKgJcD3S1nSWPLcP7n9+t0XBose0wYp8KWTYonkj1BK7G2wxf/JEChgDXRcOhObbDSHCokKVO4onUbnjLsE8CSizHyVVzgQHAQ9FwKN3NnyQPqZClXuKJVBvgMuAc0t/is1B8gLc3yHCd/CwbokKWBoknUs2B8/E2xd/ecpwgWo63f8h90XBoku0wkhtUyJK2eCLVDTgROB7Y1nIc26bhndzxSDQcmm87jOQWFbL4Jp5IGWAvfi/nrewmyprPgOHAiGg4NNV2GMldKmTJiOpy3g+vnP8CtLabyFcrgXHASODlaDg03XIeyRMqZMmKeCLVDtj3D28dyZ0VgSuBqXjbX44CxkbDoV/tRpJ8pEIWK+KJVFNgb34v6L2AcquhPMuAT4FJf3ibEg2HVlpNJQVBhSyBEE+kivBONNkBaFf9tgPQFm+6w8+yXoC3XHle9dscYDJe+X6hPYfFFhWy5IR4ItUEr5hbA5vhbRNajLdIpWQ977vAT/xevPOAH3UtsASVCllEJCBy5UUVEZG8p0IWEQkIFbKISECokEVEAkKFLCISECpkEZGAUCGLiASECllEJCBUyCIiAaFCFhEJCBWyiEhAqJBFRAJChSwiEhAqZBGRgFAhi4gEhApZRCQgVMgiIgGhQhYRCQgVsohIQKiQRUQC4v8BoURPTrjqepYAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Self-Play Data from 5 of 5 networks proved sufficient to reject the null hypothesis at α = 0.01.\n"
     ]
    }
   ],
   "source": [
    "query = \"\"\"\n",
    "SELECT\n",
    " Network.id, Network.upload_date,\n",
    " black_victories,\n",
    " white_victories\n",
    " FROM SelfPlay\n",
    " JOIN Network on Network.id = SelfPlay.network_id\n",
    " GROUP BY SelfPlay.network_id\n",
    " ORDER BY upload_date DESC\n",
    "\"\"\"\n",
    "present_self_play_black_white_win_rate(query.format(1), '(self-play games)', history=5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Distribution of Match Win/Loss"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "def present_match_win_loss_distribution(query, bin_width):\n",
    "    win_loss = []\n",
    "    total_matches = 0\n",
    "    short_matches = 0\n",
    "    less_50 = 0\n",
    "    less_55 = 0\n",
    "\n",
    "    with sqlite3.connect(db_path) as sql:\n",
    "        cursor = sql.execute(query)\n",
    "\n",
    "        for r in cursor:\n",
    "            (id, start_date, challenger_victories, defender_victories) = r\n",
    "            win_rate = challenger_victories / (challenger_victories + defender_victories)\n",
    "            win_loss.append(win_rate)\n",
    "            total_matches += 1\n",
    "            if ((challenger_victories + defender_victories) < 400):\n",
    "                short_matches += 1\n",
    "                \n",
    "            if (win_rate < 0.5):\n",
    "                less_50 += 1\n",
    "            \n",
    "            if (win_rate < 0.55):\n",
    "                less_55 += 1\n",
    "                \n",
    "    bins = np.arange(0.0, 1.0 + bin_width, bin_width)\n",
    "    print(bins, bins.shape)\n",
    "\n",
    "    pyplot.figure(figsize=(12, 6))\n",
    "    pyplot.suptitle('Match Win/Loss Histogram')\n",
    "    pyplot.title('({0} matches. {1} with less than 400 games.)'.format(total_matches, short_matches))\n",
    "    pyplot.hist(win_loss, bins=bins, histtype='step')\n",
    "    pyplot.axvline(0.5, linestyle='--', color='k', alpha=0.3)\n",
    "    pyplot.axvline(0.55, linestyle='--', color='k', alpha=0.3)\n",
    "    pyplot.show()\n",
    "    \n",
    "    pyplot.figure(figsize=(12, 6))\n",
    "    pyplot.suptitle('Match Win/Loss Cumulative')\n",
    "    pyplot.title('({0} matches. {1} with less than 400 games.)'.format(total_matches, short_matches))\n",
    "    pyplot.hist(win_loss, bins=bins, cumulative=True, histtype='step')\n",
    "    pyplot.axvline(0.5, linestyle='--', color='k', alpha=0.3)\n",
    "    pyplot.axvline(0.55, linestyle='--', color='k', alpha=0.3)\n",
    "    pyplot.show()\n",
    "    \n",
    "    print(\"Total Matches: {0}\".format(total_matches))\n",
    "    print(\"Short Matches: {0}\".format(short_matches))\n",
    "    print(\"Matches with < 50%: {0}\".format(less_50))\n",
    "    print(\"Matches with < 55%: {0}\".format(less_55))\n",
    "    print()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.    0.025 0.05  0.075 0.1   0.125 0.15  0.175 0.2   0.225 0.25  0.275\n",
      " 0.3   0.325 0.35  0.375 0.4   0.425 0.45  0.475 0.5   0.525 0.55  0.575\n",
      " 0.6   0.625 0.65  0.675 0.7   0.725 0.75  0.775 0.8   0.825 0.85  0.875\n",
      " 0.9   0.925 0.95  0.975 1.   ] (41,)\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Total Matches: 644\n",
      "Short Matches: 496\n",
      "Matches with < 50%: 331\n",
      "Matches with < 55%: 584\n",
      "\n"
     ]
    }
   ],
   "source": [
    "query = \"\"\"\n",
    "SELECT\n",
    " mv.match_id, mv.start_date,\n",
    " challenger_victories, defender_victories\n",
    " FROM MatchVictor mv\n",
    " JOIN Match m ON m.id=mv.match_id\n",
    " WHERE m.result is not null\n",
    " ORDER BY mv.start_date DESC\n",
    "\"\"\"\n",
    "present_match_win_loss_distribution(query, bin_width=0.025)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Data Sources\n",
    "\n",
    "### Fetch Web Data\n",
    "\n",
    "Scrape http://zero.sjeng.org/ for data from Leela Zero's training matches and store that data in a Sqlite database that can be queried offline."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "web.fetch_database(db_path)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "(networks, matches) = web.fetch_index()\n",
    "print(\"Listed Networks: \", len(networks))\n",
    "print(\"Listed Matches:  \", len(matches))\n",
    "\n",
    "match = matches['5b07ca55888bab42e3cde074']\n",
    "if (None == match):\n",
    "    print(\"Match not found!\")\n",
    "else:\n",
    "    print(\"Match: \", match['id'])\n",
    "    games = web.fetch_match_index(match)\n",
    "    print(\"Games: \", len(games))\n",
    "    print(games)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Import Self-Training SGF Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "sgf_path = r\"~ ~ ~/all.sgf\"\n",
    "\n",
    "def report_progress(imported, failed, ignored):\n",
    "    display.clear_output(wait = True)\n",
    "    print('{0} self-play game records imported. ({1} failed, {2} ignored)'.format(imported, failed, ignored))\n",
    "    \n",
    "sgf.import_self_plays(db_path, sgf_path, report_progress)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " "
   ]
  }
 ],
 "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": "3.6.6"
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