notebooks/odds_math.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 博彩赔率背后的数学公式\n",
    "\n",
    "首先简单介绍一下什么是赔率。\n",
    "\n",
    "2007年12月8日，阿森纳在英超联赛中主场迎战富勒姆。博彩公司BET365开出的赔率组合是：阿森纳获胜，赔率1.33；两队打平，赔率4.5；客队富勒姆获胜，赔率10。那么这些数字代表什么意思呢？\n",
    "\n",
    "假设比赛前你押1元猜主队阿森纳获胜，而最终比赛结果确实是主队获胜，那么你就能赢回1.33元。扣除你押的1元，那么你的盈利就是0.33元。如果比赛结果是双方打平，或者客队胜，那么你就输掉了你押的1元钱。剩下两个赔率类似，代表你押对结果博彩公司会返回给你的钱。扣除你的本金1元，你获得的盈利分别为3.5元和9元。\n",
    "\n",
    "#### 事件发生的可能性越小，赔率越大\n",
    "\n",
    "赔率数字有大有小，这意味着你猜对结果的收益会不一样。比如你猜主队阿森纳胜并猜对结果，你获利0.33元；如果你猜客队获胜并猜对结果，那么你将获利9元。这样看来，似乎你应该押客队富勒姆获胜，因为这样盈利更多。但是如果你稍微有点足球概念，你就会知道在英超联赛中阿森纳的实力要比富勒姆强很多，而阿森纳又是在主场有着所谓的“主场优势”，这就意味着阿森纳赢得比赛结果的可能性更大。因此，虽然押富勒姆获胜你的盈利会很大，但是这件事情发生的可能性却很小。\n",
    "\n",
    "#### 赔率是怎么定下来的\n",
    "\n",
    "赔率是博彩公司制定的。博彩公司会根据自己的经验开出一个初始赔率。但这并没有那么重要。重要的是：博彩公司会根据彩民的投注比例调整赔率，从而保证无论出现什么样的比赛结果，博彩公司都能赚钱。\n",
    "\n",
    "以上面提到的阿森纳对阵富勒姆的比赛为例。假设在全体彩民中，押阿森纳获胜的投注比例是$f_{0}$，对应博彩公司开出的赔率是$b_{0}$；押两队打平的比例是$f_{1}$，对应博彩公司开出的赔率为$b_{1}$；押富勒姆获胜的比例是$f_{2}$，对应博彩公司开出的赔率为$b_{2}$。容易知道，所有结果的投注比例之和为1：\n",
    "\n",
    "$$f_{0}+f_{1}+f_{2}=1$$\n",
    "\n",
    "如果最终比赛结果是阿森纳赢，那么博彩公司的收益为（假设总的投注额为1）：\n",
    "\n",
    "$$-f_{0}(b_{0}-1)+f_{1}+f_{2}=1-f_{0}\\times b_{0}$$\n",
    "\n",
    "上面公式左侧第一部分为博彩公司返还给押对结果的彩民的钱，而后面部分$f_1+f_2$为博彩公司从押错结果的彩民那里得到的钱。\n",
    "博彩公司只要能够保证这一收益大于$0$即可：\n",
    "\n",
    "$$f_{0}\\times b_{0}<1$$\n",
    "\n",
    "同样地，若比赛结果是双方打平或者富勒姆获胜时，博彩公司需保证下面两个不等式成立才能赚钱：\n",
    "\n",
    "$$f_{1}\\times b_{1}<1$$\n",
    "\n",
    "$$f_{2}\\times b_{2}<1$$\n",
    "\n",
    "只要能同时保证上述三个不等式成立，博彩公司就一定能赚钱。而$f_{0}$，$f_{1}$和$f_{2}$代表着投注比例，因此博彩公司只要根据投注比例和上述三个不等式调整赔率，就肯定能赚钱。\n",
    "\n",
    "当上述三个不等式成立时：\n",
    "\n",
    "$$f_{0}<\\frac{1}{b_{0}}$$\n",
    "$$f_{1}<\\frac{1}{b_{1}}$$\n",
    "$$f_{2}<\\frac{1}{b_{2}}$$\n",
    "\n",
    "又$f_{0}+f_{1}+f_{2}=1$，所以：\n",
    "\n",
    "$$\\frac{1}{b_{0}}+\\frac{1}{b_{1}}+\\frac{1}{b_{2}}>1$$\n",
    "\n",
    "因此，博彩公司开出的赔率一定满足：\n",
    "\n",
    "#### 所有结果对应赔率的倒数之和大于1。\n",
    "\n",
    "无一例外。\n",
    "\n",
    "通过前面阿森纳和富勒姆比赛的赔率简单验证一下：$1/1.33+1/4.5+1/10=1.074$，大于1。通常情况下，博彩公司会使得这一赔率倒数和介于1到1.1之间。这一数字比1越大，博彩公司可能赚的就更多；离1越近，可能赚的更少。但只要大于1，博彩公司就一定能赚钱。\n",
    "\n",
    "对22592场欧洲各大联赛比赛的赔率做一个统计，计算出赔率倒数和，其值的分布如下所示。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import pandas as pd\n",
    "import os\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "\n",
    "sns.set_style('white')\n",
    "sns.set_context('poster')\n",
    "sns.set_style({'font.sans-serif':['simhei','Arial']}) #图中显示中文"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 导入包含赔率信息的比赛数据\n",
    "data_folder = os.path.join(os.path.pardir, 'data_source', 'kaggle')\n",
    "match = pd.read_csv(os.path.join(data_folder, 'match.csv'))\n",
    "\n",
    "# 选择赔率源：B365, BW, IW, LB, PS, WH, SJ, VC, GB, BS\n",
    "odds_source= 'B365'\n",
    "odds_columns = ['{}H'.format(odds_source), '{}D'.format(odds_source), '{}A'.format(odds_source)]\n",
    "\n",
    "match_sel = match\n",
    "for col in odds_columns:\n",
    "    match_sel = match_sel[match_sel[col].notnull()]\n",
    "\n",
    "odds = match_sel[odds_columns].values\n",
    "odds_inv = 1/odds"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(12, 8))\n",
    "plt.hist(np.sum(odds_inv, axis=1))\n",
    "plt.xlabel('赔率倒数之和')\n",
    "plt.ylabel('比赛场次')\n",
    "plt.title('赔率倒数之和的分布（{}）'.format(odds_source));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "BET365开出的赔率一定使得赔率的倒数之和大于1，并且集中分布在1.07左右。其他博彩公司的赔率也有类似的结果。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "match_sel = match\n",
    "for odds_source in ['B365', 'BW', 'IW', 'LB', 'WH']:\n",
    "    odds_columns = ['{}H'.format(odds_source), '{}D'.format(odds_source), '{}A'.format(odds_source)]    \n",
    "    for col in odds_columns:\n",
    "        match_sel = match_sel[match_sel[col].notnull()]\n",
    "    odds = match_sel[odds_columns].values\n",
    "    odds_inv = 1/odds\n",
    "    match_sel['{}_inv'.format(odds_source)] = np.sum(odds_inv, axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "labels = ['B365', 'BW', 'IW', 'LB', 'WH']\n",
    "all_data = [match_sel['{}_inv'.format(odds_source)].values for odds_source in labels]\n",
    "plt.figure(figsize=(12, 8))\n",
    "plt.boxplot(all_data, vert=True, patch_artist=True, labels=labels)\n",
    "plt.ylim(0.95, 1.2)\n",
    "plt.title('比较不同赔率源')\n",
    "plt.ylabel('赔率倒数之和')\n",
    "plt.xlabel('赔率来源');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "若赔率的倒数之和小于1，则彩民一定可以找到投注比例满足下面不等式使得博彩公司赔钱：\n",
    "\n",
    "$$f_{0}>\\frac{1}{b_{0}}$$\n",
    "$$f_{1}>\\frac{1}{b_{1}}$$\n",
    "$$f_{2}>\\frac{1}{b_{2}}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 参考资料\n",
    "数据来源：https://www.kaggle.com/hugomathien/soccer"
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "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": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}