March_Madness_Kendalls_Tau.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# March Madness and Analytics:\n",
    "\n",
    "## How Correlated are the Strengths the Men's and Women's NCAA D-1 Basketball Teams?\n",
    "\n",
    "We were watching the first weekend of the NCAA Division 1 Basketball Tournaments, switching back and forth between the men and the women. My wife asked, \"Doesn't it seem like we're watching teams from the same schools?\" We wondered whether it was the case that having a strong men's team implies that a school also has a strong women's team.\n",
    "\n",
    "Clearly this was calling out for some data analysis in Python!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I downloaded Massey Ratings to the csv files `Massey_men_d1.csv` and `Massey_women_d1.csv` \n",
    "from [here](https://www.masseyratings.com/cb/ncaa-d1/ratings) for the men and\n",
    "from [here](https://www.masseyratings.com/cbw/ncaa-d1/ratings) for the women. The *rating* is a continuous \n",
    "numerical variable, and it is accompanied by a *ranking* according to those values. You can read on the Massey Ratings site how they derive the ratings. In this notebook we are only concerned with rankings. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "df_mens_ratings = pd.read_csv('Massey_men_d1.csv',usecols=['Team','Rat'],index_col='Team')\\\n",
    ".rename(columns={'Rat':'Ranking'})\n",
    "\n",
    "df_womens_ratings = pd.read_csv('Massey_women_d1.csv',usecols=['Team','Rat'],index_col='Team')\\\n",
    ".rename(columns={'Rat':'Ranking'})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Ranking</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Team</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Virginia</th>\n",
       "      <td>26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Pepperdine</th>\n",
       "      <td>110</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Kansas St</th>\n",
       "      <td>130</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>UC Riverside</th>\n",
       "      <td>141</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Vermont</th>\n",
       "      <td>176</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              Ranking\n",
       "Team                 \n",
       "Virginia           26\n",
       "Pepperdine        110\n",
       "Kansas St         130\n",
       "UC Riverside      141\n",
       "Vermont           176"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_mens_ratings.sample(5).sort_values('Ranking')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Ranking</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Team</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Stanford</th>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>NC State</th>\n",
       "      <td>7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Loy Marymount</th>\n",
       "      <td>173</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Campbell</th>\n",
       "      <td>253</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Dixie St</th>\n",
       "      <td>351</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "               Ranking\n",
       "Team                  \n",
       "Stanford             1\n",
       "NC State             7\n",
       "Loy Marymount      173\n",
       "Campbell           253\n",
       "Dixie St           351"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_womens_ratings.sample(5).sort_values('Ranking')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The next steps are to join the two dataframes using an outer join to retain all of the teams. However, some schools have only one D-I basketball program; so this introduces some missing values. We fill these in with an artifical number which is one more than the worst ranking of any existing program by gender. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "df_combined = df_mens_ratings.merge(df_womens_ratings,on='Team',how='outer',suffixes=['_Men','_Women'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "Index: 358 entries, Gonzaga to MD E Shore\n",
      "Data columns (total 2 columns):\n",
      " #   Column         Non-Null Count  Dtype  \n",
      "---  ------         --------------  -----  \n",
      " 0   Ranking_Men    347 non-null    float64\n",
      " 1   Ranking_Women  355 non-null    float64\n",
      "dtypes: float64(2)\n",
      "memory usage: 8.4+ KB\n"
     ]
    }
   ],
   "source": [
    "df_combined.info()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Ranking_Men</th>\n",
       "      <th>Ranking_Women</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Team</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>VMI</th>\n",
       "      <td>185.0</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Citadel</th>\n",
       "      <td>216.0</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>TN Martin</th>\n",
       "      <td>325.0</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Princeton</th>\n",
       "      <td>NaN</td>\n",
       "      <td>58.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Mid</th>\n",
       "      <td>NaN</td>\n",
       "      <td>99.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Penn</th>\n",
       "      <td>NaN</td>\n",
       "      <td>108.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Yale</th>\n",
       "      <td>NaN</td>\n",
       "      <td>121.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Harvard</th>\n",
       "      <td>NaN</td>\n",
       "      <td>136.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Columbia</th>\n",
       "      <td>NaN</td>\n",
       "      <td>144.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Cornell</th>\n",
       "      <td>NaN</td>\n",
       "      <td>176.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Dartmouth</th>\n",
       "      <td>NaN</td>\n",
       "      <td>210.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Brown</th>\n",
       "      <td>NaN</td>\n",
       "      <td>249.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Bethune-Cookman</th>\n",
       "      <td>NaN</td>\n",
       "      <td>262.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>MD E Shore</th>\n",
       "      <td>NaN</td>\n",
       "      <td>319.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                 Ranking_Men  Ranking_Women\n",
       "Team                                       \n",
       "VMI                    185.0            NaN\n",
       "Citadel                216.0            NaN\n",
       "TN Martin              325.0            NaN\n",
       "Princeton                NaN           58.0\n",
       "Mid                      NaN           99.0\n",
       "Penn                     NaN          108.0\n",
       "Yale                     NaN          121.0\n",
       "Harvard                  NaN          136.0\n",
       "Columbia                 NaN          144.0\n",
       "Cornell                  NaN          176.0\n",
       "Dartmouth                NaN          210.0\n",
       "Brown                    NaN          249.0\n",
       "Bethune-Cookman          NaN          262.0\n",
       "MD E Shore               NaN          319.0"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_combined[df_combined.Ranking_Men.isna() | df_combined.Ranking_Women.isna()]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "df_combined.Ranking_Women = df_combined.Ranking_Women.fillna(df_combined.Ranking_Women.max() + 1)\n",
    "df_combined.Ranking_Men = df_combined.Ranking_Men.fillna(df_combined.Ranking_Men.max() + 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Ranking_Men</th>\n",
       "      <th>Ranking_Women</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Team</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>VMI</th>\n",
       "      <td>185.0</td>\n",
       "      <td>356.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Citadel</th>\n",
       "      <td>216.0</td>\n",
       "      <td>356.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>TN Martin</th>\n",
       "      <td>325.0</td>\n",
       "      <td>356.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Princeton</th>\n",
       "      <td>348.0</td>\n",
       "      <td>58.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Mid</th>\n",
       "      <td>348.0</td>\n",
       "      <td>99.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Penn</th>\n",
       "      <td>348.0</td>\n",
       "      <td>108.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Yale</th>\n",
       "      <td>348.0</td>\n",
       "      <td>121.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Harvard</th>\n",
       "      <td>348.0</td>\n",
       "      <td>136.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Columbia</th>\n",
       "      <td>348.0</td>\n",
       "      <td>144.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Cornell</th>\n",
       "      <td>348.0</td>\n",
       "      <td>176.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Dartmouth</th>\n",
       "      <td>348.0</td>\n",
       "      <td>210.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Brown</th>\n",
       "      <td>348.0</td>\n",
       "      <td>249.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Bethune-Cookman</th>\n",
       "      <td>348.0</td>\n",
       "      <td>262.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>MD E Shore</th>\n",
       "      <td>348.0</td>\n",
       "      <td>319.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                 Ranking_Men  Ranking_Women\n",
       "Team                                       \n",
       "VMI                    185.0          356.0\n",
       "Citadel                216.0          356.0\n",
       "TN Martin              325.0          356.0\n",
       "Princeton              348.0           58.0\n",
       "Mid                    348.0           99.0\n",
       "Penn                   348.0          108.0\n",
       "Yale                   348.0          121.0\n",
       "Harvard                348.0          136.0\n",
       "Columbia               348.0          144.0\n",
       "Cornell                348.0          176.0\n",
       "Dartmouth              348.0          210.0\n",
       "Brown                  348.0          249.0\n",
       "Bethune-Cookman        348.0          262.0\n",
       "MD E Shore             348.0          319.0"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_combined[(df_combined.Ranking_Men == df_combined.Ranking_Men.max()) | (df_combined.Ranking_Women == df_combined.Ranking_Women.max())]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Rank Correlation\n",
    "\n",
    "Now that we have a combined dataframe, let's generate a scatterplot to visulaize the relationship between the rankings of men's and women's programs."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "t = np.linspace(0,1,101)\n",
    "\n",
    "plt.figure(figsize=(10,10))\n",
    "plt.scatter(df_combined.Ranking_Men, df_combined.Ranking_Women)\n",
    "plt.plot(356*t, 356*t,'--r',alpha=0.5)\n",
    "plt.xlabel(\"Men's Team Ranking\")\n",
    "plt.ylabel(\"Women's Team Ranking\")\n",
    "plt.axis('square');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The scatterplot shows a clear relationship between the rankings of men's teams and women's teams --- a positive correlation as we suspected.  How do we quantify what we see qualitatively?  \n",
    "\n",
    "Kendall's tau is used to measure rank correlation.  Like Pearson's coefficient of correlation (usually denoted by _r_), Kendall's tau is a numeric quantity taking values between -1 and 1 where +1 indicates a perfect, positive correlation and -1 indicates a perfect, negative correlation.  However, Kendall's tau is computed in very differently from Pearson's r.\n",
    "\n",
    "In the case of tau, we look at rankings for pairs of observations. Consider this subset of the dataframe using three randomly chose universities:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "# This would truly be random:\n",
    "# df_combined.sample(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Ranking_Men</th>\n",
       "      <th>Ranking_Women</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Team</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Minnesota</th>\n",
       "      <td>51.0</td>\n",
       "      <td>89.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Georgia Tech</th>\n",
       "      <td>41.0</td>\n",
       "      <td>29.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Wisconsin</th>\n",
       "      <td>12.0</td>\n",
       "      <td>115.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              Ranking_Men  Ranking_Women\n",
       "Team                                    \n",
       "Minnesota            51.0           89.0\n",
       "Georgia Tech         41.0           29.0\n",
       "Wisconsin            12.0          115.0"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Three not so random schools.\n",
    "df_combined.loc[['Minnesota', 'Georgia Tech','Wisconsin']]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that Georgia Tech's teams both have better rankings than Minnesota's teams. These rankings are called *concordant*, i.e. they are in harmony. On the other hand, Winsconsin's men have a better ranking than Georgia Tech's while the Wisconsin women's team is ranked worse than Georgia Tech women's team. Those rankings are called *discordant*; they disagree.  Kendall's tau is computed by taking all pairs of observations and comparing the rankings, counting the concordant and discordant pairs.\n",
    "$$\n",
    "\\tau = \\frac{\\textrm{# concordant pairs} - \\textrm{# discordant pairs}}{\\textrm{# all pairs}}\n",
    "$$\n",
    "\n",
    "Tau reminds me of *hitting percentage* in volleyball which is computed as (kills - errors)/attempts.\n",
    "\n",
    "Of course, there is a function in pandas that computes this for us. (The output is a dataframe; you can always extract the individual values.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Ranking_Men</th>\n",
       "      <th>Ranking_Women</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Ranking_Men</th>\n",
       "      <td>1.0000</td>\n",
       "      <td>0.4365</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Ranking_Women</th>\n",
       "      <td>0.4365</td>\n",
       "      <td>1.0000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "               Ranking_Men  Ranking_Women\n",
       "Ranking_Men         1.0000         0.4365\n",
       "Ranking_Women       0.4365         1.0000"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_combined[['Ranking_Men','Ranking_Women']].corr('kendall')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Tournament Appearances: A Binary Approach\n",
    "\n",
    "We note that there appears to be a strong cluster of points in the lowere left-hand corner of the scatterplot above."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "t = np.linspace(0,1,101)\n",
    "\n",
    "plt.figure(figsize=(10,10))\n",
    "plt.scatter(df_combined.Ranking_Men, df_combined.Ranking_Women)\n",
    "plt.plot(68.5*np.ones(t.shape), 356*t,'--k')\n",
    "plt.plot(356*t, 64.5*np.ones(t.shape),'--k')\n",
    "plt.xlabel(\"Men's Team Ranking\")\n",
    "plt.ylabel(\"Women's Team Ranking\")\n",
    "plt.axis('square');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here I have drawn in a vertical line that separates the men's programs into two groups: one containing the teams with the top 68 ratings and its complement. I have also drawn a horizontal line that  separates the women's programs into two groups: one containing the teams with the top 64 ratings and its complement. Note the higher density of points in the lower left-hand portion and the relative sparsity of the lower right-hand and upper left-hand portions.\n",
    "\n",
    "Let's create new binary variables and count programs in each quadrant."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th>Top_68_Mens_Team</th>\n",
       "      <th>False</th>\n",
       "      <th>True</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Top_64_Womens_Team</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>False</th>\n",
       "      <td>269</td>\n",
       "      <td>25</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>True</th>\n",
       "      <td>21</td>\n",
       "      <td>43</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "Top_68_Mens_Team    False  True \n",
       "Top_64_Womens_Team              \n",
       "False                 269     25\n",
       "True                   21     43"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_combined['Top_64_Womens_Team'] = (df_combined.Ranking_Women < 65)\n",
    "df_combined['Top_68_Mens_Team'] = (df_combined.Ranking_Men < 69)\n",
    "df_combined.pivot_table(index ='Top_64_Womens_Team',\n",
    "                        columns='Top_68_Mens_Team',\n",
    "                        values='Ranking_Men', \n",
    "                        aggfunc='count')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We see that 43 schools have teams with high ranks. Of course the top-ranked teams do not necessarily get into the tournament, but we will postpone any discussion of tournament team selection for now.  Instead, let's import lists of schools that actually made the tournament."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "df_womens_field = pd.read_csv('tournament_women.csv')\n",
    "df_womens_field['Womens_Field'] = True\n",
    "df_mens_field = pd.read_csv('tournament_men.csv')\n",
    "df_mens_field['Mens_Field'] = True"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "df_combined_plus = df_combined.merge(df_womens_field,on='Team',how='outer')\\\n",
    ".merge(df_mens_field,on='Team',how='outer')\\\n",
    ".fillna(False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can compare the women's field to the men's field."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th>Mens_Field</th>\n",
       "      <th>False</th>\n",
       "      <th>True</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Womens_Field</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>False</th>\n",
       "      <td>251</td>\n",
       "      <td>43</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>True</th>\n",
       "      <td>39</td>\n",
       "      <td>25</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "Mens_Field    False  True \n",
       "Womens_Field              \n",
       "False           251     43\n",
       "True             39     25"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_combined_plus.pivot_table(index ='Womens_Field',columns='Mens_Field',values='Ranking_Men', aggfunc='count')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.36764705882352944, 0.390625, 0.770949720670391)"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "25/68, 25/64, 276/358"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We see that 25 schools with teams in the women's field also have teams in the men's field. Consider using the variable `Womens_Field` to predict the value of `Mens_Field`: as such it has a *recall* of 25/68 (0.368) and a *precision* of 25/64 (0.391) and an accuracy of 276/358 (0.771).\n",
    "\n",
    "From a stats perspective, we can compute the chi-squared statistic. Here we see that the Chi-squared value is 18.7 for 1 degree of freedom, and the p-value is extremely small at 1.5e-05.  See the documentation at [scipy.stats.chi2_contingency](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.chi2_contingency.html) for details."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(18.84069047338763,\n",
       " 1.4210296580948978e-05,\n",
       " 1,\n",
       " array([[238.15642458,  55.84357542],\n",
       "        [ 51.84357542,  12.15642458]]))"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from scipy.stats import chi2_contingency\n",
    "chi2_contingency(df_combined_plus.pivot_table(index ='Womens_Field',\n",
    "                                              columns='Mens_Field',\n",
    "                                              values='Ranking_Men',\n",
    "                                              aggfunc='count').values)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Do the best teams make the tournaments?\n",
    "\n",
    "You can also examine the contingency tables showing what fraction of the top-ranked teams also made the tournaments.  How you interpret this is a matter of perspective. A full 70% of the top-ranked men's teams and 67% of the top-ranked women's teams make the tournament, and that seems pretty good ... unless you are a fan of one of the 20 men's or 21 women's teams that did not."
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    "df_combined_plus.pivot_table(index ='Top_68_Mens_Team',\n",
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