/Soccer Analysis Notebook.ipynb

## Soccer Analysis Notebook.ipynb
{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Anaconda3\\envs\\threesix\\lib\\site-packages\\IPython\\html.py:14: ShimWarning: The `IPython.html` package has been deprecated since IPython 4.0. You should import from `notebook` instead. `IPython.html.widgets` has moved to `ipywidgets`.\n",
      "  \"`IPython.html.widgets` has moved to `ipywidgets`.\", ShimWarning)\n"
     ]
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "from matplotlib import pyplot as plt\n",
    "import seaborn as sns\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "from scipy import optimize"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "df = pd.read_csv(\"superleague1617.csv\", usecols=[1,2,3,4])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "teams = list(set(df.home.unique()) & set(df.away.unique()))\n",
    "\n",
    "# pre-make some indices for use with the objective function\n",
    "\n",
    "df['hidx'] = df.home.apply(lambda x: teams.index(x))\n",
    "df['aidx'] = df.away.apply(lambda x: teams.index(x))\n",
    "df['xhdefidx'] = df.hidx + len(teams)\n",
    "df['xhoffidx'] = df.hidx\n",
    "df['xadefidx'] = df.aidx + len(teams)\n",
    "df['xaoffidx'] = df.aidx"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The inputs are:\n",
    "\n",
    "* $o$: offensive rating vector\n",
    "* $d$: defensive rating vector  \n",
    "* $g$: adjusted average number of goals scored (not per team, but for the whole league)\n",
    "\n",
    "The $x$ vector will have length `2 * n_teams + 2`. The first `n_teams` portion is offense, the second is defense.\n",
    "\n",
    "The constraint is that $o$ and $d$ must both average to one."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "n_teams = len(teams)\n",
    "ghome = n_teams*2\n",
    "gaway = n_teams*2+1\n",
    "\n",
    "def off_constr(x):\n",
    "    return np.mean(x[:n_teams]) - 1\n",
    "\n",
    "def def_constr(x):\n",
    "    return np.mean(x[n_teams:n_teams*2]) - 1\n",
    "\n",
    "def obj(x):\n",
    "    err = ((df['GH'] - x[ghome] * df.xhoffidx.apply(lambda i: x[i]) * df.xadefidx.apply(lambda i: x[i]))**2).sum()\n",
    "    err += ((df['GA'] - x[gaway] * df.xaoffidx.apply(lambda i: x[i]) * df.xhdefidx.apply(lambda i: x[i]))**2).sum()\n",
    "    return err"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Both of these work well for initializations.\n",
    "# Starting at all zeros gets bad results, probably because of how the minimizer handles the constraints\n",
    "x0 = np.random.random(size=len(teams)*2 + 2)\n",
    "#x0 = np.ones(shape=len(teams)*2 + 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(True, 'Optimization terminated successfully.')"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "res = optimize.minimize(obj, x0, constraints=[{'type':'eq', 'fun':off_constr}, {'type':'eq', 'fun':def_constr}],\n",
    "                        options={'maxiter':300})\n",
    "res.success, res.message"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "57"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "res.nit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Home average points: 1.448\n",
      "Away average points: 0.836\n",
      "\n",
      "                Team   Off Rate    Def Rate\n",
      "                 PAS    0.8041      1.1211\n",
      "          Levadiakos    0.8245      1.3710\n",
      "          Olympiacos    1.6307      0.4995\n",
      "                PAOK    1.4840      0.5731\n",
      "                 PAO    1.3208      0.6781\n",
      "              Veroia    0.8034      1.7478\n",
      "              Xanthi    1.0216      0.7469\n",
      "                 AEK    1.6083      0.7055\n",
      "             Iraklis    0.7620      1.0261\n",
      "             Asteras    0.8934      1.3617\n",
      "           Atromitos    0.7370      1.0214\n",
      "                 AEL    0.6964      1.1276\n",
      "             Kerkira    0.6324      1.2594\n",
      "           Platanias    0.9914      1.0990\n",
      "           Panionios    0.9138      0.5325\n",
      "        Panaitolikos    0.8761      1.1292\n"
     ]
    }
   ],
   "source": [
    "print(\"Home average points: {:.3f}\".format(res.x[ghome]))\n",
    "print(\"Away average points: {:.3f}\".format(res.x[gaway]))\n",
    "print()\n",
    "print(\"                Team   Off Rate    Def Rate\")\n",
    "for i, t in enumerate(teams):\n",
    "    print(\"{:>20s}    {:.4f}      {:.4f}\".format(t, res.x[i], res.x[i+n_teams]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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BAGAKBD4AACZA4AMAYALBCxYsWODrIgLZoEGDfF1Cm6Et7RNtaZ9oS/tk5rb4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\nAwBgAgQ+AAAmQOADAGACBD4AACbw/wBBLxa3qHx/8AAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x9619f98>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.set_style('ticks')\n",
    "plt.scatter(res.x[n_teams:n_teams*2], res.x[:n_teams]); plt.ylabel(\"Offensive Rating\"); plt.xlabel(\"Defensive Rating\")\n",
    "plt.xlim(0.25, 2); plt.ylim(0.5, 1.7);\n",
    "sns.despine()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python [root]",
   "language": "python",
   "name": "Python [root]"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
	{
	"cells": [
	{
	"cell_type": "code",
	"execution_count": 1,
	"metadata": {
	"collapsed": false
	},
	"outputs": [
	{
	"name": "stderr",
	"output_type": "stream",
	"text": [
	"C:\\Anaconda3\\envs\\threesix\\lib\\site-packages\\IPython\\html.py:14: ShimWarning: The `IPython.html` package has been deprecated since IPython 4.0. You should import from `notebook` instead. `IPython.html.widgets` has moved to `ipywidgets`.\n",
	" \"`IPython.html.widgets` has moved to `ipywidgets`.\", ShimWarning)\n"
	]
	}
	],
	"source": [
	"%matplotlib inline\n",
	"from matplotlib import pyplot as plt\n",
	"import seaborn as sns\n",
	"import pandas as pd\n",
	"import numpy as np\n",
	"from scipy import optimize"
	]
	},
	{
	"cell_type": "code",
	"execution_count": 2,
	"metadata": {
	"collapsed": false
	},
	"outputs": [],
	"source": [
	"df = pd.read_csv(\"superleague1617.csv\", usecols=[1,2,3,4])"
	]
	},
	{
	"cell_type": "code",
	"execution_count": 3,
	"metadata": {
	"collapsed": false
	},
	"outputs": [],
	"source": [
	"teams = list(set(df.home.unique()) & set(df.away.unique()))\n",
	"\n",
	"# pre-make some indices for use with the objective function\n",
	"\n",
	"df['hidx'] = df.home.apply(lambda x: teams.index(x))\n",
	"df['aidx'] = df.away.apply(lambda x: teams.index(x))\n",
	"df['xhdefidx'] = df.hidx + len(teams)\n",
	"df['xhoffidx'] = df.hidx\n",
	"df['xadefidx'] = df.aidx + len(teams)\n",
	"df['xaoffidx'] = df.aidx"
	]
	},
	{
	"cell_type": "markdown",
	"metadata": {},
	"source": [
	"The inputs are:\n",
	"\n",
	"* $o$: offensive rating vector\n",
	"* $d$: defensive rating vector \n",
	"* $g$: adjusted average number of goals scored (not per team, but for the whole league)\n",
	"\n",
	"The $x$ vector will have length `2 * n_teams + 2`. The first `n_teams` portion is offense, the second is defense.\n",
	"\n",
	"The constraint is that $o$ and $d$ must both average to one."
	]
	},
	{
	"cell_type": "code",
	"execution_count": 4,
	"metadata": {
	"collapsed": false
	},
	"outputs": [],
	"source": [
	"n_teams = len(teams)\n",
	"ghome = n_teams*2\n",
	"gaway = n_teams*2+1\n",
	"\n",
	"def off_constr(x):\n",
	" return np.mean(x[:n_teams]) - 1\n",
	"\n",
	"def def_constr(x):\n",
	" return np.mean(x[n_teams:n_teams*2]) - 1\n",
	"\n",
	"def obj(x):\n",
	" err = ((df['GH'] - x[ghome] * df.xhoffidx.apply(lambda i: x[i]) * df.xadefidx.apply(lambda i: x[i]))**2).sum()\n",
	" err += ((df['GA'] - x[gaway] * df.xaoffidx.apply(lambda i: x[i]) * df.xhdefidx.apply(lambda i: x[i]))**2).sum()\n",
	" return err"
	]
	},
	{
	"cell_type": "code",
	"execution_count": 5,
	"metadata": {
	"collapsed": false
	},
	"outputs": [],
	"source": [
	"# Both of these work well for initializations.\n",
	"# Starting at all zeros gets bad results, probably because of how the minimizer handles the constraints\n",
	"x0 = np.random.random(size=len(teams)*2 + 2)\n",
	"#x0 = np.ones(shape=len(teams)*2 + 2)"
	]
	},
	{
	"cell_type": "code",
	"execution_count": 6,
	"metadata": {
	"collapsed": false,
	"scrolled": true
	},
	"outputs": [
	{
	"data": {
	"text/plain": [
	"(True, 'Optimization terminated successfully.')"
	]
	},
	"execution_count": 6,
	"metadata": {},
	"output_type": "execute_result"
	}
	],
	"source": [
	"res = optimize.minimize(obj, x0, constraints=[{'type':'eq', 'fun':off_constr}, {'type':'eq', 'fun':def_constr}],\n",
	" options={'maxiter':300})\n",
	"res.success, res.message"
	]
	},
	{
	"cell_type": "code",
	"execution_count": 7,
	"metadata": {
	"collapsed": false
	},
	"outputs": [
	{
	"data": {
	"text/plain": [
	"57"
	]
	},
	"execution_count": 7,
	"metadata": {},
	"output_type": "execute_result"
	}
	],
	"source": [
	"res.nit"
	]
	},
	{
	"cell_type": "code",
	"execution_count": 8,
	"metadata": {
	"collapsed": false
	},
	"outputs": [
	{
	"name": "stdout",
	"output_type": "stream",
	"text": [
	"Home average points: 1.448\n",
	"Away average points: 0.836\n",
	"\n",
	" Team Off Rate Def Rate\n",
	" PAS 0.8041 1.1211\n",
	" Levadiakos 0.8245 1.3710\n",
	" Olympiacos 1.6307 0.4995\n",
	" PAOK 1.4840 0.5731\n",
	" PAO 1.3208 0.6781\n",
	" Veroia 0.8034 1.7478\n",
	" Xanthi 1.0216 0.7469\n",
	" AEK 1.6083 0.7055\n",
	" Iraklis 0.7620 1.0261\n",
	" Asteras 0.8934 1.3617\n",
	" Atromitos 0.7370 1.0214\n",
	" AEL 0.6964 1.1276\n",
	" Kerkira 0.6324 1.2594\n",
	" Platanias 0.9914 1.0990\n",
	" Panionios 0.9138 0.5325\n",
	" Panaitolikos 0.8761 1.1292\n"
	]
	}
	],
	"source": [
	"print(\"Home average points: {:.3f}\".format(res.x[ghome]))\n",
	"print(\"Away average points: {:.3f}\".format(res.x[gaway]))\n",
	"print()\n",
	"print(\" Team Off Rate Def Rate\")\n",
	"for i, t in enumerate(teams):\n",
	" print(\"{:>20s} {:.4f} {:.4f}\".format(t, res.x[i], res.x[i+n_teams]))"
	]
	},
	{
	"cell_type": "code",
	"execution_count": 9,
	"metadata": {
	"collapsed": false
	},
	"outputs": [
	{
	"data": {
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BAGAKBD4AACZA4AMAYALBCxYsWODrIgLZoEGDfF1Cm6Et7RNtaZ9oS/tk5rb4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\nAwBgAgQ+AAAmQOADAGACBD4AACbw/wBBLxa3qHx/8AAAAABJRU5ErkJggg==\n",
	"text/plain": [
	"<matplotlib.figure.Figure at 0x9619f98>"
	]
	},
	"metadata": {},
	"output_type": "display_data"
	}
	],
	"source": [
	"sns.set_style('ticks')\n",
	"plt.scatter(res.x[n_teams:n_teams*2], res.x[:n_teams]); plt.ylabel(\"Offensive Rating\"); plt.xlabel(\"Defensive Rating\")\n",
	"plt.xlim(0.25, 2); plt.ylim(0.5, 1.7);\n",
	"sns.despine()"
	]
	},
	{
	"cell_type": "code",
	"execution_count": null,
	"metadata": {
	"collapsed": true
	},
	"outputs": [],
	"source": []
	},
	{
	"cell_type": "code",
	"execution_count": null,
	"metadata": {
	"collapsed": true
	},
	"outputs": [],
	"source": []
	},
	{
	"cell_type": "code",
	"execution_count": null,
	"metadata": {
	"collapsed": true
	},
	"outputs": [],
	"source": []
	}
	],
	"metadata": {
	"kernelspec": {
	"display_name": "Python [root]",
	"language": "python",
	"name": "Python [root]"
	},
	"language_info": {
	"codemirror_mode": {
	"name": "ipython",
	"version": 3
	},
	"file_extension": ".py",
	"mimetype": "text/x-python",
	"name": "python",
	"nbconvert_exporter": "python",
	"pygments_lexer": "ipython3",
	"version": "3.6.1"
	}
	},
	"nbformat": 4,
	"nbformat_minor": 2
	}