Análise de modelos de campeonato..ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Randon Pairing vs Power Pairing e Page Rank vs Trivial Rank\n",
    "Neste documento, queremos investigar qual é o melhor jeito de fazer o rankeamento e o pairing, para o Campeonato Fluminense de Debates.\n",
    "\n",
    "O objetivo é que os 8 melhores debatedores passem de fase com a menor variância para o 8º colocado. Também objetivamos que cada debate (sala) seja mais equilibrado quanto o possível. Talvez algunas destes requisitos entrem em conflito entre si."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib\n",
    "import matplotlib.pyplot as plt\n",
    "import networkx as nx\n",
    "import random\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 147,
   "metadata": {},
   "outputs": [],
   "source": [
    "duplas = 16\n",
    "rodadas = 4\n",
    "teste = 10000"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "power = [random.random() for i in range(duplas)]\n",
    "power.sort(reverse=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Paring aleatório e trivial rank"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 148,
   "metadata": {},
   "outputs": [],
   "source": [
    "def campeonato_aleatorio_padrao(power, rodadas): #Trivial Rank, Random Pairing\n",
    "    global Avar\n",
    "    duplas = len(power)\n",
    "    tabela = [[0,0] for i in range(duplas)]\n",
    "    def gerar_rodada_aleatoria(duplas): \n",
    "        numeros = list(range(duplas))\n",
    "        random.shuffle(numeros)\n",
    "        rodada = [[]]\n",
    "        while len(numeros) != 0:\n",
    "            if len(rodada[-1]) != 4:\n",
    "                rodada[-1].append(numeros.pop())\n",
    "            else:\n",
    "                rodada.append([])\n",
    "        return rodada\n",
    "    for i in range(rodadas):\n",
    "        rodada = gerar_rodada_aleatoria(duplas)\n",
    "        for sala in rodada:\n",
    "            A = [(power[dupla]+0.05*np.random.randn(), dupla) for dupla in sala]\n",
    "            azinho = [i[0] for i in A]\n",
    "            Avar += np.var(azinho)\n",
    "            A.sort(key = lambda x: x[1])\n",
    "            tabela[A[0][1]][0] += 3\n",
    "            tabela[A[0][1]][1] += A[0][0]\n",
    "            tabela[A[1][1]][0] += 2\n",
    "            tabela[A[1][1]][1] += A[1][0]\n",
    "            tabela[A[2][1]][0] += 1\n",
    "            tabela[A[2][1]][1] += A[2][0]\n",
    "            tabela[A[3][1]][1] += A[3][0]\n",
    "    return tabela"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 149,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.05650426001089521"
      ]
     },
     "execution_count": 149,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A = [[] for i in range(duplas)]\n",
    "Avar = 0 #variância das partidas\n",
    "for i in range(teste):\n",
    "    tabela = campeonato_aleatorio_padrao(power, rodadas) #executa um campeonato e gera a tabela\n",
    "    tabela1 = [(tabela[i][0], tabela[i][1], i) for i in range(len(tabela))] #ordena\n",
    "    tabela1.sort(key=lambda x: (x[0], x[1]), reverse=True)\n",
    "    tabela2 = tabela[:]\n",
    "    tabela2.sort(key=lambda x: (x[0], x[1]), reverse=True)\n",
    "    n = 0\n",
    "    for item in tabela1:\n",
    "        A[item[2]].append(n)\n",
    "        n += 1\n",
    "Avar/(teste*duplas) #Variância média das salas. Mede o quanto que neste modelo de campeonato o nível das duplas é díspar."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 150,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "a = [(sum(item)/len(item), np.var(item)) for item in A]\n",
    "plt.plot(a)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A variância é maior justamente no meio, onde menos gostaríamos que houvesse variância."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 151,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "25.35312298"
      ]
     },
     "execution_count": 151,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "varianciatotal = [i[1] for i in a]\n",
    "sum(varianciatotal) #variância total do campeonato"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 152,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.6222111329910174"
      ]
     },
     "execution_count": 152,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(np.var(A[7]))**0.5 #desvio padrão do 8º colocado"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "## Power paring, trivial ranking\n",
    "### Caso 1: Primeira rodada aleatória, demais por power paring."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 153,
   "metadata": {},
   "outputs": [],
   "source": [
    "def campeonato_power_paired_rank_padrao(power, rodadas):\n",
    "    global Bvar\n",
    "    duplas = len(power)\n",
    "    tabela = [[0,0] for i in range(duplas)]\n",
    "    def gerar_rodada_power_paired(duplas, tabela): \n",
    "        if sum([sum(x) for x in tabela])== 0:\n",
    "            numeros = list(range(duplas))\n",
    "            random.shuffle(numeros)\n",
    "            rodada = [[]]\n",
    "            while len(numeros) != 0:\n",
    "                if len(rodada[-1]) != 4:\n",
    "                    rodada[-1].append(numeros.pop())\n",
    "                else:\n",
    "                    rodada.append([])\n",
    "            return rodada\n",
    "        else:\n",
    "            tabela1 = [(tabela[i][0], tabela[i][1], i) for i in range(duplas)]\n",
    "            tabela1.sort(key=lambda x: (x[0], x[1]), reverse=True)\n",
    "            numeros = [i[2] for i in tabela1]\n",
    "            rodada = [[]] \n",
    "            while len(numeros) != 0:\n",
    "                if len(rodada[-1]) != 4:\n",
    "                    rodada[-1].append(numeros.pop())\n",
    "                else:\n",
    "                    rodada.append([])\n",
    "            return rodada\n",
    "    for i in range(rodadas):\n",
    "        rodada = gerar_rodada_power_paired(duplas, tabela)\n",
    "        for sala in rodada:\n",
    "            A = [(power[dupla]+0.05*np.random.randn(), dupla) for dupla in sala]\n",
    "            azinho = [i[0] for i in A]\n",
    "            Bvar += np.var(azinho)\n",
    "            A.sort(key = lambda x: x[1])\n",
    "            tabela[A[0][1]][0] += 3\n",
    "            tabela[A[0][1]][1] += A[0][0]\n",
    "            tabela[A[1][1]][0] += 2\n",
    "            tabela[A[1][1]][1] += A[1][0]\n",
    "            tabela[A[2][1]][0] += 1\n",
    "            tabela[A[2][1]][1] += A[2][0]\n",
    "            tabela[A[3][1]][1] += A[3][0]\n",
    "    return tabela"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 154,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0267226504851434"
      ]
     },
     "execution_count": 154,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "B = [[] for i in range(duplas)]\n",
    "Bvar = 0\n",
    "for i in range(teste):\n",
    "    tabela = campeonato_power_paired_rank_padrao(power, rodadas) #executa um campeonato e gera a tabela\n",
    "    tabela1 = [(tabela[i][0], tabela[i][1], i) for i in range(len(tabela))] #ordena\n",
    "    tabela1.sort(key=lambda x: (x[0], x[1]), reverse=True)\n",
    "    tabela2 = tabela[:]\n",
    "    tabela2.sort(key=lambda x: (x[0], x[1]), reverse=True)\n",
    "    n = 0\n",
    "    for item in tabela1:\n",
    "        B[item[2]].append(n)\n",
    "        n += 1\n",
    "Bvar/(teste*duplas) #mostra a variância média das partidas neste modelo de campeonato"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 155,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "b = [(sum(item)/len(item), np.var(item), B.index(item)) for item in B]\n",
    "plt.plot(b)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "É interessante que a variância seja menor justamente no break e mesmo havendo algumas duplas que não ficam no seu lugar de fato na maioria das vezes, é pouco importante porque acontece justamente longe do break."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 156,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "24.44103788"
      ]
     },
     "execution_count": 156,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "varianciatotal = [i[1] for i in b]\n",
    "sum(varianciatotal) #Desvio padrão médio total"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 157,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.4874303983716346"
      ]
     },
     "execution_count": 157,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(np.var(B[7]))**0.5 #Desvio padrão do 8º colocado"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Aqui a variância total do campeonato é menor que no outro caso."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "# Campeonato Comum + Pairing por reputação"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 192,
   "metadata": {},
   "outputs": [],
   "source": [
    "def campeonato_power_paired_rank_padrao(power, rodadas):\n",
    "    global Dvar\n",
    "    duplas = len(power)\n",
    "    tabela = [[0,0] for i in range(duplas)]\n",
    "    def gerar_rodada_power_paired(duplas, tabela): \n",
    "        if sum([sum(x) for x in tabela])== 0:\n",
    "            tabela1 = [(tabela[i][0], (0.1*np.random.randn()+power[i]), i) for i in range(duplas)]\n",
    "            tabela1.sort(key=lambda x: (x[0], x[1]), reverse=True)\n",
    "            numeros0 = []\n",
    "            while len(numeros0) < 0.25*len(tabela1):\n",
    "                a = tabela1.pop(0)\n",
    "                numeros0.append(a[2])\n",
    "            numeros = [i[2] for i in tabela1]\n",
    "            random.shuffle(numeros)\n",
    "            rodada = [[]] \n",
    "            while len(numeros) != 0:\n",
    "                if len(rodada[-1]) == 0:\n",
    "                    rodada[-1].append(numeros0.pop())\n",
    "                elif len(rodada[-1]) != 4:\n",
    "                    rodada[-1].append(numeros.pop())\n",
    "                else:\n",
    "                    rodada.append([])\n",
    "            return rodada\n",
    "        else:\n",
    "            tabela1 = [(tabela[i][0], tabela[i][1], i) for i in range(duplas)]\n",
    "            tabela1.sort(key=lambda x: (x[0], x[1]), reverse=True)\n",
    "            numeros = [i[2] for i in tabela1]\n",
    "            rodada = [[]] \n",
    "            while len(numeros) != 0:\n",
    "                if len(rodada[-1]) != 4:\n",
    "                    rodada[-1].append(numeros.pop())\n",
    "                else:\n",
    "                    rodada.append([])\n",
    "            return rodada\n",
    "    for i in range(rodadas):\n",
    "        rodada = gerar_rodada_power_paired(duplas, tabela)\n",
    "        for sala in rodada:\n",
    "            A = [(power[dupla]+0.05*np.random.randn(), dupla) for dupla in sala]\n",
    "            A.sort(key = lambda x: x[1])\n",
    "            azinho = [i[0] for i in A]\n",
    "            Dvar += np.var(azinho)\n",
    "            tabela[A[0][1]][0] += 3\n",
    "            tabela[A[0][1]][1] += A[0][0]\n",
    "            tabela[A[1][1]][0] += 2\n",
    "            tabela[A[1][1]][1] += A[1][0]\n",
    "            tabela[A[2][1]][0] += 1\n",
    "            tabela[A[2][1]][1] += A[2][0]\n",
    "            tabela[A[3][1]][1] += A[3][0]\n",
    "    return tabela"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 193,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[[12, 3.7990071946001573],\n",
       " [9, 3.1569610780893327],\n",
       " [8, 3.3299261697449687],\n",
       " [7, 3.0854000395157746],\n",
       " [7, 2.8691627123844565],\n",
       " [6, 2.6250049375222586],\n",
       " [7, 2.2193621200978186],\n",
       " [6, 1.9289481979268601],\n",
       " [6, 1.5286358544417102],\n",
       " [5, 1.4176188716707396],\n",
       " [6, 1.5115066023841428],\n",
       " [5, 1.0908358640662894],\n",
       " [5, 1.0444254821835395],\n",
       " [4, 0.9643789060949685],\n",
       " [3, 0.8645230695340096],\n",
       " [0, 0.07290117256654079]]"
      ]
     },
     "execution_count": 193,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "campeonato_power_paired_rank_padrao(power, rodadas)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 194,
   "metadata": {},
   "outputs": [
    {
     "ename": "KeyboardInterrupt",
     "evalue": "",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mKeyboardInterrupt\u001b[0m                         Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-194-49d90d77f27a>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m      2\u001b[0m \u001b[0mDvar\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;36m0\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      3\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mi\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mteste\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 4\u001b[0;31m     \u001b[0mtabela\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mcampeonato_power_paired_rank_padrao\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mpower\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mrodadas\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;31m#executa um campeonato e gera a tabela\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      5\u001b[0m     \u001b[0mtabela1\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mtabela\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mtabela\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mi\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mi\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mtabela\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;31m#ordena\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      6\u001b[0m     \u001b[0mtabela1\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msort\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mkey\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mlambda\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mreverse\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mTrue\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m<ipython-input-192-358a09c20f77>\u001b[0m in \u001b[0;36mcampeonato_power_paired_rank_padrao\u001b[0;34m(power, rodadas)\u001b[0m\n\u001b[1;32m     39\u001b[0m             \u001b[0mA\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msort\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mkey\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;32mlambda\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     40\u001b[0m             \u001b[0mazinho\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mi\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mA\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 41\u001b[0;31m             \u001b[0mDvar\u001b[0m \u001b[0;34m+=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mvar\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mazinho\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     42\u001b[0m             \u001b[0mtabela\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mA\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m+=\u001b[0m \u001b[0;36m3\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     43\u001b[0m             \u001b[0mtabela\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mA\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m+=\u001b[0m \u001b[0mA\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/usr/local/lib/python3.5/dist-packages/numpy/core/fromnumeric.py\u001b[0m in \u001b[0;36mvar\u001b[0;34m(a, axis, dtype, out, ddof, keepdims)\u001b[0m\n\u001b[1;32m   3192\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   3193\u001b[0m     return _methods._var(a, axis=axis, dtype=dtype, out=out, ddof=ddof,\n\u001b[0;32m-> 3194\u001b[0;31m                          **kwargs)\n\u001b[0m",
      "\u001b[0;32m/usr/local/lib/python3.5/dist-packages/numpy/core/_methods.py\u001b[0m in \u001b[0;36m_var\u001b[0;34m(a, axis, dtype, out, ddof, keepdims)\u001b[0m\n\u001b[1;32m    114\u001b[0m         \u001b[0mx\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mum\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmultiply\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mum\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mconjugate\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mout\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mreal\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    115\u001b[0m     \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 116\u001b[0;31m         \u001b[0mx\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mum\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmultiply\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mout\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    117\u001b[0m     \u001b[0mret\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mumr_sum\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0maxis\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdtype\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mout\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mkeepdims\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    118\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mKeyboardInterrupt\u001b[0m: "
     ]
    }
   ],
   "source": [
    "D = [[] for i in range(duplas)]\n",
    "Dvar = 0\n",
    "for i in range(teste):\n",
    "    tabela = campeonato_power_paired_rank_padrao(power, rodadas) #executa um campeonato e gera a tabela\n",
    "    tabela1 = [(tabela[i][0], tabela[i][1], i) for i in range(len(tabela))] #ordena\n",
    "    tabela1.sort(key=lambda x: (x[0], x[1]), reverse=True)\n",
    "    tabela2 = tabela[:]\n",
    "    tabela2.sort(key=lambda x: (x[0], x[1]), reverse=True)\n",
    "    n = 0\n",
    "    for item in tabela1:\n",
    "        D[item[2]].append(n)\n",
    "        n += 1\n",
    "Dvar/(teste*duplas) #mostra a variância média das partidas neste modelo de campeonato"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 161,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "18.827114160000004"
      ]
     },
     "execution_count": 161,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "varianciatotal = [i[1] for i in d]\n",
    "sum(varianciatotal) #Desvio padrão médio total"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 162,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9382425912310739"
      ]
     },
     "execution_count": 162,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(np.var(D[7]))**0.5 #Desvio padrão do 8º colocado"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "O que é relevante neste último teste é que **estimar os melhores debatedores** ajuda a diminuir o desvio padrão médio em quase 3 colocações e o desvio padrão do 8º colocado é diminuido em $16\\%$. Isso é muito relevante e será capaz de que o campeonato tenha semi-finais com os melhores debatedores."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 196,
   "metadata": {},
   "outputs": [],
   "source": [
    "def campeonato_page_rank_paired(power, rodadas):\n",
    "    global Evar\n",
    "    duplas = len(power)\n",
    "    tabela = [[0,0] for i in range(duplas)]\n",
    "    def gerar_rodada_power_paired(duplas, tabela): \n",
    "        if sum([sum(x) for x in tabela])== 0:\n",
    "            tabela1 = [(tabela[i][0], (0.1*np.random.randn()+power[i]), i) for i in range(duplas)]\n",
    "            tabela1.sort(key=lambda x: (x[0], x[1]), reverse=True)\n",
    "            numeros0 = []\n",
    "            while len(numeros0) <= 0.25*len(tabela1):\n",
    "                a = tabela1.pop(0)\n",
    "                numeros0.append(a[2])\n",
    "            numeros = [i[2] for i in tabela1]\n",
    "            random.shuffle(numeros)\n",
    "            rodada = [[]] \n",
    "            while len(numeros) != 0:\n",
    "                if len(rodada[-1]) == 0:\n",
    "                    rodada[-1].append(numeros0.pop())\n",
    "                elif len(rodada[-1]) != 4:\n",
    "                    rodada[-1].append(numeros.pop())\n",
    "                else:\n",
    "                    rodada.append([])\n",
    "            return rodada\n",
    "        else:\n",
    "            tabela1 = [(tabela[i][0], tabela[i][1], i) for i in range(duplas)]\n",
    "            tabela1.sort(key=lambda x: (x[0], x[1]), reverse=True)\n",
    "            numeros = [i[2] for i in tabela1]\n",
    "            rodada = [[]] \n",
    "            while len(numeros) != 0:\n",
    "                if len(rodada[-1]) != 4:\n",
    "                    rodada[-1].append(numeros.pop())\n",
    "                else:\n",
    "                    rodada.append([])\n",
    "            return rodada\n",
    "    ADJ = np.zeros(duplas*duplas)\n",
    "    ADJ = ADJ.reshape(duplas, duplas)\n",
    "    for i in range(rodadas):\n",
    "        rodada = gerar_rodada_power_paired(duplas, tabela)\n",
    "        for sala in rodada:\n",
    "            A = [(power[dupla]+0.05*np.random.randn(), dupla) for dupla in sala]\n",
    "            A.sort(key = lambda x: x[1])\n",
    "            azinho = [i[0] for i in A]\n",
    "            ADJ[A[0][1], A[1][1]] += 1\n",
    "            ADJ[A[0][1], A[2][1]] += 1\n",
    "            ADJ[A[0][1], A[3][1]] += 1\n",
    "            ADJ[A[1][1], A[2][1]] += 1\n",
    "            ADJ[A[1][1], A[3][1]] += 1\n",
    "            ADJ[A[2][1], A[3][1]] += 1\n",
    "            Evar += np.var(azinho)\n",
    "            tabela[A[0][1]][0] += 3\n",
    "            tabela[A[0][1]][1] += A[0][0]\n",
    "            tabela[A[1][1]][0] += 2\n",
    "            tabela[A[1][1]][1] += A[1][0]\n",
    "            tabela[A[2][1]][0] += 1\n",
    "            tabela[A[2][1]][1] += A[2][0]\n",
    "            tabela[A[3][1]][1] += A[3][0]\n",
    "    G = nx.from_numpy_matrix(ADJ, parallel_edges=True, create_using=nx.DiGraph())\n",
    "    PR = nx.pagerank(G, alpha=0.9)\n",
    "    tabelosa = [PR[duplas - i - 1] for i in range(duplas)]\n",
    "    return tabelosa"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 197,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.026749555332823235"
      ]
     },
     "execution_count": 197,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "E = [[] for i in range(duplas)]\n",
    "Evar = 0\n",
    "for i in range(teste):\n",
    "    tabela = campeonato_page_rank_paired(power, rodadas) #executa um campeonato e gera a tabela\n",
    "    tabela1 = [(tabela[i], i) for i in range(len(tabela))] #ordena\n",
    "    tabela1.sort(reverse=True)\n",
    "    n = 0\n",
    "    for item in tabela1:\n",
    "        E[item[1]].append(n)\n",
    "        n += 1\n",
    "Evar/(teste*duplas) #mostra a variância média das partidas neste modelo de campeonato"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 198,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "e = [(sum(item)/len(item), np.var(item), E.index(item)) for item in E]\n",
    "plt.plot(e)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 199,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4.5625275400000005"
      ]
     },
     "execution_count": 199,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "varianciatotal = [i[1] for i in e]\n",
    "sum(varianciatotal) #Desvio padrão médio total"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 200,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8764493767468833"
      ]
     },
     "execution_count": 200,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(np.var(E[7]))**0.5 #Desvio padrão do 8º colocado"
   ]
  }
 ],
 "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": "3.5.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}