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@carterk
Created October 29, 2013 22:33
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{
"metadata": {
"name": "SportsRankingPartThree"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "code",
"collapsed": true,
"input": "import numpy as np\nimport matplotlib.pyplot as plt\n%pylab inline\nfrom scipy import stats\nimport matplotlib.mlab as mlab\nimport bisect\n\ncolours=['y','c']",
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": "Populating the interactive namespace from numpy and matplotlib\n"
}
],
"prompt_number": 172
},
{
"cell_type": "markdown",
"metadata": {},
"source": "<h1>Tango's variance equation</h1>\n\nHere we use Tom Tango's equation to find the true variance (variance due to skill) of win percentages for each league.\n\n$ var(observed) = var(skill) + var(luck) $\n\nwhere\n\n$ var(luck)=.5*.5/gp $, where $gp$ is the number of games played\n\nand $ var(observed) $ is found from looking at historical win percentages data for each league. Numbers from:\n\nhttp://www.insidethebook.com/ee/index.php/site/comments/true_talent_levels_for_sports_leagues/"
},
{
"cell_type": "code",
"collapsed": false,
"input": "#actual variances of winning percentage\navNHL=0.0997**2\navNBA=0.1449**2\navNFL=0.1899**2\navMLB=0.0717**2\n\n#random variace (variance due to luck) of winning percentage \nrvNHL=.5*.5/82\nrvNBA=.5*.5/82\nrvNFL=.5*.5/16\nrvMLB=.5*.5/162\n\n#true variance (variance due to skill) of winning percentage\ntvNHL=avNHL-rvNHL\ntvNBA=avNBA-rvNBA\ntvNFL=avNFL-rvNFL\ntvMLB=avMLB-rvMLB\n\navs={'NHL':avNHL, 'NBA':avNBA, 'NFL':avNFL, 'MLB':avMLB}\nrvs={'NHL':rvNHL, 'NBA':rvNBA, 'NFL':rvNFL, 'MLB':rvMLB}\ntvs={'NHL':tvNHL, 'NBA':tvNBA, 'NFL':tvNFL, 'MLB':tvMLB}\n\nleagues=['NHL','NBA','NFL','MLB']",
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 173
},
{
"cell_type": "markdown",
"metadata": {},
"source": "<h1> Upset probability function </h1>\n\nThis function takes 6 intputs:\n<ul>\n<li>Rank of higher ranked team</li>\n<li>Rank of lower ranked team</li>\n<li>A specific percentage (probability) at which you want to know the corresponding games required to be played for the top seed to win</li>\n<li>A specific number of games played at which you want to know the corresponding probability of the top seed winning</li>\n<li>Range of games to calculate probabilities over</li>\n<li>League that the teams are in</li>\n</ul>\n\nIt returns a list of three values:\n<ul>\n<li>Probability across range of games (gp)</li>\n<li>Games needed corresponding to specific probability input</li>\n<li>Probability corresponding to specific number of games input</li>\n</ul>\n\nI chose to model the 'skill points' that a team gets by creating a guassian-ish distribution between 0 and 1. That is; only very few high ranked teams get close to '1 point', and only very few low ranked teams get close to '0 points', and the majority of the teams get close to '0.5 points'.\n\nThe 'skill points' of the lower ranked team are subtracted from the 'skill points' of the higher ranked team. The difference is then weighted by the percentage of the actual variance that skill accounts for, given the number of games played. In order for the under dogs to win, the 'luck points' they get, subtracted from the 'luck points' the higher seeded team gets (each weighted by the percentage of the actual variance that luck accounts for), will have to be equal to the difference in 'skill points'.\n\n\n\nSo for an upset:\n\n$ luck\\%*(points(luck)_{lowseed} - points(luck)_{highseed}) = skill\\%*(points(skill)_{highseed} - points(skill)_{lowseed}) $\n\n\nwhere:\n\n$ luck\\% = \\frac{.5*.5/gp}{var(skill)+.5*.5/gp} $\n\n$ skill\\% = \\frac{var(skill)}{var(skill)+.5*.5/gp} $\n\nTo solve for the unknown, we rearange:\n\n$ (points(luck)_{lowseed} - points(luck)_{highseed}) = skill\\%*(points(skill)_{highseed} - points(skill)_{lowseed})/luck\\% $\n\nIf we assume luck is normally-ish distributed between 0 and 1, and each team picks their 'luck points' from such a distribution, to find the probability that the difference between the lower seed's 'luck points' and higher seed's 'luck points' is equal to the RHS of the above equation, we can create a new difference distribution.\n\nThis distribution will have a mean of $\\mu_{1} - \\mu_{2} $, or $ 0 $, and the variance will be $2*\\sigma^2$. Then we can find the z-score in that distribution corresponding to the LHS of the above equation, and find the corresponding probability.\n\nI'm using normal approximations for the distributions here, so nothing is mathematically perfect. My 0-1 distribution is approximated by a normal distribution with mean $ 0.5 $ and $ \\sigma = 0.14 $"
},
{
"cell_type": "code",
"collapsed": false,
"input": "#function that calculates the chance that the team that won the most games is the more skilled team\n\ndef calcchance(t1rank,t2rank,percentage,numgames,gp,league):\n \n luckperc=(.5*.5/gp)/(tvs[league]+.5*.5/gp)\n skillperc=tvs[league]/(tvs[league]+.5*.5/gp)\n \n #find skill points for each team from the skill distribution\n pvals=np.arange(1,numteams[league]+1)\n pvals=pvals*(1.0/float(numteams[league]+1))\n zscores=stats.norm.isf(pvals)\n skillscores=.5+zscores/(2*max(zscores))\n t1skillpoints=skillscores[t1rank-1]\n t2skillpoints=skillscores[t2rank-1]\n\n #find difference of skill points weighted by skill%\n skilldiff=t1skillpoints-t2skillpoints \n efskilldiff=skilldiff*skillperc\n\n #find the required z-score in the difference distribution\n z_score2=(efskilldiff-0)/(np.sqrt(2*(.14**2))*luckperc)\n \n #find the probability of no upset corresponding to that z-score\n p_val =1-stats.norm.sf(z_score2)\n\n #create a plot only for the purpose of extracting x/y pairs\n datapoints=plt.plot(gp,p_val)\n xvalues = datapoints[0].get_xdata()\n yvalues = datapoints[0].get_ydata()\n \n #find number of games required for given win probability\n for i in range(len(yvalues)):\n if yvalues[i] >= percentage:\n saveindex=i\n break\n \n #reuturn: [probabilities for all games in gp, probability at given games played, games played at given probability]\n results=[p_val,yvalues[numgames-1],xvalues[saveindex]]\n plt.close()\n return results ",
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 174
},
{
"cell_type": "markdown",
"metadata": {},
"source": "<h1>Call the function and plot results</h1>\n\nHere we just set the first 5 function parameters and call the function while cycling through the leagues. If you want to play around with the function parameters, here's the place to do it."
},
{
"cell_type": "code",
"collapsed": true,
"input": "#call function defined above and plot the results for every league\n\n#function parameters (these are the first 5. The 6th, league, is varied in for loop)\nt1rank=1\nt2rank=15\npercentage=.8\nnumgames=5\ngp=np.arange(1,101)\n\nnumteams={'MLB':30, 'NHL':30, 'NBA':30, 'NFL':32}\n\nallchances=[] #for the combined plot\n\nfor league in leagues:\n \n #call the function\n resultarray=calcchance(t1rank,t2rank,percentage,numgames,gp,league)\n \n #plot results for each league\n plt.title(league)\n plt.xlabel(\"# of games\")\n plt.ylabel('chance seed %d wins more games than seed %d' %(t1rank,t2rank))\n plt.legend()\n datapoints=plt.plot(gp,resultarray[0])\n plt.show()\n \n allchances.append(resultarray[0].tolist()) #for the combined plot\n \n print percentage*100,'% chance at', resultarray[2], 'games' \n print resultarray[1]*100, '% chance at', numgames, 'games'\n\n#combined plot\nfor i in range(len(allchances)):\n plt.plot(gp,allchances[i],label=leagues[i]) \n plt.xlabel(\"# of games\")\n plt.ylabel('chance seed %d wins more games than seed %d' %(t1rank,t2rank))\n plt.legend()\nplt.show() ",
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
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aNGnCc889R3h4OI0aNXJWbBb2bjlMmQJJSTBjht2KFBFxOw497OfUqVMkJCSQ\nk5PD66+/Tvv27RkyZIhNlbkLjTeIiNyc1eSQnZ1NRkYGP//8M+np6Zw9e5YKpfi4tHPnYONGiIhw\ndSQiIu7L6phDx44d6dChA506deKFF17A29vbGXE5zMqV0KED1Krl6khERNyX1eSwc+dOZ8ThNIsW\nQa9ero5CRMS9lau9lfLyoF492LoVfH3tEJiIiBtz6IB0WZKcDHffrcQgImJNuUoOS5aoS0lEpDhs\nSg5vvfWWveNwisWLoWdPV0chIuL+bBpz8PHx4fDhw46I54bsMeZw+DAEBcGJE1Cxop0CExFxYw7Z\nPqPWTeZ6Xrp0yabKXGnJEnj4YSUGEZHiKDI53HHHHSQnJ1OvXr1C7/n4+Dg0KEdYvBieeMLVUYiI\nlA5Fjjk88cQTZGRk3PC9qKgohwXkCBcvwrp1EBnp6khEREqHcrHOYckSeO89+O47OwYlIuLmtM7B\nisWLNYVVRKQkrG6fUdoZhrnlsGKFqyMRESk9ynzLYfduqFQJ/PxcHYmISOlRZMshMzPzph+sU6eO\n3YNxhKVLoUcPMJlcHYmISOlRZHIIDg62DGZkZGRQtWpVAC5fvoyvry+HDh1yWpC3YulSeOUVV0ch\nIlK6FJkc0tPTAYiNjaVVq1YMHjwYgDlz5rB9+3anBHerzp6F7dshPNzVkYiIlC5Wp7L6+fmxZ88e\ny+lv+fn5BAQEsHfvXqcECLZPx/rqK/jsM3PrQUSkvHHI9hnX9OzZkxdffJGnnnoKwzCYOXMmPUvJ\n7nXXxhtERKRkrLYczp49S0JCAsuXLwfg4YcfZvjw4Xh4eDglQLAt++Xnwz33mM+LbtzYQYGJiLix\nW2k5FHuF9KVLl6hevbpNldwqW77gtm0weDA4sfdLRMStOHSF9I4dO+jZsycBAQGW5yNGjLCpMmdS\nl5KIiO2sJoe///3vTJgwgdq1awPQunVr1q5d6/DAbpWSg4iI7awmh2PHjtGiRQvL88uXL1OjRo1i\nFb5u3Tr8/f1p1qwZkydPvuE1W7ZsoV27dvj7+xNupzmnp07Bnj3QqZNdihMRKXeszlaKiIjgm2++\nASAjI4PJkyfTt2/fYhU+cuRI4uPj8fX1JTIykqioKLy8vCzvG4bB8OHD+eCDD+jWrRunTp2y8WsU\ntHKleW3D/9btiYhICVltOcTGxpKSkkJeXh4PP/wwtWvXJiYmxmrBWVlZAISFheHr60tERARJSUkF\nrtm6dSuPHz01AAARRElEQVSBgYF069YNoEDiuBXLlplPfRMREdtYTQ533HEHY8eOZefOnezevZvX\nX3+9WNNYt2zZgt91u90FBASwefPmAtesWLECk8lEp06d6N27NyvssHVqfr55B1YlBxER21ntVjp0\n6BD/+Mc/2Lx5MykpKezcuZOFCxcyZsyYW648JyeHHTt2sHr1ai5evMhDDz3Erl27bjhlduzYsZaf\nw8PDixyf2LYNvLzA1/eWwxMRKVUSExNJTEy0S1lW1zkMHTqUgQMH8vrrr5OSkoJhGLRo0YLdu3ff\ntOCsrCzCw8NJSUkBICYmhu7duxdYXb1kyRISExN59913ARg4cCDDhw8n8nfneZZkru5bb5n3VPrn\nP4t1uYhImeXQdQ779u2jx3VzQvPz86lSpYrVgq91Pa1bt4709HRWrVpFSEhIgWvuv/9+1q5dy8WL\nF8nMzCQlJYUOHTqU9DsUsHy5upRERG6V1W6ljh07sm3bNsA8jXXq1KmF/rIvysSJE4mOjiY3N5fY\n2Fi8vLyIj48HIDo6Gk9PT4YNG0bbtm2pW7cub731FrfddpvNXyYzE3btgrAwm4sQERGK0a109OhR\n3njjDZYuXUqFChXo0aMHcXFx3HPPPc6KsdhNoy++gNmzYdEiJwQlIuLmnLK3Um5uLoZhFKtLyd6K\n+wWHDoX27eH5550QlIiIm3PomMPEiRM5d+4clStX5q9//SsRERGFpqS6A01hFRGxH6vJISEhgdtv\nv52NGzeyY8cO4uLi+Otf/+qM2Epkxw7w8ND23CIi9mA1OVSuXBmAzz//nP/7v/8jNDTUbttc2NOy\nZdC9u6ujEBEpG6wmh4ceeoiwsDA2bNhAv379OHfunOXIUHeiKawiIvZTrAHpgwcP4u3tTZUqVTh9\n+jRHjx4lMDDQGfEB1gdVsrLA2xt+/RVcdB6RiIjbcegZ0gCNr+vI9/T0xNPT06bKHOXbb+GBB5QY\nRETsxf36h2ywfLnGG0RE7KnUJwfDME9hVXIQEbGfYiWH48ePM3v2bABOnjzJoUOHHBpUSezda/73\nut3BRUTkFllNDp988glRUVHExcUBcOXKFYYMGeLwwIpr+XKIjASTydWRiIiUHVaTw8yZM1m5ciU1\na9YEoH79+mRnZzs8sOLSeIOIiP1ZTQ4eHh4F1jVkZGTg7e3t0KCK69Il2LgRHnzQ1ZGIiJQtVpPD\n0KFDGTx4MGfPniUuLo5evXrxzDPPOCM2q9auhdatzdtmiIiI/RRrEVx6ejrz588nPz+fQYMG4ePj\n44zYLIpayPHii1C3Lrz+ulPDEREpFRy6ZfehQ4eoV6+e5VznS5cuceLECRo2bGhThbYo6gv6+8PM\nmdC2rdNCEREpNRy6ZXf//v2pWLHibx+oUIH+/fvbVJk9/fwznD4NwcGujkREpOyxmhx+f2Z0lSpV\nuHLlikODKo4VK+Chh8AN9wAUESn1rP5q7dq1K1OmTCE3N5crV64wZcoUHnSD6UErVpjXN4iIiP1Z\nTQ4vvvgiycnJNG3alKZNm5KcnMzLL7/sjNiKdPUqrFkDEREuDUNEpMwq0RnS8NvhP870+0GV7783\nnxO9Y4fTQxERKTUcumV3bm4umzZtYtOmTVy+fBnDMDCZTLzxxhs2VWgP6lISEXEsq8khJiaG9PR0\nOnfubNlCw9VWrIB33nF1FCIiZZfVbqWAgAB27drl0qNBr28anT4NjRvDyZNw3SQqERH5HYeuc+jS\npQvfffedTYU7wurVEBamxCAi4kjFajns3buX+vXrU7t2bfOHTCZ27tzplACv1XctzOHDzQvfXnjB\nadWLiJRKDt0+Iz09/Yavu2L7DMMAb29ITIRmzZxWvYhIqeTQ2UrXkkBWVhZZWVk2VWIvu3dD1arQ\ntKlLwxARKfOsjjmsXbuWLl26UL9+fYKDg2nYsCE9evRwRmyF3Huv+XAfnfomIuJYVpPDhAkTmDFj\nBk2aNOHXX39l1qxZhIWFOSO2QqpUMScIERFxLKvJ4ZdffqFBgwbUrFmTCxcu8Ic//MGtZi+JiIj9\nWR1zqFOnDtnZ2fTo0YP+/ftTv359/P39nRGbiIi4iNXZSufPn6d69epUrFiRxMREjh49Sr9+/Zy6\nWvpWRtxFRMorh05ldQdKDiIiJefQFdKrV6+ma9eu1K5dm1q1alGrVi1uv/12myoTEZHSwWrLoW3b\ntkyaNInQ0FCX7a+kloOISMk5tOVQpUoV2rRpY1NiWLduHf7+/jRr1ozJkycXej8xMREPDw+CgoII\nCgpi3LhxJa6jvElMTHR1CG5D9+I3uhe/0b2wjyJnK82fPx+AsLAw+vXrx4ABAwrsrfToo49aLXzk\nyJHEx8fj6+tLZGQkUVFReHl5Fbimc+fOLFy48Fa+Q7mSmJhIeHi4q8NwC7oXv9G9+I3uhX0UmRwW\nLVqE6X9LkevVq8eGDRsKvG8tOVzbauPagrmIiAiSkpLo2bNngevUXSQi4n6KTA7Tp0+/pYK3bNmC\nn5+f5XlAQACbN28ukBxMJhMbN26kdevWdO3aleeff54mTZrcUr0iImIHhhVPPvmkcebMGcvzzMxM\nY9iwYdY+ZqxatcoYNGiQ5fnUqVONMWPGFLjm3LlzxoULF4wrV64Y06ZNM3r27HnDsgA99NBDDz1s\neNjK6myl1q1bs2PHjgKvtWrVih9++OFmHyMrK4vw8HBSUlIA83Gj3bt3L9StdI1hGNSrV4+MjAyq\nVq1607JFRMSxrE5B8vX1Zf/+/Zbn+/btw9vb22rBHh4egHnGUnp6OqtWrSIkJKTANSdOnLCMOSxa\ntIjAwEAlBhERN2B1b6URI0bw8MMP061bNwzDYPXq1UydOrVYhU+cOJHo6Ghyc3OJjY3Fy8uL+Ph4\nAKKjo5k3bx5Tp06lUqVKBAYG8v7779/atxEREfsoTt/ThQsXjLlz5xpz5841Lly4YHMfVkmtXbvW\n8PPzM5o2bWp8+OGHTqvXHWRkZBjh4eFGQECA0blzZ2P27NmGYZjHafr06WP4+PgYffv2NbKzs10c\nqfNcvXrVaN26tdGrVy/DMMrvvTh//rzx5JNPGs2aNTP8/f2NzZs3l9t78cknnxihoaFGcHCwMXLk\nSMMwys9/F8OGDTPuvPNOo0WLFpbXbvbdJ02aZDRt2tTw9/c31q9fb7X8Yq1sq1GjBgMGDGDAgAHU\nqFHD0fnK4to6idWrV/Ovf/2LU6dOOa1uV6tcuTIffPABu3fvZt68eYwZM4bs7GymTp1KgwYN2L9/\nP97e3nz88ceuDtVpJk2aREBAgGWKdXm9F2+++SYNGjRg586d7Ny5Ez8/v3J5LzIzMxk/fjyrVq1i\ny5Yt7Nu3jxUrVpSbezFs2DCWL19e4LWivvuvv/7KlClT+Pbbb5k6dSqxsbFWy3fNfhjFcP06CV9f\nX8s6ifKiXr16tG7dGgAvLy/uu+8+tmzZQnJyMk8//TRVq1Zl+PDh5eaeHDlyhKVLl/LMM89YxqnK\n671YvXo1f/nLX6hWrRqVKlXCw8OjXN6L6tWrYxgGWVlZXLp0iYsXL1K7du1ycy86derEHXfcUeC1\nor57UlIS3bt3p0GDBnTu3BnDMMjOzr5p+W6bHIpaJ1Ee/fTTT+zevZv27dsXuC9+fn4kJye7ODrn\neOmll3j33XcLbONSHu/FkSNHyMnJ4bnnniMkJIQJEyZw6dKlcnkvqlevztSpU2nYsCH16tWjQ4cO\nhISElMt7cU1R3z0pKanAOTzNmze3el/cNjmIWXZ2NgMHDuSDDz7gtttuK5cryhcvXsydd95JUFBQ\nge9fHu9FTk4O+/bt47HHHiMxMZHdu3czd+7ccnkvTp48yXPPPceePXtIT09n06ZNLF68uFzei2tK\n8t2vdc8WxW2TQ7t27di7d6/l+e7du7n//vtdGJHz5ebm8thjj/HEE0/Qt29fwHxf0tLSAEhLS6Nd\nu3auDNEpNm7cyMKFC2nUqBFRUVGsWbOGJ554olzei6ZNm9K8eXN69+5N9erViYqKYvny5eXyXiQn\nJ3P//ffTtGlTPD09GTBgAOvXry+X9+Kaor57SEgIe/bssVy3d+9eq/fFbZNDcdZJlGWGYfD000/T\nokULXnzxRcvrISEhJCQkcOnSJRISEspFwhw/fjyHDx/m0KFDfPHFF3Tt2pWZM2eWy3sB0KxZM5KS\nksjPz2fJkiV069atXN6LTp06sXXrVjIzM7l8+TLLli0jIiKiXN6La4r67u3bt2fFihVkZGSQmJhI\nhQoVqFWr1s0Ls+PMKrtLTEw0/Pz8jCZNmhiTJk1ydThOtX79esNkMhmtWrUyWrdubbRu3dpYtmxZ\nuZmmV5TExESjd+/ehmGUnymLv/fjjz8aISEhRqtWrYyXX37ZOH/+fLm9F5999pkRFhZmtG3b1hgz\nZoyRl5dXbu7FoEGDjLvvvtuoUqWK4e3tbSQkJNz0u0+cONFo0qSJ4e/vb6xbt85q+aXimFAREXEu\nt+1WEhER11FyEBGRQpQcRESkECUHEREpRMlByqTXXnuNxMREvv76a955550SfTYnJ4cePXrQpk0b\nvv/+ewdFKOLelBykTLq2QGrt2rWWc8yLa+XKldx5551s27aNDh06OChCEfem5CBlyiuvvEKrVq3Y\nsmULoaGhfPrppzz33HOMGzeu0LXHjh1j5MiRtGrVipdeeokTJ06wY8cOYmJiWLp0KUFBQeTk5BT4\nTFJSEg8++CBBQUG8+uqr9O7dGzAnowceeICgoCCGDh1Keno6YD6LfeDAgURERNC4cWNmzJjB1KlT\nCQwMJCoqyrL52dGjR/nTn/5EaGgoQ4cO5dChQwCsWrWKsLAwWrVqRefOnR1450R+x3FLNERcY8uW\nLUZsbKyRm5trdOjQocjrXnrpJeMf//iHYRiGMX78eOOVV14xDMMwpk+fbsTExNzwMy1btjS2b99u\nXLhwwejRo0eBBXlXr141DMMwvvzyS+PVV181DMO8SKtevXrGiRMnjPT0dKN69erGuHHjDMMw78c/\nb948wzAMY/jw4cbWrVsNwzCMJUuWGH/84x8NwzCMzp07GwcOHDAMwzCysrJsvykiJWT1JDiR0mbb\ntm0EBgaSlpZWYCfK31u2bBkbNmwA4OmnnyY8PJwJEyZgGMYNNzA7cuQIJpOJoKAgAB5//HHmzZsH\nwKVLl3j99ddZu3YthmFQqVIl3n77bQC6devGnXfeCcAdd9xBVFQUAKGhoWzatIm+ffuydOlStm/f\nXqjOjh078vTTTzN06FDL50ScQclByowffviBp556iiNHjuDl5cXFixcxDIPg4GA2btxItWrVCn3m\nRkmguK7/7JQpU/D09GTr1q3s3r2bRx55xPJe7dq1LT9XqVLF8rxKlSpcvnyZ/Px8KlSowObNmwud\noT5u3Dh27tzJrFmzaNGiBXv27KFy5co2xyxSXBpzkDKjVatWpKSkcO+995KWlkbXrl1ZuXIl27dv\nv2Fi6NGjBzNmzCA/P5+EhAT69Olz0/K9vb0xDIMdO3Zw8eJF5s2bZ9n2+OjRozRq1AiAadOmFSve\na8mlSpUq9OjRg6lTp5KXl4dhGOzcuROAAwcOEBgYyIQJE6hatSonTpwo9v0QuRVKDlKmnDx5kjp1\n6gDmbYmvPzDq90aPHk1GRgZBQUGcOHGCUaNGAeZ97ova6z4+Pp5Ro0bRoUMHGjRoYEkIMTExxMfH\n07ZtW3x8fCyf/31Zv//52vO4uDh++eUX2rZtS4sWLVi4cCFgHmAPDAwkNDSUIUOG4O3tbeutESkR\nbbwnUgIXLlygZs2aXLp0iaeeeorhw4cTGRnp6rBE7E4tB5ESmDZtGkFBQYSGhtKiRQu6dOni6pBE\nHEItBxERKUQtBxERKUTJQUREClFyEBGRQpQcRESkECUHEREpRMlBREQK+X/8KJJu8HXOHAAAAABJ\nRU5ErkJggg==\n",
"text": "<matplotlib.figure.Figure at 0x14f88bf0>"
},
{
"output_type": "stream",
"stream": "stdout",
"text": "80.0 % chance at 13 games\n63.3240914287 % chance at 5 games\n"
},
{
"metadata": {},
"output_type": "display_data",
"png": 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3KSkp900ahYWFJCYmsmTJEuPvNBoNISEheHh4MGXKFEaMGFGp+9+PNE8JIUTV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\n4cCqkjRUm6eKiorYtWsXu3b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"text": "<matplotlib.figure.Figure at 0x3404270>"
},
{
"output_type": "stream",
"stream": "stdout",
"text": "80.0 % chance at 5 games\n81.2364080839 % chance at 5 games\n"
},
{
"metadata": {},
"output_type": "display_data",
"png": 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LF4GgIODKFRMERURk4ZpS02jckKhmKj8faEJFhYiIfiWZNHbu3Ik7d+4AANat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\n2rRpFjE7vCmdOURErVVT/nb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"text": "<matplotlib.figure.Figure at 0x3687dd0>"
},
{
"output_type": "stream",
"stream": "stdout",
"text": "80.0 % chance at 5 games\n83.3829447059 % chance at 5 games\n"
},
{
"metadata": {},
"output_type": "display_data",
"png": 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cjRs3MmTIELKyssjNzTV64QMHDuD6t2m/7u7u7N+//67n3rhxg23btvHkk08W\nI/TyIzoadu6UyW5CiPLD6GiliIgI9Ho9H330ETVq1ODChQt89NFHpRrEhg0b6Nq16z13mJv2t1/W\nwMBAAgMDSzUGc8nJgXHjYPZssLOzdjRCiIpMr9ej1+tL5VpFnudw8eJFsrKyDM+dnZ3veX56ejqB\ngYHExcUBEBoaSt++fenfv3+Bcx9//HGefvpphg4devcgy/E8h7lzYdMm2L4dZL1CIYQlmXUS3Jdf\nfsnUqVOpXLlyvp3gjhw5YvTiPj4+zJs3D2dnZ/r27Ut0dDSOjo75zklPT6dFixacPXuWmjVr3j3I\ncpocLlyAtm21ZiVZWE8IYWlmnQQ3c+ZMfvzxR5ycnIp98blz5xISEkJ2djZhYWE4OjoSHh4OQEhI\nCADfffcdffr0KTQxlGevvqrt0yCJQQhR3hitOfTo0YN169bdsz/A3MpjzSEyEoYNg4QEqF3b2tEI\nIWyR2bcJDQgIYNCgQfl2gpswYYJJBdqCnBwIDdU6oSUxCCHKI6PJ4f777+eJJ55Ap9Nx7do1lFKy\nE5wRn38Ojo7w1FPWjkQIIUwjq7KWsosXteW49XrtrxBCWItZRiuNHz+eefPmMWDAgLsWuH79epMK\nNEV5Sg7PPQd16sB//mPtSIQQts4sfQ4jRowAYOLEiXctUBQUG6vNaTh+3NqRCCFEyRSaHNq1awdA\nTk4OXbp0qZBDTUtTXh6EhcH774O9vbWjEUKIkjG6ttKyZcvw8vLCz8+PV199lQ0bNnDlyhVLxFau\nrFgBSsFfFS4hhCjXitwhff78edasWcPHH3/M+fPnycnJMXdsBmW9zyEjA9q0gXXrwM/P2tEIIYTG\nrPMcli9fTnR0NPHx8TRo0ICXXnqJrl27mlRYRTVjBgQFSWIQQlQcRmsODg4OtGzZkhdffJHAwECa\nN29uqdgMynLN4bffwN8fjhyBxo2tHY0QQtxh1oX3lFIcPXqUqKgooqKiOHnyJA8++CArVqwwqUBT\nlOXkMHAgdO2qbeYjhBBliVmblTIyMkhOTub06dMkJSWRlpZGpUpG+7FtwvbtcOwYfPONtSMRQojS\nZbTm4OnpSZcuXejWrRsBAQE0bdrUUrEZlMWaQ04OeHnBzJkwaJC1oxFCiILM2qxUFpTF5PDpp/Dd\nd7Bjh2ziI4QomyQ5WFhqqrZHww8/aJv5CCFEWSTJwcLCwiA3Fz77zNqRCCFE4czaIS3yS0iA1au1\nv0IIUVEkrDKkAAAU3UlEQVSZNOzonXfeKe04yo1Jk+C117T9GoQQoqIyqVnJycmJM2fOmCOeuyor\nzUrbt8P//R8cPQrVqlk7GiGEuDezNCvZ2dkV+qHMzEyTCivPcnJgwgT46CNJDEKIiq/Q5FCvXj1i\nY2Np1KhRgfecnJzMGlRZ9N//QsOGMqdBCGEbCk0Ow4cPJzk5+a7JITg42KxBlTXp6TBtGmzdKnMa\nhBC2QYayFsG//w1//gmLF1stBCGEKDaZ52BGiYnQvr226uoDD1glBCGEMElJfjtlBT0jXnsNxo+X\nxCCEsC1Sc7iHfftg8GD49VeoXdvixQshRImYZShramrqPT9Yv359kwosL5TShq7OmCGJQQhhewpN\nDr6+voask5ycTPXq1QG4efMmLi4uJCYmWixIa/jmG7h5E0aMsHYkQghheYUmh6SkJADCwsLw8vLi\n2WefBWD16tUcOnTIIsFZy82bMGWKNrdB9jUSQtgio30Orq6uHDt2zLD7W15eHu7u7hw/ftwiAYLl\n+xzmzNGW49640WJFCiFEqTPrUNaJEyeSnZ3NqFGjUEqxfPlyKleuzOzZs00q0BSWTA6392rQ68Hd\n3SJFCiGEWZg1OaSlpREREcHWrVsBeOSRRxgzZgz29vYmFWgKSyaHiRPh+nX4/HOLFCeEEGZjkUlw\nmZmZ1KxZ06RCSspSyeH336FjR/jlF7jLqiFCCFGumHUS3OHDh+nfvz/uf7WxHD58mHHjxplUWFn3\n+uvw8suSGIQQwmhyeO+995g1axZ169YFwNvbm927d5s9MEuLjYXoaHjlFWtHIoQQ1mc0OZw/fx4P\nDw/D85s3b1KrVq0iXTwyMhI3Nzdat27N/Pnz73rOgQMH6NChA25ubgQGBhYt6lKmFLz6KkyfLhPe\nhBACirCHdFBQEN9//z0AycnJzJ8/n0FF3NRg/PjxhIeH4+LiQp8+fQgODsbxb/trKqUYM2YMc+bM\noXfv3vz5558mfo2S2bgRLl+GkSOtUrwQQpQ5RmsOYWFhxMXFkZubyyOPPELdunUJDQ01euH09HQA\nAgICcHFxISgoiJiYmHznHDx4EE9PT3r37g2QL3FYSk4OTJ4Ms2ZBFaOpUgghbIPR5FCvXj2mTZtG\nfHw8R48e5Y033ijSMNYDBw7g6upqeO7u7s7+/fvznbNt2zZ0Oh3dunVjwIABbNu2zYSvUDIREdC4\nMfTrZ/GihRCizDL6b+XExEQ+/PBD9u/fT1xcHPHx8axfv56pU6eWuPCsrCwOHz7Mzp07uXHjBg8/\n/DC//PLLXYfMTps2zfA4MDCwVPonrl3Tdnhbv152eBNClH96vR69Xl86F1NGjBgxQm3atEl5e3sr\npZTKy8tT7u7uxj6m0tLSDJ9RSqmXXnpJbdy4Md85GzduVJMmTTI8HzJkiNq6dWuBaxUhTJNMn67U\n0KFmubQQQlhdSX47jTYrnThxgn5/a3PJy8ujWrVqRpPO7aanyMhIkpKS2LFjB35+fvnO6dSpE7t3\n7+bGjRukpqYSFxdHly5dipfdTHTxInzyCcycaZHihBCiXDHarNS1a1d++uknQBvGunDhQvr06VOk\ni8+dO5eQkBCys7MJCwvD0dGR8PBwAEJCQnBwcGD06NG0b9+eBg0a8M4773DfffeV4OsU3TvvwLBh\n0Ly5RYoTQohyxejyGefOneOtt95i8+bNVKpUiX79+jF9+nQesOC+maW9fMZvv4G/Pxw/DlYYICWE\nEBZhkbWVsrOzUUoVqUmptJV2chgyBLy9teUyhBCiojLr2kpz587l6tWrVK1alTfffJOgoKACQ1LL\nk9hY2LtXW0NJCCHE3RlNDhEREdSpU4e9e/dy+PBhpk+fzptvvmmJ2EqdUtqEt2nToIgrgAghhE0y\nmhyqVq0KwLJly/jXv/6Fv7+/1Za5KKmtW7VRSqNGWTsSIYQo24yOVnr44YcJCAggNTWVzz77jKtX\nrxq2DC1PcnPh3/+G99+XZTKEEMKYInVI//777zRt2pRq1apx+fJlzp07h6enpyXiA0qnQ3r5cm13\nt+homQ0thLANFhmtZE0lTQ5ZWdq+0CtWQNeupRiYEEKUYWYdrVQRLFwIXl6SGIQQoqgqfM0hPR0e\nfBB27YKHHirlwIQQogwze83hwoULrFy5EoBLly6RmJhoUmHW8NFH2nLckhiEEKLojNYcvvjiC1at\nWsX58+c5ceIE586dY8iQIezZs8dSMZqc/S5cAA8PiIsDZ2czBCaEEGWYWWsOy5cvZ/v27dT+a3Pl\nJk2akJGRYVJhlvbuuzB6tCQGIYQoLqMj/u3t7fPNa0hOTqZp06ZmDao0nDwJ33yjLa4nhBCieIzW\nHEaOHMmzzz5LWloa06dP59FHH+W5556zRGwlMnUqvPIKODhYOxIhhCh/ijRaKSkpibVr15KXl8fQ\noUNxcnKyRGwGxW03++knGDgQTpyAv1rDhBDC5ph1ElxiYiKNGjUy7OucmZlJSkoKzZo1M6lAUxT3\nCwYFwRNPwAsvmDEoIYQo48zaIf3UU09RuXLlOx+oVImnnnrKpMIs4YcfIDERxo61diRCCFF+GU0O\n/9wzulq1aty6dcusQZlKKXjtNZgxA/5aTFYIIYQJjCaHnj17smDBArKzs7l16xYLFiygV69eloit\n2Nau1VZfHTzY2pEIIUT5ZjQ5vPzyy8TGxtKqVStatWpFbGwsEydOtERsxZKTA2+8oS3JXQ5XFBdC\niDKlWHtIw53NfyypKJ0qixbB6tVan4MsyS2EEGYerZSdnc2+ffvYt28fN2/eRCmFTqfjrbfeMqlA\nUxj7gpmZ0Lo1fPstdOxosbCEEKJMK0lyMDpDOjQ0lKSkJLp3725YQqOs+fRT8POTxCCEEKXFaM3B\n3d2dX375xapbg94r+6WlaUty794Nbm4WDkwIIcows85z6NGjBz/++KNJF7eEjz+GAQMkMQghRGkq\nUs3h+PHjNGnShLp162of0umIj4+3SIC3y7tbmH/8oe3TIEtyCyFEQWbtkE5KSrrr62Vh+YyXXoJq\n1eA//7FYKEIIUW6YNTnclp6eTnp6uuG5swX/qX63L/j771oHdEICNGhgsVCEEKLcMGufw+7du+nR\nowdNmjTB19eXZs2a0a9fP5MKK01vvQVhYZIYhBDCHIwmh1mzZrF06VJatmzJxYsXWbFiBQEBAZaI\nrVDx8bBzp7ZfgxBCiNJnNDn88ccfODs7U7t2ba5fv84zzzxj9dFLb7yhLbBnZ2fVMIQQosIyOgmu\nfv36ZGRk0K9fP5566imaNGmCmxXHje7Zo9Uc1qyxWghCCFHhGe2QvnbtGjVr1qRy5cro9XrOnTvH\nY489ZtHZ0rc7VZSC7t1hzBgYNcpixQshRLlkkdFK1nT7Cx45As88A4cPw9/2HxJCCHEXZh2ttHPn\nTnr27EndunWxs7PDzs6OOnXqmFRYSbVtCwcPSmIQQghzM1pzaN++PfPmzcPf399q6yuVJPsJIYSt\nMmvNoVq1arRr186kxBAZGYmbmxutW7dm/vz5Bd7X6/XY29vj4+ODj48PM2bMKHYZtkav11s7hDJD\n7sUdci/ukHtROgodrbR27VoAAgICeOyxxxg8eHC+tZWeeOIJoxcfP3484eHhuLi40KdPH4KDg3F0\ndMx3Tvfu3Vm/fn1JvoNN0ev1BAYGWjuMMkHuxR1yL+6Qe1E6Ck0OGzZsQPfXlmqNGjUiOjo63/vG\nksPtpTZuT5gLCgoiJiaG/v375ztPmouEEKLsKTQ5LFmypEQXPnDgAK6urobn7u7u7N+/P19y0Ol0\n7N27F29vb3r27Mn//d//0bJlyxKVK4QQohQoI0aMGKGuXLlieJ6amqpGjx5t7GNqx44daujQoYbn\nCxcuVFOnTs13ztWrV9X169fVrVu31KJFi1T//v3vei1ADjnkkEMOEw5TGR2t5O3tzeHDh/O95uXl\nxc8//3yvj5Genk5gYCBxcXGAtt1o3759CzQr3aaUolGjRiQnJ1O9evV7XlsIIYR5GR2C5OLiwm+/\n/WZ4fuLECZo2bWr0wvb29oA2YikpKYkdO3bg5+eX75yUlBRDn8OGDRvw9PSUxCCEEGWA0bWVxo0b\nxyOPPELv3r1RSrFz504WLlxYpIvPnTuXkJAQsrOzCQsLw9HRkfDwcABCQkJYs2YNCxcupEqVKnh6\nejJ79uySfRshhBCloyhtT9evX1dff/21+vrrr9X169dNbsMqrt27dytXV1fVqlUr9cknn1is3LIg\nOTlZBQYGKnd3d9W9e3e1cuVKpZTWTzNw4EDl5OSkBg0apDIyMqwcqeXk5OQob29v9eijjyqlbPde\nXLt2TY0YMUK1bt1aubm5qf3799vsvfjiiy+Uv7+/8vX1VePHj1dK2c5/F6NHj1YNGzZUHh4ehtfu\n9d3nzZunWrVqpdzc3FRUVJTR6xdpZlutWrUYPHgwgwcPplatWubOVwa350ns3LmTzz77jD///NNi\nZVtb1apVmTNnDkePHmXNmjVMnTqVjIwMFi5ciLOzM7/99htNmzbl888/t3aoFjNv3jzc3d0NQ6xt\n9V68/fbbODs7Ex8fT3x8PK6urjZ5L1JTU5k5cyY7duzgwIEDnDhxgm3bttnMvRg9ejRbt27N91ph\n3/3ixYssWLCAH374gYULFxIWFmb0+tZZD6MI/j5PwsXFxTBPwlY0atQIb29vABwdHXnooYc4cOAA\nsbGxjB07lurVqzNmzBibuSdnz55l8+bNPPfcc4Z+Klu9Fzt37uT111+nRo0aVKlSBXt7e5u8FzVr\n1kQpRXp6OpmZmdy4cYO6devazL3o1q0b9erVy/daYd89JiaGvn374uzsTPfu3VFKkZGRcc/rl9nk\nUNg8CVt08uRJjh49SseOHfPdF1dXV2JjY60cnWW88sorfPTRR/mWcbHFe3H27FmysrJ48cUX8fPz\nY9asWWRmZtrkvahZsyYLFy6kWbNmNGrUiC5duuDn52eT9+K2wr57TExMvn142rRpY/S+lNnkIDQZ\nGRk8/fTTzJkzh/vuu88mZ5Rv3LiRhg0b4uPjk+/72+K9yMrK4sSJEzz55JPo9XqOHj3K119/bZP3\n4tKlS7z44oscO3aMpKQk9u3bx8aNG23yXtxWnO9+u3m2MGU2OXTo0IHjx48bnh89epROnTpZMSLL\ny87O5sknn2T48OEMGjQI0O5LQkICAAkJCXTo0MGaIVrE3r17Wb9+Pc2bNyc4OJhdu3YxfPhwm7wX\nrVq1ok2bNgwYMICaNWsSHBzM1q1bbfJexMbG0qlTJ1q1aoWDgwODBw8mKirKJu/FbYV9dz8/P44d\nO2Y47/jx40bvS5lNDkWZJ1GRKaUYO3YsHh4evPzyy4bX/fz8iIiIIDMzk4iICJtImDNnzuTMmTMk\nJiby5Zdf0rNnT5YvX26T9wKgdevWxMTEkJeXx6ZNm+jdu7dN3otu3bpx8OBBUlNTuXnzJlu2bCEo\nKMgm78VthX33jh07sm3bNpKTk9Hr9VSqVAk7O7t7X6wUR1aVOr1er1xdXVXLli3VvHnzrB2ORUVF\nRSmdTqe8vLyUt7e38vb2Vlu2bLGZYXqF0ev1asCAAUop2xmy+E+//vqr8vPzU15eXmrixInq2rVr\nNnsv/ve//6mAgADVvn17NXXqVJWbm2sz92Lo0KGqcePGqlq1aqpp06YqIiLint997ty5qmXLlsrN\nzU1FRkYavX652CZUCCGEZZXZZiUhhBDWI8lBCCFEAZIchBBCFCDJQQghRAGSHESF9Nprr6HX6/nu\nu+/44IMPivXZrKws+vXrR7t27dizZ4+ZIhSibJPkICqk2xOkdu/ebdjHvKi2b99Ow4YN+emnn+jS\npYuZIhSibJPkICqUyZMn4+XlxYEDB/D392fx4sW8+OKLzJgxo8C558+fZ/z48Xh5efHKK6+QkpLC\n4cOHCQ0NZfPmzfj4+JCVlZXvMzExMfTq1QsfHx+mTJnCgAEDAC0Zde7cGR8fH0aOHElSUhKg7cX+\n9NNPExQURIsWLVi6dCkLFy7E09OT4OBgw+Jn586d49VXX8Xf35+RI0eSmJgIwI4dOwgICMDLy4vu\n3bub8c4J8Q/mm6IhhHUcOHBAhYWFqezsbNWlS5dCz3vllVfUhx9+qJRSaubMmWry5MlKKaWWLFmi\nQkND7/qZtm3bqkOHDqnr16+rfv365ZuQl5OTo5RS6quvvlJTpkxRSmmTtBo1aqRSUlJUUlKSqlmz\nppoxY4ZSSluPf82aNUoppcaMGaMOHjyolFJq06ZN6oUXXlBKKdW9e3d16tQppZRS6enppt8UIYrJ\n6E5wQpQ3P/30E56eniQkJORbifKftmzZQnR0NABjx44lMDCQWbNmoZS66wJmZ8+eRafT4ePjA8CQ\nIUNYs2YNAJmZmbzxxhvs3r0bpRRVqlTh/fffB6B37940bNgQgHr16hEcHAyAv78/+/btY9CgQWze\nvJlDhw4VKLNr166MHTuWkSNHGj4nhCVIchAVxs8//8yoUaM4e/Ysjo6O3LhxA6UUvr6+7N27lxo1\nahT4zN2SQFH9/bMLFizAwcGBgwcPcvToUR5//HHDe3Xr1jU8rlatmuF5tWrVuHnzJnl5eVSqVIn9\n+/cX2EN9xowZxMfHs2LFCjw8PDh27BhVq1Y1OWYhikr6HESF4eXlRVxcHA8++CAJCQn07NmT7du3\nc+jQobsmhn79+rF06VLy8vKIiIhg4MCB97x+06ZNUUpx+PBhbty4wZo1awzLHp87d47mzZsDsGjR\noiLFezu5VKtWjX79+rFw4UJyc3NRShEfHw/AqVOn8PT0ZNasWVSvXp2UlJQi3w8hSkKSg6hQLl26\nRP369QFtWeK/bxj1T5MmTSI5ORkfHx9SUlKYMGECoK1zX9ha9+Hh4UyYMIEuXbrg7OxsSAihoaGE\nh4fTvn17nJycDJ//57X++fj28+nTp/PHH3/Qvn17PDw8WL9+PaB1sHt6euLv78+wYcNo2rSpqbdG\niGKRhfeEKIbr169Tu3ZtMjMzGTVqFGPGjKFPnz7WDkuIUic1ByGKYdGiRfj4+ODv74+Hhwc9evSw\ndkhCmIXUHIQQQhQgNQchhBAFSHIQQghRgCQHIYQQBUhyEEIIUYAkByGEEAVIchBCCFHA/wNiHaEx\nK9kedgAAAABJRU5ErkJggg==\n",
"text": "<matplotlib.figure.Figure at 0x14fae050>"
},
{
"output_type": "stream",
"stream": "stdout",
"text": "80.0 % chance at 24 games\n57.0534503331 % chance at 5 games\n"
},
{
"metadata": {},
"output_type": "display_data",
"png": 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1c0diHGVlZcq6y5cV14MHlY8uXFDKysrMHZKoZ4xyTTAALy8v5ddff1UURVFC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\n",
"text": "<matplotlib.figure.Figure at 0x337f9b0>"
}
],
"prompt_number": 175
},
{
"cell_type": "markdown",
"metadata": {},
"source": "<h1>Playoffs</h1>\n\nThis section is like the previous section, but the function parameters are set to simulate an average first round playoff scenario in each league."
},
{
"cell_type": "code",
"collapsed": false,
"input": "#playoffs\n\n#playoff parameters\nt1rank=1\nt2rankNHL=16\nt2rankNBA=16\nt2rankNFL=8\nt2rankMLB=8\nnumgamesNHL=7\nnumgamesNBA=7\nnumgamesMLB=5\nnumgamesNFL=1\n\npercentage=.9\ngp=np.arange(1,100)\n\nrlplayoffchance=[]\nrlplayoffgames=[]\n\n#NHL\nresultNHL=calcchance(t1rank,t2rankNHL,percentage,numgamesNHL,gp,'NHL')\nrlplayoffchance.append(resultNHL[1])\nrlplayoffgames.append(resultNHL[2])\n#NBA\nresultNBA=calcchance(t1rank,t2rankNBA,percentage,numgamesNBA,gp,'NBA')\nrlplayoffchance.append(resultNBA[1])\nrlplayoffgames.append(resultNBA[2])\n#NFL\nresultNFL=calcchance(t1rank,t2rankNFL,percentage,numgamesNFL,gp,'NFL')\nrlplayoffchance.append(resultNFL[1])\nrlplayoffgames.append(resultNFL[2])\n#MLB\nresultMLB=calcchance(t1rank,t2rankMLB,percentage,numgamesMLB,gp,'MLB')\nrlplayoffchance.append(resultMLB[1])\nrlplayoffgames.append(resultMLB[2])\n\nprint \"bar graph values from left to right\"\nprint rlplayoffchance\n\n#plot chances\nN = len( rlplayoffchance )\nx = np.arange(1, N+1)\ny = rlplayoffchance\nlabels = leagues\nwidth = .75\nbar1 = plt.bar( x, y, width, color='CornflowerBlue')\nplt.ylabel( 'chances top seed wins their first playoff series' )\nplt.xticks(x + width/2.0, labels )\nplt.ylim(0,1)\nplt.show()\n\nprint \"bar graph values from left to right\"\nprint rlplayoffgames\n\n#plot games needed\nN = len( rlplayoffgames )\nx = np.arange(1, N+1)\ny = rlplayoffgames\nlabels = leagues\nwidth = .75\nbar1 = plt.bar( x, y, width, color='CornflowerBlue')\nplt.ylabel( 'games needed for .%d chance top seed wins first playoff series' %(percentage*100))\nplt.xticks(x + width/2.0, labels )\nplt.ylim(0,60)\nplt.show()",
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": "bar graph values from left to right\n[0.69074010022432986, 0.90265398096013816, 0.55155467019250737, 0.54692025781761511]\n"
},
{
"metadata": {},
"output_type": "display_data",
"png": 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gDP6lS5dizZo16NKlCy5duoTU1FT4+PioURsRESlAGPx//vknnJycYGFhgZs3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\nfiKiRobBT0TUyPw/j/5hqTVtNN0AAAAASUVORK5CYII=\n",
"text": "<matplotlib.figure.Figure at 0x3367090>"
},
{
"output_type": "stream",
"stream": "stdout",
"text": "bar graph values from left to right\n[19, 7, 10, 55]\n"
},
{
"metadata": {},
"output_type": "display_data",
"png": 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"text": "<matplotlib.figure.Figure at 0x3625d70>"
}
],
"prompt_number": 176
}
],
"metadata": {}
}
]
}
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