{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "In a [previous post](https://danvatterott.com/blog/2019/04/19/are-some-mlb-players-more-likely-to-hit-into-errors-than-others/), I described how to download and clean data for understanding how likely a baseball player was to hit into an error given that they hit the ball into play.\n", "\n", "This analysis will statisically demonstrate that some players are more likely to hit into errors than others.\n", "\n", "Errors are uncommon, so players hit into errors very infrequently. Estimating the liklihood of an infrequent event is hard and requires lots of data. To generate as much data as possible, I wrote a bash script that will download data for all players between 1970 and 2018.\n", "\n", "Having many years of data enables me to use data from multiple years for each player. This gives me more data to use when estimating how likely a particular player is to hit into an error." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# %%bash\n", "\n", "# for i in {1970..2018}; do\n", "# echo \"YEAR: $i\"\n", "# ../scripts/get_data.sh ${i};\n", "# done\n", "\n", "# find processed_data/* -type f -name 'errors_bip.out' | \\\n", "# xargs awk '{print $0\", \"FILENAME}' | \\\n", "# sed s1processed_data/11g1 | \\\n", "# sed s1/errors_bip.out11g1 > \\\n", "# processed_data/all_errors_bip.out" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Looking at the data we see 5 columns: playerid, playername, errors hit into, balls hit into play (BIP), and year. The file does not have a header." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "aaroh101, Hank Aaron, 8, 453, 1970\n", "aarot101, Tommie Aaron, 0, 53, 1970\n", "abert101, Ted Abernathy, 0, 10, 1970\n", "adaij101, Jerry Adair, 0, 24, 1970\n", "ageet101, Tommie Agee, 12, 480, 1970\n", "akerj102, Jack Aker, 0, 10, 1970\n", "alcal101, Luis Alcaraz, 1, 107, 1970\n", "alleb105, Bernie Allen, 1, 240, 1970\n", "alled101, Dick Allen, 4, 341, 1970\n", "alleg101, Gene Alley, 6, 356, 1970\n" ] } ], "source": [ "%%bash\n", "head ../processed_data/all_errors_bip.out" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "I can load the data into pandas using the following command." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": true }, "outputs": [], "source": [ "import pandas as pd\n", "\n", "DF = pd.read_csv('../processed_data/all_errors_bip.out',\n", " header=None,\n", " names=['playerid', 'player_name', 'errors', 'bip', 'year'])" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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playeridplayer_nameerrorsbipyear
0aaroh101Hank Aaron84531970
1aarot101Tommie Aaron0531970
2abert101Ted Abernathy0101970
3adaij101Jerry Adair0241970
4ageet101Tommie Agee124801970
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" ], "text/plain": [ " playerid player_name errors bip year\n", "0 aaroh101 Hank Aaron 8 453 1970\n", "1 aarot101 Tommie Aaron 0 53 1970\n", "2 abert101 Ted Abernathy 0 10 1970\n", "3 adaij101 Jerry Adair 0 24 1970\n", "4 ageet101 Tommie Agee 12 480 1970" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "DF.head()" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "38870" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "len(DF)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "I have almost 39,000 year, player combinations.... a good amount of data to play with.\n", "\n", "While playing with the data, I noticed that players used to hit into more errors frequently than they do now. Let's see how the probability that a player hits into an error changes across the years." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "%matplotlib inline\n", "\n", "YEAR_DF = (DF\n", " .groupby(\"year\")\n", " .agg({\n", " \"errors\": \"sum\",\n", " \"bip\": \"sum\"\n", " })\n", " .assign(prop_error=lambda x: x[\"errors\"] / x[\"bip\"])\n", " )\n", "\n", "YEAR_DF[\"prop_error\"].plot(style=\"o-\");" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Interestingly, the proportion of errors per BIP [has been dropping over time](https://www.pinstripealley.com/2013/8/16/4623050/mlb-errors-trends-statistics). I am not sure if this is a conscious effort by MLB score keepers or improved fielding (but I suspect it's the score keepers). It looks like this drop in errors per BIP leveled off around 2015. Zooming in." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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mdhxqoKK6kR2HPvvY18/EpDWNbZz/0NvExwnjR6UyyZPOpOw0JnnSyPOkk+dNY/yoNFIS44fpqzEnw8IkwmWmJnJ6bibvba/hJreLMTFBVTl4tNUvLBrYcaiRiupGdtc20eF3qXpmaiIFOemUFHopyEkn35vOncs2cfBo63H9ejOS+MElU9lV08Su2iZ21TSyfvdhjrZ0HGsjAqeMTGGSEy6TPOnkeXyfJ3nSSEuyX2luse98FCgp8vL/3qmgobWDjGT7JzWhUd/c/llYVDdS4XeU0dT22WmqlMQ48jzpTD1lBJeePpZ8bwb53nQKvOmMSk86rt+2ji5uf2Vjj1NdqYnx/PsXpnHFzNwebVWVuqZ2dtb4gmrnIV/I7KxpZMWmA9Q0tvVonzMi+Vi45HnSmOgXNpmpiSH+Dhl/9psnCnyuyMt/v72dD3fUcMHUMW6XYyJIS3snu2ubehxldD/2/0UdJzAhO418bzqz87Mp8KaT782gICedsSNTiIsLuNZdQN2B8eDybVTVNTMuK5VbLp5yXJCA7+bcUelJjEpPYubEUce9frSl3XckU9PkCxzn87ufHmLJ2p6n1UalJR47gvE/osnzpJGdnoSz4qsZoKDCREQuAf4L37K9T6jqfb1eTwaeAWYBNcCXVHWniHiAJcA5wK9U9Qa/99wLXAuMUtUMv+0TgaeBLGd/tzkrPZo+zJo0iqSEON4rtzCJFUvX7w3qlzFAZ5dSVdfsO7Kodk5JOUcYe+ua8Z94OmdEMgXedOZNH0O+Exj53nQmZqeRlBC663WumJnbZ70nY0RKIjNyM5mRm3nca81tvqDcVdN4LGx21TSxdtdhXv24Cv+JIzKSE46NzXR/nuh8Hj0i+biwPJnvf6zoN0xEJB54DLgIqATWiMgyVd3s1+x64LCqFonIAuB+4EtAC3AHMMP58Pcq8Cjwaa/t/w68pKr/LSLT8C0XnHeyX1gsSUmMp3jSKLvfJEZ0X1rbfZrId2ntBo62tjN17Mhjp6QqnODYVdNEm98VUhnJCRTkpDNr0iiunDXeOSWVQZ43jREp0XMqKDUpniljRzBl7IjjXmvr6KLycFOPkNlZ08iWfUdYvml/j3GflMQ4JmV3H9GkcbipnWUfVR37nnZf2gzEdKAEc2QyGyhX1QoAEXkBmA/4h8l84E7n8RLgURERVW0E3hWRot6dquoHTn/HvQSMdB5nAlVBfSUxrrTIy4PLt3GooRVvRrLb5Zgh9ODybQEure3ijqWbjj1PjBcmeXwD3hdMHe0LjBzfUYY3w07pJCXEUZCTQUFOxnGvdXR2sa++5VjI+MZofGHz579W09px/KXLze2d3PH7TxCBotEZFHgzSE2KravOggmTXGCP3/NK4Ny+2qhqh4jUAx5gIH8q3wmsEJHvAOnAhYEaicgiYBHAxIkTB7Cb6FJS6Lss+P3tNVx25jiXqzFDqaquuc/XfvXVcyjwZjAuK4WEeLuNbCAS4uOYkJ3GhOw0Pj+552tdXUrhv71BoKlVj7Z08N0XPgJ8V53lZqVSmJNB0egMv8/peKL0j71gwiTQnzC9v5fBtAnW1fjGV/5TROYAz4rIDFXt8eeAqi4GFgMUFxfH/LS5p+dmMiI5gVXbD1mYRLmxmSkB79nIzUrl/CmjXagodsTFCeOyUtkbINDHZabwy6/OZnt1A+UHG459Xr2jhpb2z359jUpLDBAyGeSOSiX+JC5kCDfBhEklMMHv+XiOP/XU3aZSRBLwnZ6qHWBN1wOXAKjq+yKSAniBgwPsLyYkxMdxboHH1oWPci3tnaQkHn/EkZoYzy0XT3Ghothzy8VTAl7afOslUwOO0XR1KVX1zWyvbqT84GdB8z+bD/BC42cnfZIT4sj3ph8XMgU56RFxo2YwYbIGmCwi+cBeYAHw5V5tlgHXAe8DVwJv6cAXJ98NzAV+JSKnASlA9QD7iimlRR7+tOUAe2qbmJCd5nY5JsQ6Oru44bl17Kxp4ro5k/jTloN2NZELTubSZvAdzYwf5bt7/29Pzenx2uHGNrZXN/gdzTSyobKe1zfuO3aVnQiMH5VKUY5fyIzOoCgnI+B9PG7pN0ycMZAbgOX4LtV9SlU3ichdQJmqLgOexHc6qhzfEcmC7veLyE58A+pJInIFME9VN4vIA/hCKU1EKvFdcnwn8K/A/xOR7+M7VbZwEMEUU7qX8l21/RBfyrZxpGiiqvzg5Y38actB7r5iBtecN4kfz3e7qtgVqkubR6UnUZyeTXFedo/tLe2d7DjU2CNkyg82sGp7TY8LALLTk3whMzq95ymzrNQT3vvTfWlz0tiiWYP+IhwSDb+ni4uLtayszO0yXKeqzP7Jm8wp8PDzq2e6XY4JoZ+8sYXF71Tw/QtP5bsXTu7/DSYqdXUpe+uae4zJdH8+3NR+rF1KYhwF3l7jMqPTyfOk88dP9h87Tbfv6e/Ruu/TkAzU2B3wUUREKCn0jZuoasxf/hktHv/zdha/U8F1cyZx49zjrrI3MSQuTo5dafZ3U3tebFHb2HZcyKzbfZhXN1QdO2UWJ77fE0Ox1LeFSZQpLfTy+4+q+OuBhoA3a5nI8lLZHn76h61cduY4/uOy6fYHgulTdnoSs/OzmZ3f85RZc1snFYc+O1X28zd73yceGhYmUaakyHe/yXvlhyxMItz/bD7AbS9v4POTvfznVWee1PxXxnRLTYpn+rhMpo/zTTnz8trKgJc2D5bd1RRlxo/yTfmwytaFj2irK2r49nPrOGN8Fr/4yqyQzotlYtstF08hdQguNbaf0ChUUuhldUUtHbZiXUTaXHWErz9dxsTsNH658BzSbVkBE0JXzMzlp/90OrlZqSHt18IkCpUWeTja2sGGvfVul2JO0q6aRq596kNGpCTwzNdmh9V9BCZ6XDEzl/duu4C2/eVrQ9WnhUkUmuMs37vKZhGOKAePtnDNkx/S2dXFM9efy7gQ/+VozFCyMIlCnoxkTjtlpE2tEkHqm9u57qk1HGpo5ZdfnU3R6ONnszUmnFmYRKnSQg9rdx+mpddU5Sb8tLR38o1nyig/eJTHr5nFWROy3C7JmJNmYRKlSou8tHV0UbbzsNulmBPwzbe1njU7a3n4i2fx+ck5/b/JmDBkYRKlZudnkxAnvGeXCIctVeX2Vzbypy0HuOvy6bZ0gIloFiZRKj05gbMmZNkgfBi7749b+e3aSr47dzLXzMlzuxxjBsXCJIqVFHnZuLee+ub2/hubYbX4ne08/ucKrjlvEt+ziRtNFLAwiWKlhR66FD6osKu6wsmStZX85I2t/MMZp3Dn5TbflokOFiZRbObEUaQmxtuprjDyp80H+IEz39bDXzwropdpNcafhUkUS0qI45z8bN7bbkcm4eDDHbV8+7l1zBg30ubbMlEnqJ9mEblERLaJSLmI3Bbg9WQRedF5fbWI5DnbPSKyUkQaROTRXu+5V0T2iEhDgP6+KCKbRWSTiDw3sC/NgO9UV/nBBg4caXG7lJi2Zd8Rrn96DbmjUvnlV2fbfFsm6vQbJiISDzwGXApMA64WkWm9ml0PHFbVIuAR4H5newtwB3BzgK5fBWYH2N9k4HagVFWnA98L7ksxgfgv5WvcsbumiWuf+pCM5ASevf5csm2+LROFgjkymQ2Uq2qFqrYBLwC9V5+eDzztPF4CzBURUdVGVX0XX6j0oKofqOq+APv7BvCYqh522h0M8msxAUw7ZSRZaYk2tYpLDh5t4ZqnVtPe2cUzX5sd8plajQkXwYRJLrDH73mlsy1gG1XtAOoBzwBrOhU4VUTeE5EPROSSAfZj8C3zOafAw6ryQ6iGfqlO07cjLe0sfGoNB4+08tTCc5g8xhYrM9ErmDAJdLlJ799KwbQJVgIwGTgfuBp4QkSOm6xIRBaJSJmIlFVXVw9wV7GhpMhLVX0LO2ua3C4lZrS0d/KNp8v49OBRfnHNLM6eOMrtkowZUsGESSUwwe/5eKCqrzYikgBkArUDrKkS+L2qtqvqDmAbvnDpQVUXq2qxqhbn5Nh8RidSWvjZUr5m6HV0dnHj8+v5cGctD111Jn97qv18mugXTJisASaLSL6IJAELgGW92iwDrnMeXwm8pQM/p7IU+DsAEfHiO+1VMcC+DJDvTeeUzBQbhB8GqsoPf/cJKzYf4M7LpjP/rN5nhI2JTv2GiTMGcgOwHNgCvKSqm0TkLhG53Gn2JOARkXLgJuDY5cMishN4GFgoIpXdV4KJyAMiUgmkOdvvdN6yHKgRkc3ASuAWVbXR40EQEUoKvazaXkNXl42bDKUHlm/jxbI93Dh3MteV5LldjjHDRqJhULa4uFjLysrcLiOsvbKukpte+pjXvvM5ZuRmul1OVHriLxXc8/oW/te5E7nnihk2TYoJeyKyVlWLQ9GX3YIbI7rvN7Fxk6Hx8tpK7nl9C184/RTumm9BYmKPhUmMGDMyhcKcdJtaZQi8ueUAt768gc8VeXn4S2fafFsmJlmYxJDSIi9rdtTS1tHldilRY83OWv7lN+uYPm4kv7hmFskJ8W6XZIwrLExiSEmhl+b2TtbvtqV8Q2Hr/iNc/ytnvq2F55Bh822ZGGZhEkPmFHiIE+xUVwjsqW3i2ic/JC0pgWe+NhtPRrLbJRnjKguTGJKZlsjpuZm2vskgVR9t5ZonV9Pa0cUz189m/Kg0t0syxnUWJjGmpMjLR3vqaGztcLuUiHS0pZ2Fv/yQA858W6fafFvGABYmMae00EtHl/LhjoHOdhO7Wto7+cYzZWzbf5T//srZzJpk820Z083CJMYU540iKSHO7jc5SZ1dyndfWM8HFbX85xfP5Pwpo90uyZiwYmESY1IS45k1cZQNwp8E33xbG1m+6QD/cdk0m2/LmAAsTGJQaZGHLfuOUNPQ6nYpEeGhFdt4Yc0evnNBEV8tzXe7HGPCkoVJDCpxplZ5v8KOTvrz5Ls7eGzldr587kRuuuhUt8sxJmxZmMSgM3IzGZGcYEv59uN36yu5+7XNXDpjLHfbfFvGnJCFSQxKiI/j3IJsW9/kBFZuPcgtv91ASaGHny04y+bbMqYfFiYxqqTQy66aJioP21K+va3dVcv//s1aTjtlJIuvLbb5towJgoVJjOqekn6VnerqYdv+o3z1l2sYl5nKL79q820ZEywLkxh16pgMvBnJvGenuo7ZU9vEtU+tJjUpnqe/NhuvzbdlTNCCChMRuUREtolIuYjcFuD1ZBF50Xl9tYjkOds9IrJSRBpE5NFe77lXRPaISEMf+7xSRFREQrIKmOnJt5Svh1Xba4iG1TYH61BDK9c+9SEt7V0887VzmZBt820ZczL6PYYXkXjgMeAioBJYIyLLVHWzX7PrgcOqWiQiC4D7gS8BLcAdwAznw9+rwKPApwH2OQK4EVh90l+RCVppkYdlH1fx6cGGmJxjaun6vTy4fBtVdc0kxAuqyovfnMOUsbH3vTBmsII5MpkNlKtqhaq2AS8A83u1mQ887TxeAswVEVHVRlV9F1+o9KCqH6jqvj72eTfwQKD3mdApKYzdpXyXrt/L7a9sZG9dMwq0dypxEsee2ma3SzMmIgUTJrnAHr/nlc62gG1UtQOoBzwDKUhEZgITVPW1ftotEpEyESmrrq4eyK5i3oTsNCZmp8Xk/SYPLt9Gc3tnj21tnV08uHybSxUZE9mCCZNAF9j3PskeTJv+dyQSBzwC/Gt/bVV1saoWq2pxTk7Oye7KOEqLPKyuqKGjM7aW8q2qC3wE0td2Y8yJBRMmlcAEv+fjgaq+2ohIApAJDGSO8xH4xlbeFpGdwHnAMhuEHzolhV6OtnawcW+926UMq6y0xIDbx2WlDnMlxkSHYMJkDTBZRPJFJAlYACzr1WYZcJ3z+ErgLR3AJUKqWq+qXlXNU9U84APgclUtO9m+THBKCn1nI1fF0CzCW/YdoaGlg96zo6QmxnPLxVPcKcqYCNdvmDhjIDcAy4EtwEuquklE7hKRy51mTwIeESkHbgKOXT7sHGE8DCwUkUoRmeZsf0BEKoE0Z/udIfy6TJA8GclMHTsiZgbh65raWPRsGdkZSfz4smnkZqUiQG5WKj/9p9O5YqZNL2/MQEg03GNQXFysZWV28DJQd7+2mWc/2MWG/5gzZEH8AAARNUlEQVRHSmL0Th3S0dnFV3+1htUVtbz4zfOYOdFWSjSxTUTWqmpIhhHsDnhDaZGHto4u1u467HYpQ+rB5dv4y6eHuOeKGRYkxoSYhYlhdr6HhDiJ6lNdv/9oL4+/U8E1503ii+dM6P8NxpiTYmFiyEhO4MwJWVG7lO+mqnp+8PIGZudlc8c/THO7HGOikoWJAaC00MPGyjrqm9vdLiWkahvbWPTMWkalJfHY/zqbpAT7kTdmKNj/LAP4lvLtUlgdRUv5dnR2ccNz66huaOXxa2aRM8JmATZmqFiYGABmTswiJTEuqu43+ekftrJqew0//cfTOWN8ltvlGBPVLEwMAMkJ8ZyTlx01g/C/W1/Jk+/uYGFJHv88a7zb5RgT9SxMzDGlRV4+PdjAwSORPVnzJ3vrue3ljZxXkM0Pv3Ca2+UYExMsTMwxpc6U9JF8qutQQyuLninDm5HMY18+m8R4+xE3ZjjY/zRzzLRxI8lMTYzYU13tnV18+zfrqGls4/FrZuGxZXeNGTYWJuaY+DhhTkHkLuV77+tbWL2jlvv/+Qxm5Ga6XY4xMcXCxPRQWuRhb10zu2qa3C7lpPy2bA+/WrWTr38u3yZrNMYFFiamh5IiZynf7ZFzquvjPXX8cOknlBZ5uO3SqW6XY0xMsjAxPRR40xk7MoVVEbKUb/XRVr757FpGj0jm/1x9Ngk24G6MK+x/nulBRCgp8rBq+yG6usJ73KSto4t/+c1a6prbWHxNMdnpSW6XZEzMsjAxxykt9HK4qZ0t+4+4XcoJ3f3aZtbsPMwDV57JtHEj3S7HmJgWVJiIyCUisk1EykXktgCvJ4vIi87rq0Ukz9nuEZGVItIgIo/2es+9IrJHRBp6bb9JRDaLyAYReVNEJg38yzMDUdo9bhLGlwi/uGY3z36wi2/+bQGXnznO7XKMiXn9homIxAOPAZcC04Cru5fe9XM9cFhVi4BHgPud7S3AHcDNAbp+FZgdYPt6oFhVzwCWAA8E8XWYEBqbmUJBTjrvhem4ybrdh7lj6SY+P9nLrRfbgLsx4SCYI5PZQLmqVqhqG/ACML9Xm/nA087jJcBcERFVbVTVd/GFSg+q+oGq7guwfaWqdl+X+gFgEyu54HNFXj7cUUtbR5fbpfRw8EgL33p2LWMzU/g/V88kPk7cLskYQ3Bhkgvs8Xte6WwL2EZVO4B6wBOC+q4H/hCCfsxJKin00tzeyUd76twu5ZjWjk6+9eu1NLR2sPjaWWSl2YC7MeEimDAJ9Kdf78t8gmlzUkTkK0Ax8GAfry8SkTIRKauurh7MrkwAcwo8xEl4jZvcuWwz63bX8dBVZzJ1rA24GxNOggmTSsB/0ezxQFVfbUQkAcgEagdalIhcCPwQuFxVWwO1UdXFqlqsqsU5OTkD3ZXpQ2ZaIjNyM1kVJjcv/mb1Lp7/cDf/cn4hf3/6KW6XY4zpJZgwWQNMFpF8EUkCFgDLerVZBlznPL4SeEsHOLmTiMwEHscXJAcH0ocJjZJCL+t319HY2uFqHWU7a7lz2SbOn5LDv86b4motxpjA+g0TZwzkBmA5sAV4SVU3ichdInK50+xJwCMi5cBNwLHLh0VkJ/AwsFBEKruvBBORB0SkEkhztt/pvOVBIAP4rYh8JCK9g8sMk9IiDx1dyoc7B3yQOWj761v41q/XkZuVyn8tsAF3Y8JVQjCNVPUN4I1e237k97gFuKqP9+b1sf1W4NYA2y8MpiYz9IonZZMUH8eq8kP83ZTRw77/lvZOvvnrtTS3dfDcN84lMzVx2GswxgQnqDAxsSk1KZ6zJ2W5cr+JqvKj33/Cx3vq+MVXZnHqmBHDXoMxJng2nYo5odJCL5v3HaG2sW1Y9/vrD3bxUlklN15QxCUzxg7rvo0xJ8/CxJxQ95T07w/jUr6rK2r48aubmTt1NN+78NRh268xZuAsTMwJnTk+k4zkhGFb36SqrplvP7eOiZ40HllwFnE24G5MRLAxE3NCCfFxnJufzaphuHmxpd13h3tLexcvLCpmZIoNuBsTKezIxPSrpMjLzpom9tY1D9k+VJUf/u4TNlTW88iXzqJodMaQ7csYE3oWJqZfpUW+adaGcmqVX63aycvrKvn+hady0bQxQ7YfY8zQsDAx/ZoyZgTejKQhO9X1/vYa7nl9C/OmjeE7FxQNyT6MMUPLwsT0S0SYU+jlve01DHCWnD5VHm7i28+tI9+bzn9+8UwbcDcmQlmYmKCUFnqoPtpK+cGG/hsHqbmtk28+u5b2zi4WXzOLETbgbkzEsjAxQQn1Ur6qyu2vbGDzviP814KzKMixAXdjIpmFiQnKhOw0JmSn8l6Ibl588t0dLP2oin+96FQumGoD7sZEOgsTE7TSQi8fVNTQ0Tm4pXzf/fQQP3ljC5fOGMu3/84G3I2JBhYmJmglRV6OtnTwSdWRAfexp7aJG55fR9HoDB666kxEbMDdmGhgYWKCVlI4uPtNmto6WPTsWrq6lMXXFJOebBMwGBMtLExM0LwZyUwdO2JAS/mqKrcu2cDW/Uf4+dUzyfOmD0GFxhi3BBUmInKJiGwTkXIRuS3A68ki8qLz+moRyXO2e0RkpYg0iMijvd5zr4jsEZGGYPoy4aGk0EvZzsO0tHee1PsWv1PBaxv2cevFUznfhYW2jDFDq98wEZF44DHgUmAacHX30rt+rgcOq2oR8Ahwv7O9BbgDuDlA168CswNs76svEwZKizy0dnSxbtfhoN/zzl+ruf+PW/nCGafwrb8tGMLqjDFuCebIZDZQrqoVqtoGvADM79VmPvC083gJMFdERFUbVfVdfKHSg6p+oKr7AuwvYF9B1GmGwez8bOLjJOgp6XfVNPKd59dz6pgRPHjlGTbgbkyUCiZMcoE9fs8rnW0B26hqB1APeAZYUyj7MiE2IiWRM8dnBrWUb2NrB4ueWYsILL6mmLQkG3A3JloFEyaB/pTsPUFTMG2CFVRfIrJIRMpEpKy6unqAuzIDUVrkZUNlHUda2vtso6rcsuRjPj14lEevPpuJnrRhrNAYM9yCCZNKYILf8/FAVV9tRCQByARqB1hTUH2p6mJVLVbV4pycnAHuygxESaGXLoXVFX3/E//ft7fzxsb93H7paXxusncYqzPGuCGYMFkDTBaRfBFJAhYAy3q1WQZc5zy+EnhLBz69bCj7MkPg7ElZpCTG9Xm/ycqtB3loxTbmnzWOr38+f5irM8a4od8wccYtbgCWA1uAl1R1k4jcJSKXO82eBDwiUg7cBBy7fFhEdgIPAwtFpLL7SjAReUBEKoE0Z/ud/fVlwkNyQjzn5GUHvN9kx6FGbnxhPaeNHcl9/2QD7sbEiqBGRFX1DeCNXtt+5Pe4Bbiqj/fm9bH9VuDWANv77MuEj5JCL/f/cSsHj7YwekQKAA2tHSx6poyEOOHxa2aRmhTvcpXGmOFid8CbAeleyvd9Zxbhri7lphc/ouJQI499+WwmZNuAuzGxxMLEDMj0cZmMTEk4Nm7y6MpyVmw+wL/9/WmUFNmAuzGxxi78NwMSHydM8qTx8tq9vFRWCUDxpCy+VprnbmHGGFfYkYkZkKXr97J1/1E6/S60+6TqCL//qPdV48aYWGBhYgbkweXbaO/secV2S3sXDy7f5lJFxhg3WZiYAamqaz6p7caY6GZhYgZkXFbqSW03xkQ3CxMzILdcPIXUxJ73kaQmxnPLxVNcqsgY4ya7mssMyBUzfRNHP7h8G1V1zYzLSuWWi6cc226MiS0WJmbArpiZa+FhjAHsNJcxxpgQsDAxxhgzaBYmxhhjBs3CxBhjzKBZmBhjjBk0iYZFDEXkKBDJ83h4gcDLFkYGq989kVw7WP1um6KqI0LRUbRcGrxNVYvdLmK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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "YEAR_DF[YEAR_DF.index > 2010][\"prop_error\"].plot(style=\"o-\");" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "I explore this statistically in [another notebook](https://github.com/dvatterott/mlb_errors).\n", "\n", "Because I don't want the year to confound our analyses I remove all data before 2015." ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": true }, "outputs": [], "source": [ "DF = DF[DF[\"year\"] >= 2015]" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "3591" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "len(DF)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This leaves me with 3500 year, player combinations.\n", "\n", "We collected data from multiple years so that we can combine data across years." ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": true }, "outputs": [], "source": [ "GROUPED_DF = DF.groupby([\"playerid\", \"player_name\"]).agg({\"errors\": \"sum\", \"bip\": \"sum\"}).reset_index()" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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errorsbip
count1552.0000001552.000000
mean3.835052324.950387
std6.073256494.688755
min0.0000001.000000
25%0.0000007.000000
50%1.00000069.000000
75%5.000000437.000000
max37.0000002102.000000
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" ], "text/plain": [ " errors bip\n", "count 1552.000000 1552.000000\n", "mean 3.835052 324.950387\n", "std 6.073256 494.688755\n", "min 0.000000 1.000000\n", "25% 0.000000 7.000000\n", "50% 1.000000 69.000000\n", "75% 5.000000 437.000000\n", "max 37.000000 2102.000000" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "GROUPED_DF.describe()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "I want an idea for how likely players are to hit into errors." ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.011801960251664112" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "TOTALS = GROUPED_DF.agg({\"errors\": \"sum\", \"bip\": \"sum\"})\n", "ERROR_RATE = TOTALS[\"errors\"] / TOTALS[\"bip\"]\n", "ERROR_RATE" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Again, errors are very rare, so I want know how many \"trials\" (BIP) I need to get a reasonable estimate for how likely each player is to hit into an error.\n", "\n", "A good rule of thumb is each player should have hit into at least 5 errors. I can estimate how many balls in play that would require on average." ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "423.65843413978496" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "5. /ERROR_RATE" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Looks like I should require at least 425 BIP for each player. Just to be on the safe side, I will round this to 500." ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": true }, "outputs": [], "source": [ "GROUPED_DF = GROUPED_DF[GROUPED_DF[\"bip\"] > 500]" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": true }, "outputs": [], "source": [ "GROUPED_DF = GROUPED_DF.reset_index(drop=True)" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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playeridplayer_nameerrorsbip
0abrej003Jose Abreu201864
1adamm002Matt Adams6834
2adrie001Ehire Adrianza2533
3aguij001Jesus Aguilar2551
4ahmen001Nick Ahmed121101
\n", "
" ], "text/plain": [ " playerid player_name errors bip\n", "0 abrej003 Jose Abreu 20 1864\n", "1 adamm002 Matt Adams 6 834\n", "2 adrie001 Ehire Adrianza 2 533\n", "3 aguij001 Jesus Aguilar 2 551\n", "4 ahmen001 Nick Ahmed 12 1101" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "GROUPED_DF.head()" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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errorsbip
count354.000000354.000000
mean12.9915251129.059322
std6.447648428.485467
min1.000000503.000000
25%8.000000747.250000
50%12.0000001112.000000
75%17.0000001475.750000
max37.0000002102.000000
\n", "
" ], "text/plain": [ " errors bip\n", "count 354.000000 354.000000\n", "mean 12.991525 1129.059322\n", "std 6.447648 428.485467\n", "min 1.000000 503.000000\n", "25% 8.000000 747.250000\n", "50% 12.000000 1112.000000\n", "75% 17.000000 1475.750000\n", "max 37.000000 2102.000000" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "GROUPED_DF.describe()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "I've identified 354 players in the last year who have enough BIP for us to estimate how frequently they hit into errors. \n", "\n", "Below, I plot how the liklihood of hitting into errors is distributed." ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "%matplotlib inline\n", "\n", "GROUPED_DF[\"prop_error\"] = GROUPED_DF[\"errors\"] / GROUPED_DF[\"bip\"]\n", "GROUPED_DF[\"prop_error\"].hist();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It looks relatively normal. Now the question is whether someone who has hit into errors in 2% of their BIP is more likely to hit into errors than someone who has only hit into errors 0.5% of their BIP (or is this all just random variation).\n", "\n", "To try and estimate this, I treat each BIP as a bernoulli trial. Hitting into an error is a \"success\". I can then use a binomial distribution to model the number of \"successes\" per trial (BIP). I would like to know if different players are more or less likely to hit into errors. To do this, I model each player as having their own binomial distribution and the question is whether these *p* (the probability of success) differs across players. \n", "\n", "The traditional ways to answer this question would be to use a [chi square contingency test](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.chi2_contingency.html#scipy.stats.chi2_contingency) but this would just tell us whether players differ at all and not which players differ.\n", "\n", "The traditional way to identify which players differ is to do pairwise comparisons of players, but this results in TONS of comparisons making a [false positives all but certain](https://en.wikipedia.org/wiki/Multiple_comparisons_problem) when doing many comparisons.\n", "\n", "Another option is to harness bayesian statistics and build a [hierarchical beta-binomial model](http://sl8r000.github.io/ab_testing_statistics/use_a_hierarchical_model/). The intuition here is that each player's probability of hitting into an error is drawn from a [Beta distribution](https://en.wikipedia.org/wiki/Beta_distribution). We want to know whether these beta distributions are different. We then assume we can best estimate a player's beta distribution by using that a particular players data AND data from all players. \n", "\n", "The model is built so that as we accrue data about a particular player, we will trust that data more and more, relying on the data from all players less and less. This is called partial pooling. [Here's](https://dsaber.com/2016/08/27/analyze-your-experiment-with-a-multilevel-logistic-regression-using-pymc3%E2%80%8B/) a useful explaination.\n", "\n", "I largely based this analysis on [this](https://docs.pymc.io/notebooks/hierarchical_partial_pooling.html) tutorial. Reference for tutorial for an explaination of how I choose my priors. I ended up using a greater lambda value (because the model sampled better) in the Exponential prior, and while this did lead to more extreme estimates of error likihood, it didn't change the basic story." ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "Auto-assigning NUTS sampler...\n", "Initializing NUTS using jitter+adapt_diag...\n", "Multiprocess sampling (2 chains in 2 jobs)\n", "NUTS: [rates, kappa_log, phi]\n", "Sampling 2 chains: 100%|██████████| 6000/6000 [01:47<00:00, 28.06draws/s] \n" ] } ], "source": [ "import pymc3 as pm\n", "import numpy as np\n", "import theano.tensor as tt\n", "\n", "with pm.Model() as model:\n", " \n", " phi = pm.Uniform('phi', lower=0.0, upper=1.0)\n", " \n", " kappa_log = pm.Exponential('kappa_log', lam=25.)\n", " kappa = pm.Deterministic('kappa', tt.exp(kappa_log))\n", "\n", " rates = pm.Beta('rates', alpha=phi*kappa, beta=(1.0-phi)*kappa, shape=len(GROUPED_DF))\n", "\n", " trials = np.array(GROUPED_DF[\"bip\"])\n", " successes = np.array(GROUPED_DF[\"errors\"])\n", " \n", " obs = pm.Binomial('observed_values', trials, rates, observed=successes)\n", " trace = pm.sample(2000, tune=1000, chains=2, cores=2, nuts_kwargs={'target_accept': .95})" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Check wether the model converged." ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "1.0022635936332533" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "max(np.max(score) for score in pm.gelman_rubin(trace).values())" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "bfmi = pm.bfmi(trace)\n", "max_gr = max(np.max(gr_stats) for gr_stats in pm.gelman_rubin(trace).values())\n", "(pm.energyplot(trace, figsize=(6, 4)).set_title(\"BFMI = {}\\nGelman-Rubin = {}\".format(bfmi, max_gr)));" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The most challenging parameter to fit is kappa which accounts for the variance in the liklihood to hit into an error. I take a look at it to make sure things look as expected." ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
meansdmc_errorhpd_2.5hpd_97.5n_effRhat
kappa927.587178141.0275974.373954657.0665541201.922608980.2889141.000013
\n", "
" ], "text/plain": [ " mean sd mc_error hpd_2.5 hpd_97.5 n_eff \\\n", "kappa 927.587178 141.027597 4.373954 657.066554 1201.922608 980.288914 \n", "\n", " Rhat \n", "kappa 1.000013 " ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" } ], "source": [ "pm.summary(trace, varnames=[\"kappa\"])" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "pm.traceplot(trace, varnames=['kappa']);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can also look at *phi* the estimated global liklihood to hit into an error." ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "pm.traceplot(trace, varnames=['phi']);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Finally, we can lookat how all players vary in their liklihood to hit into an error." ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "pm.traceplot(trace, varnames=['rates']);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Obviously, the amove plot is a lot to look at it, so let's order players by how likely the model believes they are to hit in an error." ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "from matplotlib import pyplot as plt\n", "\n", "rate_means = trace['rates', 1000:].mean(axis=0)\n", "rate_se = trace['rates', 1000:].std(axis=0)\n", "\n", "mean_se = [(x, y, i) for i, x, y in zip(GROUPED_DF.index, rate_means, rate_se)]\n", "sorted_means_se = sorted(mean_se, key=lambda x: x[0])\n", "sorted_means = [x[0] for x in sorted_means_se]\n", "sorted_se = [x[1] for x in sorted_means_se]\n", "\n", "x = np.arange(len(sorted_means))\n", "\n", "plt.plot(x, sorted_means, 'o', alpha=0.25);\n", "\n", "for x_val, m, se in zip(x, sorted_means, sorted_se):\n", " plt.plot([x_val, x_val], [m-se, m+se], 'b-', alpha=0.5)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The ten players who are most likely to hit into an error." ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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playeridplayer_nameerrorsbipprop_errorestimated_mean
71corrc001Carlos Correa3013680.0219300.017838
227myerw001Wil Myers2712140.0222410.017724
15andre001Elvis Andrus3718250.0202740.017420
258plawk001Kevin Plawecki145280.0265150.017200
285rojam002Miguel Rojas219520.0220590.017001
118garca003Avisail Garcia2813710.0204230.016920
244pench001Hunter Pence2210260.0214420.016875
20baezj001Javier Baez2311290.0203720.016443
335turnt001Trea Turner2311400.0201750.016372
50cainl001Lorenzo Cain3216950.0188790.016332
\n", "
" ], "text/plain": [ " playerid player_name errors bip prop_error estimated_mean\n", "71 corrc001 Carlos Correa 30 1368 0.021930 0.017838\n", "227 myerw001 Wil Myers 27 1214 0.022241 0.017724\n", "15 andre001 Elvis Andrus 37 1825 0.020274 0.017420\n", "258 plawk001 Kevin Plawecki 14 528 0.026515 0.017200\n", "285 rojam002 Miguel Rojas 21 952 0.022059 0.017001\n", "118 garca003 Avisail Garcia 28 1371 0.020423 0.016920\n", "244 pench001 Hunter Pence 22 1026 0.021442 0.016875\n", "20 baezj001 Javier Baez 23 1129 0.020372 0.016443\n", "335 turnt001 Trea Turner 23 1140 0.020175 0.016372\n", "50 cainl001 Lorenzo Cain 32 1695 0.018879 0.016332" ] }, "execution_count": 27, "metadata": {}, "output_type": "execute_result" } ], "source": [ "estimated_mean = pm.summary(trace, varnames=[\"rates\"]).iloc[[x[2] for x in sorted_means_se[-10:]]][\"mean\"]\n", "\n", "GROUPED_DF.loc[[x[2] for x in sorted_means_se[-10:]], :].assign(estimated_mean=estimated_mean.values).iloc[::-1]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can also look at the 10 players who are least likely to hit in an error. " ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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playeridplayer_nameerrorsbipprop_errorestimated_mean
226murpd006Daniel Murphy416800.0023810.005670
223morrl001Logan Morrison412410.0032230.006832
343vottj001Joey Votto817240.0046400.007112
239panij002Joe Panik715420.0045400.007245
51calhk001Kole Calhoun917350.0051870.007413
55carpm002Matt Carpenter815660.0051090.007534
142hamib001Billy Hamilton814760.0054200.007822
289rosae001Eddie Rosario814700.0054420.007855
275renda001Anthony Rendon915640.0057540.007966
8alony001Yonder Alonso814400.0055560.008011
\n", "
" ], "text/plain": [ " playerid player_name errors bip prop_error estimated_mean\n", "226 murpd006 Daniel Murphy 4 1680 0.002381 0.005670\n", "223 morrl001 Logan Morrison 4 1241 0.003223 0.006832\n", "343 vottj001 Joey Votto 8 1724 0.004640 0.007112\n", "239 panij002 Joe Panik 7 1542 0.004540 0.007245\n", "51 calhk001 Kole Calhoun 9 1735 0.005187 0.007413\n", "55 carpm002 Matt Carpenter 8 1566 0.005109 0.007534\n", "142 hamib001 Billy Hamilton 8 1476 0.005420 0.007822\n", "289 rosae001 Eddie Rosario 8 1470 0.005442 0.007855\n", "275 renda001 Anthony Rendon 9 1564 0.005754 0.007966\n", "8 alony001 Yonder Alonso 8 1440 0.005556 0.008011" ] }, "execution_count": 28, "metadata": {}, "output_type": "execute_result" } ], "source": [ "estimated_mean = pm.summary(trace, varnames=[\"rates\"]).iloc[[x[2] for x in sorted_means_se[:10]]][\"mean\"]\n", "\n", "GROUPED_DF.loc[[x[2] for x in sorted_means_se[:10]], :].assign(estimated_mean=estimated_mean.values)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Looking at this list, I can't help but wonder if what causes these players to be more or less likely to hit into an error is how the score keeper feels about the player. This looks more like a list of fan favorites (e.g., Daniel Murphy, Chris Carpenter, Votto, Rizzo) than players who are particularly unlikley to hit into an error. More or less I am thinking the score keeper WANT to award these players hits. \n", "\n", "Think about it as a smaller version of the \"superstar\" call in basketball where the NBA referees pick different players to be more or less talented. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can assign a probability to how likely Correa is to be better at hitting into errors than Daniel Murphy." ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.0" ] }, "execution_count": 29, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.mean(trace['rates', 1000:][:, 71] <= trace['rates', 1000:][:, 226])" ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import seaborn as sns\n", "\n", "sns.kdeplot(trace['rates', 1000:][:, 226], shade=True, label=\"Daniel Murphy\");\n", "sns.kdeplot(trace['rates', 1000:][:, 71], shade=True, label=\"Carlos Correa\");\n", "sns.kdeplot(trace['rates', 1000:].flatten(), shade=True, label=\"Overall\");" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can also look exclusively at how the ten most likely and 10 least likely players to hit into an error compare." ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "sns.kdeplot(trace['rates', 1000:][:, [x[2] for x in sorted_means_se[-10:]]].flatten(), shade=True, label=\"10 Least Likely\");\n", "sns.kdeplot(trace['rates', 1000:][:, [x[2] for x in sorted_means_se[:10]]].flatten(), shade=True, label=\"10 Most Likely\");" ] } ], "metadata": { "kernelspec": { "display_name": "mlberrors", "language": "python", "name": "mlberrors" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.6.8" } }, "nbformat": 4, "nbformat_minor": 2 }