manujeevanprakash/gist:3762a874859159e52492

## gistfile1.txt
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  {
   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# Homework 3: Prediction and Classification\n",
      "\n",
      "Due: Thursday, October 16, 2014 11:59 PM\n",
      "\n",
      "<a href=https://raw.githubusercontent.com/cs109/2014/master/homework/HW3.ipynb download=HW3.ipynb> Download this assignment</a>\n",
      "\n",
      "#### Submission Instructions\n",
      "To submit your homework, create a folder named lastname_firstinitial_hw# and place your IPython notebooks, data files, and any other files in this folder. Your IPython Notebooks should be completely executed with the results visible in the notebook. We should not have to run any code. Compress the folder (please use .zip compression) and submit to the CS109 dropbox in the appropriate folder. If we cannot access your work because these directions are not followed correctly, we will not grade your work.\n",
      "\n",
      "---\n"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# Introduction\n",
      "\n",
      "In this assignment you will be using regression and classification to explore different data sets.  \n",
      "\n",
      "**First**: You will use data from before 2002 in the [Sean Lahman's Baseball Database](http://seanlahman.com/baseball-archive/statistics) to create a metric for picking baseball players using linear regression. This is same database we used in Homework 1. This database contains the \"complete batting and pitching statistics from 1871 to 2013, plus fielding statistics, standings, team stats, managerial records, post-season data, and more\". [Documentation provided here](http://seanlahman.com/files/database/readme2012.txt).\n",
      "\n",
      "![\"Sabermetrics Science\"](http://saberseminar.com/wp-content/uploads/2012/01/saber-web.jpg)\n",
      "http://saberseminar.com/wp-content/uploads/2012/01/saber-web.jpg\n",
      "\n",
      "**Second**: You will use the famous [iris](http://en.wikipedia.org/wiki/Iris_flower_data_set) data set to perform a $k$-neareast neighbor classification using cross validation.  While it was introduced in 1936, it is still [one of the most popular](http://archive.ics.uci.edu/ml/) example data sets in the machine learning community. Wikipedia describes the data set as follows: \"The data set consists of 50 samples from each of three species of Iris (Iris setosa, Iris virginica and Iris versicolor). Four features were measured from each sample: the length and the width of the sepals and petals, in centimetres.\" Here is an illustration what the four features measure:\n",
      "\n",
      "![\"iris data features\"](http://sebastianraschka.com/Images/2014_python_lda/iris_petal_sepal.png)\n",
      "http://sebastianraschka.com/Images/2014_python_lda/iris_petal_sepal.png\n",
      "\n",
      "**Third**: You will investigate the influence of higher dimensional spaces on the classification using another standard data set in machine learning called the The [digits data set](http://scikit-learn.org/stable/modules/generated/sklearn.datasets.load_digits.html).  This data set is similar to the MNIST data set discussed in the lecture. The main difference is, that each digit is represented by an 8x8 pixel image patch, which is considerably smaller than the 28x28 pixels from MNIST. In addition, the gray values are restricted to 16 different values (4 bit), instead of 256 (8 bit) for MNIST. \n",
      "\n",
      "**Finally**: In preparation for Homework 4, we want you to read through the following articles related to predicting the 2014 Senate Midterm Elections. \n",
      "\n",
      "* [Nate Silver's Methodology at while at NYT](http://fivethirtyeight.blogs.nytimes.com/methodology/)\n",
      "* [How The FiveThirtyEight Senate Forecast Model Works](http://fivethirtyeight.com/features/how-the-fivethirtyeight-senate-forecast-model-works/)\n",
      "* [Pollster Ratings v4.0: Methodology](http://fivethirtyeight.com/features/pollster-ratings-v40-methodology/)\n",
      "* [Pollster Ratings v4.0: Results](http://fivethirtyeight.com/features/pollster-ratings-v40-results/)\n",
      "* [Nate Silver versus Sam Wang](http://www.washingtonpost.com/blogs/plum-line/wp/2014/09/17/nate-silver-versus-sam-wang/)\n",
      "* [More Nate Silver versus Sam Wang](http://www.dailykos.com/story/2014/09/09/1328288/-Get-Ready-To-Rumbllllle-Battle-Of-The-Nerds-Nate-Silver-VS-Sam-Wang)\n",
      "* [Nate Silver explains critisims of Sam Wang](http://politicalwire.com/archives/2014/10/02/nate_silver_rebuts_sam_wang.html)\n",
      "* [Background on the feud between Nate Silver and Sam Wang](http://talkingpointsmemo.com/dc/nate-silver-sam-wang-feud)\n",
      "* [Are there swing voters?]( http://www.stat.columbia.edu/~gelman/research/unpublished/swing_voters.pdf)\n",
      "\n",
      "\n",
      "\n",
      "---"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Load Python modules"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# special IPython command to prepare the notebook for matplotlib\n",
      "%matplotlib inline \n",
      "\n",
      "import requests \n",
      "import StringIO\n",
      "import zipfile\n",
      "import numpy as np\n",
      "import pandas as pd # pandas\n",
      "import matplotlib.pyplot as plt # module for plotting \n",
      "\n",
      "# If this module is not already installed, you may need to install it. \n",
      "# You can do this by typing 'pip install seaborn' in the command line\n",
      "import seaborn as sns \n",
      "\n",
      "import sklearn\n",
      "import sklearn.datasets\n",
      "import sklearn.cross_validation\n",
      "import sklearn.decomposition\n",
      "import sklearn.grid_search\n",
      "import sklearn.neighbors\n",
      "import sklearn.metrics"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# special IPython command to prepare the notebook for matplotlib\n",
      "%matplotlib inline \n",
      "\n",
      "import numpy as np\n",
      "import pandas as pd # pandas\n",
      "import matplotlib.pyplot as plt # module for plotting \n",
      "\n",
      "# If this module is not already installed, you may need to install it. \n",
      "# You can do this by typing 'pip install seaborn' in the command line\n",
      "import seaborn as sns \n",
      "\n",
      "import sklearn\n",
      "import sklearn.datasets\n",
      "import sklearn.cross_validation\n",
      "import sklearn.decomposition\n",
      "import sklearn.grid_search\n",
      "import sklearn.neighbors\n",
      "import sklearn.metrics"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# Problem 1: Sabermetrics\n",
      "\n",
      "Using data preceding the 2002 season pick 10 offensive players keeping the payroll under $20 million (assign each player the median salary). Predict how many games this team would win in a 162 game season.  \n",
      "\n",
      "In this problem we will be returning to the [Sean Lahman's Baseball Database](http://seanlahman.com/baseball-archive/statistics) that we used in Homework 1.  From this database, we will be extract five data sets containing information such as yearly stats and standing, batting statistics, fielding statistics, player names, player salaries and biographical information. You will explore the data in this database from before 2002 and create a metric for picking players. "
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "#### Problem 1(a) \n",
      "\n",
      "Load in [these CSV files](http://seanlahman.com/files/database/lahman-csv_2014-02-14.zip) from the [Sean Lahman's Baseball Database](http://seanlahman.com/baseball-archive/statistics). For this assignment, we will use the 'Teams.csv', 'Batting.csv', 'Salaries.csv', 'Fielding.csv', 'Master.csv' tables. Read these tables into separate pandas DataFrames with the following names. \n",
      "\n",
      "CSV file name | Name of pandas DataFrame\n",
      ":---: | :---: \n",
      "Teams.csv | teams\n",
      "Batting.csv | players\n",
      "Salaries.csv | salaries\n",
      "Fielding.csv | fielding\n",
      "Master.csv | master"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "cd C:\\Users\\manu\\Dropbox\\My final projects\\2014-master\\homework\\data"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "C:\\Users\\manu\\Dropbox\\My final projects\\2014-master\\homework\\data\n"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "teams = pd.read_csv('Teams.csv')\n",
      "players = pd.read_csv('Batting.csv')\n",
      "salaries = pd.read_csv('Salaries.csv')\n",
      "fielding = pd.read_csv('Fielding.csv')\n",
      "master = pd.read_csv('Master.csv')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "master.head()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
        "<table border=\"1\" class=\"dataframe\">\n",
        "  <thead>\n",
        "    <tr style=\"text-align: right;\">\n",
        "      <th></th>\n",
        "      <th>playerID</th>\n",
        "      <th>birthYear</th>\n",
        "      <th>birthMonth</th>\n",
        "      <th>birthDay</th>\n",
        "      <th>birthCountry</th>\n",
        "      <th>birthState</th>\n",
        "      <th>birthCity</th>\n",
        "      <th>deathYear</th>\n",
        "      <th>deathMonth</th>\n",
        "      <th>deathDay</th>\n",
        "      <th>...</th>\n",
        "      <th>nameLast</th>\n",
        "      <th>nameGiven</th>\n",
        "      <th>weight</th>\n",
        "      <th>height</th>\n",
        "      <th>bats</th>\n",
        "      <th>throws</th>\n",
        "      <th>debut</th>\n",
        "      <th>finalGame</th>\n",
        "      <th>retroID</th>\n",
        "      <th>bbrefID</th>\n",
        "    </tr>\n",
        "  </thead>\n",
        "  <tbody>\n",
        "    <tr>\n",
        "      <th>0</th>\n",
        "      <td> aardsda01</td>\n",
        "      <td> 1981</td>\n",
        "      <td> 12</td>\n",
        "      <td> 27</td>\n",
        "      <td> USA</td>\n",
        "      <td> CO</td>\n",
        "      <td>     Denver</td>\n",
        "      <td>  NaN</td>\n",
        "      <td>NaN</td>\n",
        "      <td>NaN</td>\n",
        "      <td>...</td>\n",
        "      <td> Aardsma</td>\n",
        "      <td>    David Allan</td>\n",
        "      <td> 205</td>\n",
        "      <td> 75</td>\n",
        "      <td> R</td>\n",
        "      <td> R</td>\n",
        "      <td> 2004-04-06</td>\n",
        "      <td> 2013-09-28</td>\n",
        "      <td> aardd001</td>\n",
        "      <td> aardsda01</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1</th>\n",
        "      <td> aaronha01</td>\n",
        "      <td> 1934</td>\n",
        "      <td>  2</td>\n",
        "      <td>  5</td>\n",
        "      <td> USA</td>\n",
        "      <td> AL</td>\n",
        "      <td>     Mobile</td>\n",
        "      <td>  NaN</td>\n",
        "      <td>NaN</td>\n",
        "      <td>NaN</td>\n",
        "      <td>...</td>\n",
        "      <td>   Aaron</td>\n",
        "      <td>    Henry Louis</td>\n",
        "      <td> 180</td>\n",
        "      <td> 72</td>\n",
        "      <td> R</td>\n",
        "      <td> R</td>\n",
        "      <td> 1954-04-13</td>\n",
        "      <td> 1976-10-03</td>\n",
        "      <td> aaroh101</td>\n",
        "      <td> aaronha01</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>2</th>\n",
        "      <td> aaronto01</td>\n",
        "      <td> 1939</td>\n",
        "      <td>  8</td>\n",
        "      <td>  5</td>\n",
        "      <td> USA</td>\n",
        "      <td> AL</td>\n",
        "      <td>     Mobile</td>\n",
        "      <td> 1984</td>\n",
        "      <td>  8</td>\n",
        "      <td> 16</td>\n",
        "      <td>...</td>\n",
        "      <td>   Aaron</td>\n",
        "      <td>     Tommie Lee</td>\n",
        "      <td> 190</td>\n",
        "      <td> 75</td>\n",
        "      <td> R</td>\n",
        "      <td> R</td>\n",
        "      <td> 1962-04-10</td>\n",
        "      <td> 1971-09-26</td>\n",
        "      <td> aarot101</td>\n",
        "      <td> aaronto01</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>3</th>\n",
        "      <td>  aasedo01</td>\n",
        "      <td> 1954</td>\n",
        "      <td>  9</td>\n",
        "      <td>  8</td>\n",
        "      <td> USA</td>\n",
        "      <td> CA</td>\n",
        "      <td>     Orange</td>\n",
        "      <td>  NaN</td>\n",
        "      <td>NaN</td>\n",
        "      <td>NaN</td>\n",
        "      <td>...</td>\n",
        "      <td>    Aase</td>\n",
        "      <td> Donald William</td>\n",
        "      <td> 190</td>\n",
        "      <td> 75</td>\n",
        "      <td> R</td>\n",
        "      <td> R</td>\n",
        "      <td> 1977-07-26</td>\n",
        "      <td> 1990-10-03</td>\n",
        "      <td> aased001</td>\n",
        "      <td>  aasedo01</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>4</th>\n",
        "      <td>  abadan01</td>\n",
        "      <td> 1972</td>\n",
        "      <td>  8</td>\n",
        "      <td> 25</td>\n",
        "      <td> USA</td>\n",
        "      <td> FL</td>\n",
        "      <td> Palm Beach</td>\n",
        "      <td>  NaN</td>\n",
        "      <td>NaN</td>\n",
        "      <td>NaN</td>\n",
        "      <td>...</td>\n",
        "      <td>    Abad</td>\n",
        "      <td>  Fausto Andres</td>\n",
        "      <td> 184</td>\n",
        "      <td> 73</td>\n",
        "      <td> L</td>\n",
        "      <td> L</td>\n",
        "      <td> 2001-09-10</td>\n",
        "      <td> 2006-04-13</td>\n",
        "      <td> abada001</td>\n",
        "      <td>  abadan01</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
        "</table>\n",
        "<p>5 rows \u00d7 24 columns</p>\n",
        "</div>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 5,
       "text": [
        "    playerID  birthYear  birthMonth  birthDay birthCountry birthState  \\\n",
        "0  aardsda01       1981          12        27          USA         CO   \n",
        "1  aaronha01       1934           2         5          USA         AL   \n",
        "2  aaronto01       1939           8         5          USA         AL   \n",
        "3   aasedo01       1954           9         8          USA         CA   \n",
        "4   abadan01       1972           8        25          USA         FL   \n",
        "\n",
        "    birthCity  deathYear  deathMonth  deathDay    ...    nameLast  \\\n",
        "0      Denver        NaN         NaN       NaN    ...     Aardsma   \n",
        "1      Mobile        NaN         NaN       NaN    ...       Aaron   \n",
        "2      Mobile       1984           8        16    ...       Aaron   \n",
        "3      Orange        NaN         NaN       NaN    ...        Aase   \n",
        "4  Palm Beach        NaN         NaN       NaN    ...        Abad   \n",
        "\n",
        "        nameGiven weight height bats throws       debut   finalGame   retroID  \\\n",
        "0     David Allan    205     75    R      R  2004-04-06  2013-09-28  aardd001   \n",
        "1     Henry Louis    180     72    R      R  1954-04-13  1976-10-03  aaroh101   \n",
        "2      Tommie Lee    190     75    R      R  1962-04-10  1971-09-26  aarot101   \n",
        "3  Donald William    190     75    R      R  1977-07-26  1990-10-03  aased001   \n",
        "4   Fausto Andres    184     73    L      L  2001-09-10  2006-04-13  abada001   \n",
        "\n",
        "     bbrefID  \n",
        "0  aardsda01  \n",
        "1  aaronha01  \n",
        "2  aaronto01  \n",
        "3   aasedo01  \n",
        "4   abadan01  \n",
        "\n",
        "[5 rows x 24 columns]"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "#### Problem 1(b)\n",
      "\n",
      "Calculate the median salary for each player and create a pandas DataFrame called `medianSalaries` with four columns: (1) the player ID, (2) the first name of the player, (3) the last name of the player and (4) the median salary of the player. Show the head of the `medianSalaries` DataFrame.   "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sal = salaries.groupby('playerID')['playerID','salary'].median()\n",
      "medianSalaries = pd.merge(master[['playerID', 'nameFirst', 'nameLast']],\\\n",
      "                          sal, left_on= 'playerID', right_index= True)\n",
      "medianSalaries.head()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
        "<table border=\"1\" class=\"dataframe\">\n",
        "  <thead>\n",
        "    <tr style=\"text-align: right;\">\n",
        "      <th></th>\n",
        "      <th>playerID</th>\n",
        "      <th>nameFirst</th>\n",
        "      <th>nameLast</th>\n",
        "      <th>salary</th>\n",
        "    </tr>\n",
        "  </thead>\n",
        "  <tbody>\n",
        "    <tr>\n",
        "      <th>0 </th>\n",
        "      <td> aardsda01</td>\n",
        "      <td>    David</td>\n",
        "      <td> Aardsma</td>\n",
        "      <td> 419000</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>3 </th>\n",
        "      <td>  aasedo01</td>\n",
        "      <td>      Don</td>\n",
        "      <td>    Aase</td>\n",
        "      <td> 612500</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>4 </th>\n",
        "      <td>  abadan01</td>\n",
        "      <td>     Andy</td>\n",
        "      <td>    Abad</td>\n",
        "      <td> 327000</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>5 </th>\n",
        "      <td>  abadfe01</td>\n",
        "      <td> Fernando</td>\n",
        "      <td>    Abad</td>\n",
        "      <td> 451500</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>13</th>\n",
        "      <td> abbotje01</td>\n",
        "      <td>     Jeff</td>\n",
        "      <td>  Abbott</td>\n",
        "      <td> 255000</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
        "</table>\n",
        "</div>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 6,
       "text": [
        "     playerID nameFirst nameLast  salary\n",
        "0   aardsda01     David  Aardsma  419000\n",
        "3    aasedo01       Don     Aase  612500\n",
        "4    abadan01      Andy     Abad  327000\n",
        "5    abadfe01  Fernando     Abad  451500\n",
        "13  abbotje01      Jeff   Abbott  255000"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "#### Problem 1(c)\n",
      "\n",
      "Now, consider only team/season combinations in which the teams played 162 Games. Exclude all data from before 1947. Compute the per plate appearance rates for singles, doubles, triples, HR, and BB. Create a new pandas DataFrame called `stats` that has the teamID, yearID, wins and these rates.\n",
      "\n",
      "**Hint**: Singles are hits that are not doubles, triples, nor HR. Plate appearances are base on balls plus at bats."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "teams_df = teams[(teams['G'] == 162) & (teams['yearID'] > 1947)].copy()\n",
      "\n",
      "teams_df[\"1B\"] = teams_df.H -teams_df[\"2B\"] - teams_df[\"3B\"] - teams_df[\"HR\"]\n",
      "teams_df[\"PA\"] = teams_df.BB + teams_df.AB\n",
      "\n",
      "def_details = [\"teamID\",\"yearID\",\"W\",\"1B\",\"2B\",\"3B\",\"HR\",\"BB\"]\n",
      "\n",
      "\n",
      "for B in [\"1B\",\"2B\",\"3B\",\"HR\",\"BB\"]:\n",
      "    teams_df[B] = teams_df[B]/teams_df.PA\n",
      "    \n",
      "stats = teams_df[[\"teamID\",\"yearID\",\"W\",\"1B\",\"2B\",\"3B\",\"HR\",\"BB\"]].copy()\n",
      "stats.head()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
        "<table border=\"1\" class=\"dataframe\">\n",
        "  <thead>\n",
        "    <tr style=\"text-align: right;\">\n",
        "      <th></th>\n",
        "      <th>teamID</th>\n",
        "      <th>yearID</th>\n",
        "      <th>W</th>\n",
        "      <th>1B</th>\n",
        "      <th>2B</th>\n",
        "      <th>3B</th>\n",
        "      <th>HR</th>\n",
        "      <th>BB</th>\n",
        "    </tr>\n",
        "  </thead>\n",
        "  <tbody>\n",
        "    <tr>\n",
        "      <th>1366</th>\n",
        "      <td> LAA</td>\n",
        "      <td> 1961</td>\n",
        "      <td> 70</td>\n",
        "      <td> 0.147748</td>\n",
        "      <td> 0.035708</td>\n",
        "      <td> 0.003604</td>\n",
        "      <td> 0.030958</td>\n",
        "      <td> 0.111548</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1367</th>\n",
        "      <td> KC1</td>\n",
        "      <td> 1961</td>\n",
        "      <td> 61</td>\n",
        "      <td> 0.164751</td>\n",
        "      <td> 0.035982</td>\n",
        "      <td> 0.007829</td>\n",
        "      <td> 0.014993</td>\n",
        "      <td> 0.096618</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1377</th>\n",
        "      <td> NYA</td>\n",
        "      <td> 1962</td>\n",
        "      <td> 96</td>\n",
        "      <td> 0.167148</td>\n",
        "      <td> 0.038536</td>\n",
        "      <td> 0.004656</td>\n",
        "      <td> 0.031952</td>\n",
        "      <td> 0.093770</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1379</th>\n",
        "      <td> LAA</td>\n",
        "      <td> 1962</td>\n",
        "      <td> 86</td>\n",
        "      <td> 0.159482</td>\n",
        "      <td> 0.038027</td>\n",
        "      <td> 0.005737</td>\n",
        "      <td> 0.022455</td>\n",
        "      <td> 0.098672</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1381</th>\n",
        "      <td> CHA</td>\n",
        "      <td> 1962</td>\n",
        "      <td> 85</td>\n",
        "      <td> 0.165797</td>\n",
        "      <td> 0.040756</td>\n",
        "      <td> 0.009129</td>\n",
        "      <td> 0.014998</td>\n",
        "      <td> 0.101076</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
        "</table>\n",
        "</div>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 7,
       "text": [
        "     teamID  yearID   W        1B        2B        3B        HR        BB\n",
        "1366    LAA    1961  70  0.147748  0.035708  0.003604  0.030958  0.111548\n",
        "1367    KC1    1961  61  0.164751  0.035982  0.007829  0.014993  0.096618\n",
        "1377    NYA    1962  96  0.167148  0.038536  0.004656  0.031952  0.093770\n",
        "1379    LAA    1962  86  0.159482  0.038027  0.005737  0.022455  0.098672\n",
        "1381    CHA    1962  85  0.165797  0.040756  0.009129  0.014998  0.101076"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "#### Problem 1(d)\n",
      "\n",
      "Is there a noticeable time trend in the rates computed computed in Problem 1(c)? "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "for val in [\"1B\", \"2B\", \"3B\", \"HR\", \"BB\"]:\n",
      "    plt.scatter(stats.yearID, stats[val], c='b', alpha =0.7)\n",
      "    plt.xlabel('year')\n",
      "    plt.ylabel(val)\n",
      "   \n",
      "    plt.title('Trends of stats dataframe')\n",
      "    plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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V1UZobMeOu5k1axRHjhRRXW3ca0xMDj/84Q3cfff7lJQY0Vp2+/uMGjXDVMm3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\nFklEQVR2IBqNRqOJCe1ANBqNRhMT/x86ibZJJI5E7QAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x19ab3cc0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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5dKgSv/86dF2OzP3+YcTErKdXr0xqauR6QWLi5xhGP15/PYOyMimby1WHXE7t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\nHbiNhq/dbRw9uhoVWusUemwK69Y9EVeJbpqTY3qc+3weNm9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0Cu1ANBqNRtMq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\nHYhGo9FoWoV2IBqNRqNpFf8f6Oc+kNmk81EAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x19ab3c50>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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Pww9fysqVrZvPmhMMmhw4EKSpSSW3tKzddOs2D8u6ETi03T8yzPT7tFIjU8qA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\n9u3rmvL7OPPMmbRrt7x+5JiZOT/lHBSAx5NNv35GWMPhaiz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       "text": [
        "<matplotlib.figure.Figure at 0x169f5978>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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iVllrqKlJByAiIpMePWLIzw88LzExhmPHAmf6ycnx5OTkYRjp3rOK6N17DmFh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\npQ8pKLiHmhq5r802BrM5C6v1Fo9dG3A4CGoV0LVrG8xmu6/gz2y207l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       "text": [
        "<matplotlib.figure.Figure at 0x190f9390>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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KSmlsvBebrRCDwYDDcSPwISkp3e95641hZmbURe5V90IIEEG70VtFZmcXcvvtEzul/UtJ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\nQikQhUKhUMTE/w/Sj+np6j9o6gAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x1932d4e0>"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "#### Problem 1(e) \n",
      "\n",
      "Using the `stats` DataFrame from Problem 1(c), adjust the singles per PA rates so that the average across teams for each year is 0. Do the same for the doubles, triples, HR, and BB rates. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "### Your code here ###\n",
      "stat_grp = stats.groupby('yearID')[\"1B\",\"2B\",\"3B\",\"HR\",\"BB\"].mean()\n",
      "stats.head()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
        "<table border=\"1\" class=\"dataframe\">\n",
        "  <thead>\n",
        "    <tr style=\"text-align: right;\">\n",
        "      <th></th>\n",
        "      <th>teamID</th>\n",
        "      <th>yearID</th>\n",
        "      <th>W</th>\n",
        "      <th>1B</th>\n",
        "      <th>2B</th>\n",
        "      <th>3B</th>\n",
        "      <th>HR</th>\n",
        "      <th>BB</th>\n",
        "    </tr>\n",
        "  </thead>\n",
        "  <tbody>\n",
        "    <tr>\n",
        "      <th>1366</th>\n",
        "      <td> LAA</td>\n",
        "      <td> 1961</td>\n",
        "      <td> 70</td>\n",
        "      <td> 0.147748</td>\n",
        "      <td> 0.035708</td>\n",
        "      <td> 0.003604</td>\n",
        "      <td> 0.030958</td>\n",
        "      <td> 0.111548</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1367</th>\n",
        "      <td> KC1</td>\n",
        "      <td> 1961</td>\n",
        "      <td> 61</td>\n",
        "      <td> 0.164751</td>\n",
        "      <td> 0.035982</td>\n",
        "      <td> 0.007829</td>\n",
        "      <td> 0.014993</td>\n",
        "      <td> 0.096618</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1377</th>\n",
        "      <td> NYA</td>\n",
        "      <td> 1962</td>\n",
        "      <td> 96</td>\n",
        "      <td> 0.167148</td>\n",
        "      <td> 0.038536</td>\n",
        "      <td> 0.004656</td>\n",
        "      <td> 0.031952</td>\n",
        "      <td> 0.093770</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1379</th>\n",
        "      <td> LAA</td>\n",
        "      <td> 1962</td>\n",
        "      <td> 86</td>\n",
        "      <td> 0.159482</td>\n",
        "      <td> 0.038027</td>\n",
        "      <td> 0.005737</td>\n",
        "      <td> 0.022455</td>\n",
        "      <td> 0.098672</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1381</th>\n",
        "      <td> CHA</td>\n",
        "      <td> 1962</td>\n",
        "      <td> 85</td>\n",
        "      <td> 0.165797</td>\n",
        "      <td> 0.040756</td>\n",
        "      <td> 0.009129</td>\n",
        "      <td> 0.014998</td>\n",
        "      <td> 0.101076</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
        "</table>\n",
        "</div>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 9,
       "text": [
        "     teamID  yearID   W        1B        2B        3B        HR        BB\n",
        "1366    LAA    1961  70  0.147748  0.035708  0.003604  0.030958  0.111548\n",
        "1367    KC1    1961  61  0.164751  0.035982  0.007829  0.014993  0.096618\n",
        "1377    NYA    1962  96  0.167148  0.038536  0.004656  0.031952  0.093770\n",
        "1379    LAA    1962  86  0.159482  0.038027  0.005737  0.022455  0.098672\n",
        "1381    CHA    1962  85  0.165797  0.040756  0.009129  0.014998  0.101076"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def meanNormalizeRates(df):\n",
      "        subRates = df[[\"1B\",\"2B\",\"3B\",\"HR\",\"BB\"]]\n",
      "        df[[\"1B\",\"2B\",\"3B\",\"HR\",\"BB\"]] = subRates - subRates.mean(axis=0)\n",
      "        return df\n",
      "\n",
      "stats = stats.groupby('yearID').apply(meanNormalizeRates)\n",
      "stats.head()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
        "<table border=\"1\" class=\"dataframe\">\n",
        "  <thead>\n",
        "    <tr style=\"text-align: right;\">\n",
        "      <th></th>\n",
        "      <th>teamID</th>\n",
        "      <th>yearID</th>\n",
        "      <th>W</th>\n",
        "      <th>1B</th>\n",
        "      <th>2B</th>\n",
        "      <th>3B</th>\n",
        "      <th>HR</th>\n",
        "      <th>BB</th>\n",
        "    </tr>\n",
        "  </thead>\n",
        "  <tbody>\n",
        "    <tr>\n",
        "      <th>1366</th>\n",
        "      <td> LAA</td>\n",
        "      <td> 1961</td>\n",
        "      <td> 70</td>\n",
        "      <td>-0.008502</td>\n",
        "      <td>-0.000137</td>\n",
        "      <td>-0.002113</td>\n",
        "      <td> 0.007983</td>\n",
        "      <td> 0.007465</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1367</th>\n",
        "      <td> KC1</td>\n",
        "      <td> 1961</td>\n",
        "      <td> 61</td>\n",
        "      <td> 0.008502</td>\n",
        "      <td> 0.000137</td>\n",
        "      <td> 0.002113</td>\n",
        "      <td>-0.007983</td>\n",
        "      <td>-0.007465</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1377</th>\n",
        "      <td> NYA</td>\n",
        "      <td> 1962</td>\n",
        "      <td> 96</td>\n",
        "      <td> 0.001516</td>\n",
        "      <td> 0.002683</td>\n",
        "      <td>-0.002121</td>\n",
        "      <td> 0.008141</td>\n",
        "      <td> 0.005180</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1379</th>\n",
        "      <td> LAA</td>\n",
        "      <td> 1962</td>\n",
        "      <td> 86</td>\n",
        "      <td>-0.006150</td>\n",
        "      <td> 0.002174</td>\n",
        "      <td>-0.001040</td>\n",
        "      <td>-0.001356</td>\n",
        "      <td> 0.010082</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1381</th>\n",
        "      <td> CHA</td>\n",
        "      <td> 1962</td>\n",
        "      <td> 85</td>\n",
        "      <td> 0.000165</td>\n",
        "      <td> 0.004904</td>\n",
        "      <td> 0.002352</td>\n",
        "      <td>-0.008813</td>\n",
        "      <td> 0.012486</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
        "</table>\n",
        "</div>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 10,
       "text": [
        "     teamID  yearID   W        1B        2B        3B        HR        BB\n",
        "1366    LAA    1961  70 -0.008502 -0.000137 -0.002113  0.007983  0.007465\n",
        "1367    KC1    1961  61  0.008502  0.000137  0.002113 -0.007983 -0.007465\n",
        "1377    NYA    1962  96  0.001516  0.002683 -0.002121  0.008141  0.005180\n",
        "1379    LAA    1962  86 -0.006150  0.002174 -0.001040 -0.001356  0.010082\n",
        "1381    CHA    1962  85  0.000165  0.004904  0.002352 -0.008813  0.012486"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "#### Problem 1(f)\n",
      "\n",
      "Build a simple linear regression model to predict the number of wins from the average adjusted singles, double, triples, HR, and BB rates. To decide which of these terms to include fit the model to data from 2002 and compute the average squared residuals from predictions to years past 2002. Use the fitted model to define a new sabermetric summary: offensive predicted wins (OPW). Hint: the new summary should be a linear combination of one to five of the five rates.\n"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "### Your code here ###\n",
      "from sklearn.linear_model import LinearRegression\n",
      "stat_train = stats[stats.yearID < 2002]\n",
      "stat_test = stats[stats.yearID >= 2002]\n",
      "\n",
      "x_train =  stat_train[[\"1B\",\"2B\",\"3B\",\"HR\",\"BB\"]].values\n",
      "x_test  =  stat_test[[\"1B\",\"2B\",\"3B\",\"HR\",\"BB\"]].values\n",
      "\n",
      "y_train = stat_train[[\"W\"]].values\n",
      "y_test =  stat_test[[\"W\"]].values\n",
      "\n",
      "clf1 = LinearRegression()\n",
      "\n",
      "clf1.fit(x_train, y_train)\n",
      "\n",
      "clf1.coef_\n",
      "\n",
      "np.mean((y_test - clf1.predict(x_test)) **2)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 11,
       "text": [
        "83.823042489760979"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "** Your answer here: **\n",
      "\n",
      "The mean squared error is 83.82"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "#### Problem 1(g)\n",
      "\n",
      "Now we will create a similar database for individual players. Consider only player/year combinations in which the player had at least 500 plate appearances. Consider only the years we considered for the calculations above (after 1947 and seasons with 162 games). For each player/year compute singles, doubles, triples, HR, BB per plate appearance rates. Create a new pandas DataFrame called `playerstats` that has the playerID, yearID and the rates of these stats.  Remove the average for each year as for these rates as done in Problem 1(e). "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "### Your code here ###\n",
      "player_pa = players[(players.AB + players.BB > 500) & (players.yearID > 1947)].copy()\n",
      "\n",
      "player_pa[\"1B\"] = player_pa.H - player_pa[\"2B\"] - player_pa[\"3B\"] - player_pa[\"HR\"]\n",
      "player_pa[\"PA\"] = player_pa.BB + player_pa.AB\n",
      "\n",
      "\n",
      "for val in [\"1B\",\"2B\",\"3B\",\"HR\",\"BB\"]:\n",
      "    player_pa[val] = player_pa[val]/ player_pa.PA\n",
      "\n",
      "playerstats = player_pa[[\"playerID\",\"yearID\",\"1B\",\"2B\",\"3B\",\"HR\",\"BB\"]].copy()\n",
      "\n",
      "playerstats = playerstats.groupby('yearID').apply(meanNormalizeRates)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 12
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Show the head of the `playerstats` DataFrame. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "### Your code here ###\n",
      "playerstats.head()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
        "<table border=\"1\" class=\"dataframe\">\n",
        "  <thead>\n",
        "    <tr style=\"text-align: right;\">\n",
        "      <th></th>\n",
        "      <th>playerID</th>\n",
        "      <th>yearID</th>\n",
        "      <th>1B</th>\n",
        "      <th>2B</th>\n",
        "      <th>3B</th>\n",
        "      <th>HR</th>\n",
        "      <th>BB</th>\n",
        "    </tr>\n",
        "  </thead>\n",
        "  <tbody>\n",
        "    <tr>\n",
        "      <th>8 </th>\n",
        "      <td> aaronha01</td>\n",
        "      <td> 1955</td>\n",
        "      <td> 0.001060</td>\n",
        "      <td> 0.018570</td>\n",
        "      <td> 0.005585</td>\n",
        "      <td> 0.011337</td>\n",
        "      <td>-0.027249</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>9 </th>\n",
        "      <td> aaronha01</td>\n",
        "      <td> 1956</td>\n",
        "      <td> 0.021561</td>\n",
        "      <td> 0.013857</td>\n",
        "      <td> 0.012480</td>\n",
        "      <td> 0.009593</td>\n",
        "      <td>-0.044600</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>10</th>\n",
        "      <td> aaronha01</td>\n",
        "      <td> 1957</td>\n",
        "      <td> 0.004817</td>\n",
        "      <td>-0.002034</td>\n",
        "      <td> 0.000466</td>\n",
        "      <td> 0.037093</td>\n",
        "      <td>-0.013166</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>11</th>\n",
        "      <td> aaronha01</td>\n",
        "      <td> 1958</td>\n",
        "      <td> 0.018367</td>\n",
        "      <td> 0.011015</td>\n",
        "      <td>-0.002219</td>\n",
        "      <td> 0.015398</td>\n",
        "      <td>-0.007762</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>12</th>\n",
        "      <td> aaronha01</td>\n",
        "      <td> 1959</td>\n",
        "      <td> 0.016261</td>\n",
        "      <td> 0.025762</td>\n",
        "      <td> 0.002743</td>\n",
        "      <td> 0.028368</td>\n",
        "      <td>-0.022898</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
        "</table>\n",
        "</div>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 13,
       "text": [
        "     playerID  yearID        1B        2B        3B        HR        BB\n",
        "8   aaronha01    1955  0.001060  0.018570  0.005585  0.011337 -0.027249\n",
        "9   aaronha01    1956  0.021561  0.013857  0.012480  0.009593 -0.044600\n",
        "10  aaronha01    1957  0.004817 -0.002034  0.000466  0.037093 -0.013166\n",
        "11  aaronha01    1958  0.018367  0.011015 -0.002219  0.015398 -0.007762\n",
        "12  aaronha01    1959  0.016261  0.025762  0.002743  0.028368 -0.022898"
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "#### Problem 1(h)\n",
      "\n",
      "Using the `playerstats` DataFrame created in Problem 1(g), create a new DataFrame called `playerLS` containing the player's lifetime stats. This DataFrame should contain the playerID, the year the player's career started, the year the player's career ended and the player's lifetime average for each of the quantities (singles, doubles, triples, HR, BB). For simplicity we will simply compute the avaerage of the rates by year (a more correct way is to go back to the totals). "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def meanNormalizePlayerLS(df):\n",
      "    df = df[['playerID', '1B','2B','3B','HR','BB']].mean()\n",
      "    return df\n",
      "\n",
      "def getyear(x):\n",
      "    return int(x[0:4])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 21
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Show the head of the `playerLS` DataFrame. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "playerLS = playerstats.groupby('playerID').apply(meanNormalizePlayerLS).reset_index()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 22
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "playerLS = master[[\"playerID\",\"debut\",\"finalGame\"]].merge(playerLS, how='inner', on=\"playerID\")\n",
      "playerLS.head()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
        "<table border=\"1\" class=\"dataframe\">\n",
        "  <thead>\n",
        "    <tr style=\"text-align: right;\">\n",
        "      <th></th>\n",
        "      <th>playerID</th>\n",
        "      <th>debut</th>\n",
        "      <th>finalGame</th>\n",
        "      <th>1B</th>\n",
        "      <th>2B</th>\n",
        "      <th>3B</th>\n",
        "      <th>HR</th>\n",
        "      <th>BB</th>\n",
        "    </tr>\n",
        "  </thead>\n",
        "  <tbody>\n",
        "    <tr>\n",
        "      <th>0</th>\n",
        "      <td> aaronha01</td>\n",
        "      <td> 1954-04-13</td>\n",
        "      <td> 1976-10-03</td>\n",
        "      <td>-0.007157</td>\n",
        "      <td> 0.006539</td>\n",
        "      <td>-0.000270</td>\n",
        "      <td> 0.027850</td>\n",
        "      <td> 0.009447</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1</th>\n",
        "      <td> abramca01</td>\n",
        "      <td> 1949-04-20</td>\n",
        "      <td> 1956-05-09</td>\n",
        "      <td> 0.013463</td>\n",
        "      <td>-0.023915</td>\n",
        "      <td> 0.002384</td>\n",
        "      <td> 0.003842</td>\n",
        "      <td> 0.019455</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>2</th>\n",
        "      <td> abreubo01</td>\n",
        "      <td> 1996-09-01</td>\n",
        "      <td> 2012-10-02</td>\n",
        "      <td>-0.008202</td>\n",
        "      <td> 0.006421</td>\n",
        "      <td> 0.001002</td>\n",
        "      <td>-0.003252</td>\n",
        "      <td> 0.050501</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>3</th>\n",
        "      <td> ackledu01</td>\n",
        "      <td> 2011-06-17</td>\n",
        "      <td> 2013-09-29</td>\n",
        "      <td>-0.009270</td>\n",
        "      <td>-0.016605</td>\n",
        "      <td>-0.001974</td>\n",
        "      <td>-0.015274</td>\n",
        "      <td> 0.001597</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>4</th>\n",
        "      <td> adairje01</td>\n",
        "      <td> 1958-09-02</td>\n",
        "      <td> 1970-05-03</td>\n",
        "      <td> 0.011933</td>\n",
        "      <td> 0.003286</td>\n",
        "      <td>-0.002139</td>\n",
        "      <td>-0.012934</td>\n",
        "      <td>-0.037229</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
        "</table>\n",
        "</div>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 23,
       "text": [
        "    playerID       debut   finalGame        1B        2B        3B        HR  \\\n",
        "0  aaronha01  1954-04-13  1976-10-03 -0.007157  0.006539 -0.000270  0.027850   \n",
        "1  abramca01  1949-04-20  1956-05-09  0.013463 -0.023915  0.002384  0.003842   \n",
        "2  abreubo01  1996-09-01  2012-10-02 -0.008202  0.006421  0.001002 -0.003252   \n",
        "3  ackledu01  2011-06-17  2013-09-29 -0.009270 -0.016605 -0.001974 -0.015274   \n",
        "4  adairje01  1958-09-02  1970-05-03  0.011933  0.003286 -0.002139 -0.012934   \n",
        "\n",
        "         BB  \n",
        "0  0.009447  \n",
        "1  0.019455  \n",
        "2  0.050501  \n",
        "3  0.001597  \n",
        "4 -0.037229  "
       ]
      }
     ],
     "prompt_number": 23
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "playerLS[\"debut\"] = playerLS.debut.apply(getyear)\n",
      "playerLS[\"finalGame\"] = playerLS.finalGame.apply(getyear)\n",
      "cols = list(playerLS.columns)\n",
      "cols[1:3]=[\"minYear\",\"maxYear\"]\n",
      "playerLS.columns = cols"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 24
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "playerLS.head()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
        "<table border=\"1\" class=\"dataframe\">\n",
        "  <thead>\n",
        "    <tr style=\"text-align: right;\">\n",
        "      <th></th>\n",
        "      <th>playerID</th>\n",
        "      <th>minYear</th>\n",
        "      <th>maxYear</th>\n",
        "      <th>1B</th>\n",
        "      <th>2B</th>\n",
        "      <th>3B</th>\n",
        "      <th>HR</th>\n",
        "      <th>BB</th>\n",
        "    </tr>\n",
        "  </thead>\n",
        "  <tbody>\n",
        "    <tr>\n",
        "      <th>0</th>\n",
        "      <td> aaronha01</td>\n",
        "      <td> 1954</td>\n",
        "      <td> 1976</td>\n",
        "      <td>-0.007157</td>\n",
        "      <td> 0.006539</td>\n",
        "      <td>-0.000270</td>\n",
        "      <td> 0.027850</td>\n",
        "      <td> 0.009447</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1</th>\n",
        "      <td> abramca01</td>\n",
        "      <td> 1949</td>\n",
        "      <td> 1956</td>\n",
        "      <td> 0.013463</td>\n",
        "      <td>-0.023915</td>\n",
        "      <td> 0.002384</td>\n",
        "      <td> 0.003842</td>\n",
        "      <td> 0.019455</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>2</th>\n",
        "      <td> abreubo01</td>\n",
        "      <td> 1996</td>\n",
        "      <td> 2012</td>\n",
        "      <td>-0.008202</td>\n",
        "      <td> 0.006421</td>\n",
        "      <td> 0.001002</td>\n",
        "      <td>-0.003252</td>\n",
        "      <td> 0.050501</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>3</th>\n",
        "      <td> ackledu01</td>\n",
        "      <td> 2011</td>\n",
        "      <td> 2013</td>\n",
        "      <td>-0.009270</td>\n",
        "      <td>-0.016605</td>\n",
        "      <td>-0.001974</td>\n",
        "      <td>-0.015274</td>\n",
        "      <td> 0.001597</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>4</th>\n",
        "      <td> adairje01</td>\n",
        "      <td> 1958</td>\n",
        "      <td> 1970</td>\n",
        "      <td> 0.011933</td>\n",
        "      <td> 0.003286</td>\n",
        "      <td>-0.002139</td>\n",
        "      <td>-0.012934</td>\n",
        "      <td>-0.037229</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
        "</table>\n",
        "</div>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 25,
       "text": [
        "    playerID  minYear  maxYear        1B        2B        3B        HR  \\\n",
        "0  aaronha01     1954     1976 -0.007157  0.006539 -0.000270  0.027850   \n",
        "1  abramca01     1949     1956  0.013463 -0.023915  0.002384  0.003842   \n",
        "2  abreubo01     1996     2012 -0.008202  0.006421  0.001002 -0.003252   \n",
        "3  ackledu01     2011     2013 -0.009270 -0.016605 -0.001974 -0.015274   \n",
        "4  adairje01     1958     1970  0.011933  0.003286 -0.002139 -0.012934   \n",
        "\n",
        "         BB  \n",
        "0  0.009447  \n",
        "1  0.019455  \n",
        "2  0.050501  \n",
        "3  0.001597  \n",
        "4 -0.037229  "
       ]
      }
     ],
     "prompt_number": 25
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "#### Problem 1(i)\n",
      "\n",
      "Compute the OPW for each player based on the average rates in the `playerLS` DataFrame. You can interpret this summary statistic as the predicted wins for a team with 9 batters exactly like the player in question. Add this column to the playerLS DataFrame. Call this colum OPW."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "### Your code here ###\n",
      "avgRates = playerLS[[\"1B\",\"2B\",\"3B\",\"HR\",\"BB\"]].values\n",
      "\n",
      "playerLS[\"OPW\"] = clf1.predict(avgRates)\n",
      "playerLS.head()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
        "<table border=\"1\" class=\"dataframe\">\n",
        "  <thead>\n",
        "    <tr style=\"text-align: right;\">\n",
        "      <th></th>\n",
        "      <th>playerID</th>\n",
        "      <th>minYear</th>\n",
        "      <th>maxYear</th>\n",
        "      <th>1B</th>\n",
        "      <th>2B</th>\n",
        "      <th>3B</th>\n",
        "      <th>HR</th>\n",
        "      <th>BB</th>\n",
        "      <th>OPW</th>\n",
        "    </tr>\n",
        "  </thead>\n",
        "  <tbody>\n",
        "    <tr>\n",
        "      <th>0</th>\n",
        "      <td> aaronha01</td>\n",
        "      <td> 1954</td>\n",
        "      <td> 1976</td>\n",
        "      <td>-0.007157</td>\n",
        "      <td> 0.006539</td>\n",
        "      <td>-0.000270</td>\n",
        "      <td> 0.027850</td>\n",
        "      <td> 0.009447</td>\n",
        "      <td> 108.696139</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1</th>\n",
        "      <td> abramca01</td>\n",
        "      <td> 1949</td>\n",
        "      <td> 1956</td>\n",
        "      <td> 0.013463</td>\n",
        "      <td>-0.023915</td>\n",
        "      <td> 0.002384</td>\n",
        "      <td> 0.003842</td>\n",
        "      <td> 0.019455</td>\n",
        "      <td>  92.575472</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>2</th>\n",
        "      <td> abreubo01</td>\n",
        "      <td> 1996</td>\n",
        "      <td> 2012</td>\n",
        "      <td>-0.008202</td>\n",
        "      <td> 0.006421</td>\n",
        "      <td> 0.001002</td>\n",
        "      <td>-0.003252</td>\n",
        "      <td> 0.050501</td>\n",
        "      <td> 104.050008</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>3</th>\n",
        "      <td> ackledu01</td>\n",
        "      <td> 2011</td>\n",
        "      <td> 2013</td>\n",
        "      <td>-0.009270</td>\n",
        "      <td>-0.016605</td>\n",
        "      <td>-0.001974</td>\n",
        "      <td>-0.015274</td>\n",
        "      <td> 0.001597</td>\n",
        "      <td>  53.806003</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>4</th>\n",
        "      <td> adairje01</td>\n",
        "      <td> 1958</td>\n",
        "      <td> 1970</td>\n",
        "      <td> 0.011933</td>\n",
        "      <td> 0.003286</td>\n",
        "      <td>-0.002139</td>\n",
        "      <td>-0.012934</td>\n",
        "      <td>-0.037229</td>\n",
        "      <td>  56.395050</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
        "</table>\n",
        "</div>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 26,
       "text": [
        "    playerID  minYear  maxYear        1B        2B        3B        HR  \\\n",
        "0  aaronha01     1954     1976 -0.007157  0.006539 -0.000270  0.027850   \n",
        "1  abramca01     1949     1956  0.013463 -0.023915  0.002384  0.003842   \n",
        "2  abreubo01     1996     2012 -0.008202  0.006421  0.001002 -0.003252   \n",
        "3  ackledu01     2011     2013 -0.009270 -0.016605 -0.001974 -0.015274   \n",
        "4  adairje01     1958     1970  0.011933  0.003286 -0.002139 -0.012934   \n",
        "\n",
        "         BB         OPW  \n",
        "0  0.009447  108.696139  \n",
        "1  0.019455   92.575472  \n",
        "2  0.050501  104.050008  \n",
        "3  0.001597   53.806003  \n",
        "4 -0.037229   56.395050  "
       ]
      }
     ],
     "prompt_number": 26
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "#### Problem 1(j)\n",
      "\n",
      "Add four columns to the `playerLS` DataFrame that contains the player's position (C, 1B, 2B, 3B, SS, LF, CF, RF, or OF), first name, last name and median salary. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from collections import defaultdict\n",
      "\n",
      "def select_max(df):\n",
      "    positions = df.POS\n",
      "    d = defaultdict(int)\n",
      "    for pos in positions:\n",
      "        d[pos] += 1\n",
      "    result = max(d.iteritems(), key=lambda z: z[1])\n",
      "    return result[0]\n",
      "\n",
      "positions_df = fielding.groupby(\"playerID\").apply(select_max)\n",
      "positions_df = positions_df.reset_index()\n",
      "positions_df = positions_df.rename(columns={0:\"POS\"})"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 27
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "medianSalaries.head()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
        "<table border=\"1\" class=\"dataframe\">\n",
        "  <thead>\n",
        "    <tr style=\"text-align: right;\">\n",
        "      <th></th>\n",
        "      <th>playerID</th>\n",
        "      <th>nameFirst</th>\n",
        "      <th>nameLast</th>\n",
        "      <th>salary</th>\n",
        "    </tr>\n",
        "  </thead>\n",
        "  <tbody>\n",
        "    <tr>\n",
        "      <th>0 </th>\n",
        "      <td> aardsda01</td>\n",
        "      <td>    David</td>\n",
        "      <td> Aardsma</td>\n",
        "      <td> 419000</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>3 </th>\n",
        "      <td>  aasedo01</td>\n",
        "      <td>      Don</td>\n",
        "      <td>    Aase</td>\n",
        "      <td> 612500</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>4 </th>\n",
        "      <td>  abadan01</td>\n",
        "      <td>     Andy</td>\n",
        "      <td>    Abad</td>\n",
        "      <td> 327000</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>5 </th>\n",
        "      <td>  abadfe01</td>\n",
        "      <td> Fernando</td>\n",
        "      <td>    Abad</td>\n",
        "      <td> 451500</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>13</th>\n",
        "      <td> abbotje01</td>\n",
        "      <td>     Jeff</td>\n",
        "      <td>  Abbott</td>\n",
        "      <td> 255000</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
        "</table>\n",
        "</div>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 28,
       "text": [
        "     playerID nameFirst nameLast  salary\n",
        "0   aardsda01     David  Aardsma  419000\n",
        "3    aasedo01       Don     Aase  612500\n",
        "4    abadan01      Andy     Abad  327000\n",
        "5    abadfe01  Fernando     Abad  451500\n",
        "13  abbotje01      Jeff   Abbott  255000"
       ]
      }
     ],
     "prompt_number": 28
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "positions_merged= positions_df.merge(playerLS, how ='inner', on ='playerID')\n",
      "positions_merged = positions_merged.merge(medianSalaries, how='inner', on=['playerID'])\n",
      "positions_merged.head()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
        "<table border=\"1\" class=\"dataframe\">\n",
        "  <thead>\n",
        "    <tr style=\"text-align: right;\">\n",
        "      <th></th>\n",
        "      <th>playerID</th>\n",
        "      <th>POS</th>\n",
        "      <th>minYear</th>\n",
        "      <th>maxYear</th>\n",
        "      <th>1B</th>\n",
        "      <th>2B</th>\n",
        "      <th>3B</th>\n",
        "      <th>HR</th>\n",
        "      <th>BB</th>\n",
        "      <th>OPW</th>\n",
        "      <th>nameFirst</th>\n",
        "      <th>nameLast</th>\n",
        "      <th>salary</th>\n",
        "    </tr>\n",
        "  </thead>\n",
        "  <tbody>\n",
        "    <tr>\n",
        "      <th>0</th>\n",
        "      <td> abreubo01</td>\n",
        "      <td> RF</td>\n",
        "      <td> 1996</td>\n",
        "      <td> 2012</td>\n",
        "      <td>-0.008202</td>\n",
        "      <td> 0.006421</td>\n",
        "      <td> 0.001002</td>\n",
        "      <td>-0.003252</td>\n",
        "      <td> 0.050501</td>\n",
        "      <td> 104.050008</td>\n",
        "      <td>   Bobby</td>\n",
        "      <td>   Abreu</td>\n",
        "      <td> 9000000</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1</th>\n",
        "      <td> ackledu01</td>\n",
        "      <td> 1B</td>\n",
        "      <td> 2011</td>\n",
        "      <td> 2013</td>\n",
        "      <td>-0.009270</td>\n",
        "      <td>-0.016605</td>\n",
        "      <td>-0.001974</td>\n",
        "      <td>-0.015274</td>\n",
        "      <td> 0.001597</td>\n",
        "      <td>  53.806003</td>\n",
        "      <td>  Dustin</td>\n",
        "      <td>  Ackley</td>\n",
        "      <td> 2400000</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>2</th>\n",
        "      <td> adamsru01</td>\n",
        "      <td> SS</td>\n",
        "      <td> 2004</td>\n",
        "      <td> 2009</td>\n",
        "      <td>-0.007867</td>\n",
        "      <td>-0.001289</td>\n",
        "      <td> 0.004160</td>\n",
        "      <td>-0.017533</td>\n",
        "      <td> 0.002672</td>\n",
        "      <td>  67.496507</td>\n",
        "      <td>    Russ</td>\n",
        "      <td>   Adams</td>\n",
        "      <td>  329500</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>3</th>\n",
        "      <td> alfoned01</td>\n",
        "      <td> 2B</td>\n",
        "      <td> 1995</td>\n",
        "      <td> 2006</td>\n",
        "      <td> 0.013485</td>\n",
        "      <td>-0.002177</td>\n",
        "      <td>-0.003239</td>\n",
        "      <td>-0.006436</td>\n",
        "      <td> 0.010745</td>\n",
        "      <td>  83.404437</td>\n",
        "      <td> Edgardo</td>\n",
        "      <td> Alfonzo</td>\n",
        "      <td> 4112500</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>4</th>\n",
        "      <td> alicelu01</td>\n",
        "      <td> 2B</td>\n",
        "      <td> 1988</td>\n",
        "      <td> 2002</td>\n",
        "      <td> 0.035625</td>\n",
        "      <td>-0.009597</td>\n",
        "      <td> 0.007988</td>\n",
        "      <td>-0.026156</td>\n",
        "      <td>-0.006580</td>\n",
        "      <td>  78.561778</td>\n",
        "      <td>    Luis</td>\n",
        "      <td>  Alicea</td>\n",
        "      <td>  750000</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
        "</table>\n",
        "</div>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 29,
       "text": [
        "    playerID POS  minYear  maxYear        1B        2B        3B        HR  \\\n",
        "0  abreubo01  RF     1996     2012 -0.008202  0.006421  0.001002 -0.003252   \n",
        "1  ackledu01  1B     2011     2013 -0.009270 -0.016605 -0.001974 -0.015274   \n",
        "2  adamsru01  SS     2004     2009 -0.007867 -0.001289  0.004160 -0.017533   \n",
        "3  alfoned01  2B     1995     2006  0.013485 -0.002177 -0.003239 -0.006436   \n",
        "4  alicelu01  2B     1988     2002  0.035625 -0.009597  0.007988 -0.026156   \n",
        "\n",
        "         BB         OPW nameFirst nameLast   salary  \n",
        "0  0.050501  104.050008     Bobby    Abreu  9000000  \n",
        "1  0.001597   53.806003    Dustin   Ackley  2400000  \n",
        "2  0.002672   67.496507      Russ    Adams   329500  \n",
        "3  0.010745   83.404437   Edgardo  Alfonzo  4112500  \n",
        "4 -0.006580   78.561778      Luis   Alicea   750000  "
       ]
      }
     ],
     "prompt_number": 29
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Show the head of the `playerLS` DataFrame. "
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "#### Problem 1(k)\n",
      "\n",
      "Subset the `playerLS` DataFrame for players active in 2002 and 2003 and played at least three years. Plot and describe the relationship bewteen the median salary (in millions) and the predicted number of wins. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sub_players = positions_merged[(positions_merged['minYear'] <= 2002) & \\\n",
      "                               (positions_merged['maxYear'] >= 2003) &\\\n",
      "                               (positions_merged['maxYear'] - positions_merged['minYear']>=3)]\n",
      "\n",
      "fig = plt.figure()\n",
      "ax = fig.gca()\n",
      "ax.scatter(sub_players.salary/10**6, sub_players.OPW, alpha=0.5, c='red')\n",
      "ax.set_xscale('log')\n",
      "ax.set_xlabel('Salary (in Millions) on log')\n",
      "ax.set_ylabel('OPW')\n",
      "ax.set_title('Relationship between Salary and Predicted Number of Wins')\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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UpSgUCoVCERSlKBQKhUIRFKUoFAqFQhEUpSgUCoVCERSlKBQKhUIRFPP1FkChUFx/7HY7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\nT2LLrGPZP8t4ZcZMTpgzj5n+Mkd0bDw419IRHRu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XV4GrG/C5TlDLW0cw9PY+BYnBTzUK\nERGJpRqFiIjEUqAQEZFYChQiIhJLgUJERGIpUIiISKz/B2d3N7Hx355bAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x190e6358>"
       ]
      }
     ],
     "prompt_number": 30
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "#### Problem 1(l)\n",
      "Pick one players from one of each of these 10 position C, 1B, 2B, 3B, SS, LF, CF, RF, DH, or OF keeping the total median salary of all 10 players below 20 million. Report their averaged predicted wins and total salary."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "### Your code here ###\n",
      "sub_players.head(3)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
        "<table border=\"1\" class=\"dataframe\">\n",
        "  <thead>\n",
        "    <tr style=\"text-align: right;\">\n",
        "      <th></th>\n",
        "      <th>playerID</th>\n",
        "      <th>POS</th>\n",
        "      <th>minYear</th>\n",
        "      <th>maxYear</th>\n",
        "      <th>1B</th>\n",
        "      <th>2B</th>\n",
        "      <th>3B</th>\n",
        "      <th>HR</th>\n",
        "      <th>BB</th>\n",
        "      <th>OPW</th>\n",
        "      <th>nameFirst</th>\n",
        "      <th>nameLast</th>\n",
        "      <th>salary</th>\n",
        "    </tr>\n",
        "  </thead>\n",
        "  <tbody>\n",
        "    <tr>\n",
        "      <th>0</th>\n",
        "      <td> abreubo01</td>\n",
        "      <td> RF</td>\n",
        "      <td> 1996</td>\n",
        "      <td> 2012</td>\n",
        "      <td>-0.008202</td>\n",
        "      <td> 0.006421</td>\n",
        "      <td> 0.001002</td>\n",
        "      <td>-0.003252</td>\n",
        "      <td> 0.050501</td>\n",
        "      <td> 104.050008</td>\n",
        "      <td>   Bobby</td>\n",
        "      <td>   Abreu</td>\n",
        "      <td> 9000000</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>3</th>\n",
        "      <td> alfoned01</td>\n",
        "      <td> 2B</td>\n",
        "      <td> 1995</td>\n",
        "      <td> 2006</td>\n",
        "      <td> 0.013485</td>\n",
        "      <td>-0.002177</td>\n",
        "      <td>-0.003239</td>\n",
        "      <td>-0.006436</td>\n",
        "      <td> 0.010745</td>\n",
        "      <td>  83.404437</td>\n",
        "      <td> Edgardo</td>\n",
        "      <td> Alfonzo</td>\n",
        "      <td> 4112500</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>5</th>\n",
        "      <td> allench01</td>\n",
        "      <td> LF</td>\n",
        "      <td> 1999</td>\n",
        "      <td> 2005</td>\n",
        "      <td> 0.023014</td>\n",
        "      <td>-0.009664</td>\n",
        "      <td> 0.000201</td>\n",
        "      <td>-0.016584</td>\n",
        "      <td>-0.031390</td>\n",
        "      <td>  58.526131</td>\n",
        "      <td>    Chad</td>\n",
        "      <td>   Allen</td>\n",
        "      <td>  240000</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
        "</table>\n",
        "</div>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 31,
       "text": [
        "    playerID POS  minYear  maxYear        1B        2B        3B        HR  \\\n",
        "0  abreubo01  RF     1996     2012 -0.008202  0.006421  0.001002 -0.003252   \n",
        "3  alfoned01  2B     1995     2006  0.013485 -0.002177 -0.003239 -0.006436   \n",
        "5  allench01  LF     1999     2005  0.023014 -0.009664  0.000201 -0.016584   \n",
        "\n",
        "         BB         OPW nameFirst nameLast   salary  \n",
        "0  0.050501  104.050008     Bobby    Abreu  9000000  \n",
        "3  0.010745   83.404437   Edgardo  Alfonzo  4112500  \n",
        "5 -0.031390   58.526131      Chad    Allen   240000  "
       ]
      }
     ],
     "prompt_number": 31
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def norm_func(df):\n",
      "    temp = df[['resid']] \n",
      "    df[['resid']]=temp -temp.median(axis=0)\n",
      "    return df\n",
      "\n",
      "sub_players['resid']= sub_players['OPW']\n",
      "sub_players = sub_players.groupby('POS').apply(norm_func)\n",
      "sub_players.head()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
        "<table border=\"1\" class=\"dataframe\">\n",
        "  <thead>\n",
        "    <tr style=\"text-align: right;\">\n",
        "      <th></th>\n",
        "      <th>playerID</th>\n",
        "      <th>POS</th>\n",
        "      <th>minYear</th>\n",
        "      <th>maxYear</th>\n",
        "      <th>1B</th>\n",
        "      <th>2B</th>\n",
        "      <th>3B</th>\n",
        "      <th>HR</th>\n",
        "      <th>BB</th>\n",
        "      <th>OPW</th>\n",
        "      <th>nameFirst</th>\n",
        "      <th>nameLast</th>\n",
        "      <th>salary</th>\n",
        "      <th>resid</th>\n",
        "    </tr>\n",
        "  </thead>\n",
        "  <tbody>\n",
        "    <tr>\n",
        "      <th>0</th>\n",
        "      <td> abreubo01</td>\n",
        "      <td> RF</td>\n",
        "      <td> 1996</td>\n",
        "      <td> 2012</td>\n",
        "      <td>-0.008202</td>\n",
        "      <td> 0.006421</td>\n",
        "      <td> 0.001002</td>\n",
        "      <td>-0.003252</td>\n",
        "      <td> 0.050501</td>\n",
        "      <td> 104.050008</td>\n",
        "      <td>   Bobby</td>\n",
        "      <td>   Abreu</td>\n",
        "      <td> 9000000</td>\n",
        "      <td> 16.510691</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>3</th>\n",
        "      <td> alfoned01</td>\n",
        "      <td> 2B</td>\n",
        "      <td> 1995</td>\n",
        "      <td> 2006</td>\n",
        "      <td> 0.013485</td>\n",
        "      <td>-0.002177</td>\n",
        "      <td>-0.003239</td>\n",
        "      <td>-0.006436</td>\n",
        "      <td> 0.010745</td>\n",
        "      <td>  83.404437</td>\n",
        "      <td> Edgardo</td>\n",
        "      <td> Alfonzo</td>\n",
        "      <td> 4112500</td>\n",
        "      <td> 10.674691</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>5</th>\n",
        "      <td> allench01</td>\n",
        "      <td> LF</td>\n",
        "      <td> 1999</td>\n",
        "      <td> 2005</td>\n",
        "      <td> 0.023014</td>\n",
        "      <td>-0.009664</td>\n",
        "      <td> 0.000201</td>\n",
        "      <td>-0.016584</td>\n",
        "      <td>-0.031390</td>\n",
        "      <td>  58.526131</td>\n",
        "      <td>    Chad</td>\n",
        "      <td>   Allen</td>\n",
        "      <td>  240000</td>\n",
        "      <td>-14.466879</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>7</th>\n",
        "      <td> alomaro01</td>\n",
        "      <td> 2B</td>\n",
        "      <td> 1988</td>\n",
        "      <td> 2004</td>\n",
        "      <td> 0.022145</td>\n",
        "      <td> 0.001698</td>\n",
        "      <td> 0.002653</td>\n",
        "      <td>-0.009386</td>\n",
        "      <td> 0.004503</td>\n",
        "      <td>  90.800847</td>\n",
        "      <td> Roberto</td>\n",
        "      <td>  Alomar</td>\n",
        "      <td> 5466667</td>\n",
        "      <td> 18.071102</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>9</th>\n",
        "      <td>  aloumo01</td>\n",
        "      <td> OF</td>\n",
        "      <td> 1990</td>\n",
        "      <td> 2008</td>\n",
        "      <td> 0.004058</td>\n",
        "      <td> 0.001022</td>\n",
        "      <td>-0.000406</td>\n",
        "      <td> 0.009994</td>\n",
        "      <td> 0.000737</td>\n",
        "      <td>  92.104556</td>\n",
        "      <td>  Moises</td>\n",
        "      <td>    Alou</td>\n",
        "      <td> 5135000</td>\n",
        "      <td> 13.800993</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
        "</table>\n",
        "</div>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 32,
       "text": [
        "    playerID POS  minYear  maxYear        1B        2B        3B        HR  \\\n",
        "0  abreubo01  RF     1996     2012 -0.008202  0.006421  0.001002 -0.003252   \n",
        "3  alfoned01  2B     1995     2006  0.013485 -0.002177 -0.003239 -0.006436   \n",
        "5  allench01  LF     1999     2005  0.023014 -0.009664  0.000201 -0.016584   \n",
        "7  alomaro01  2B     1988     2004  0.022145  0.001698  0.002653 -0.009386   \n",
        "9   aloumo01  OF     1990     2008  0.004058  0.001022 -0.000406  0.009994   \n",
        "\n",
        "         BB         OPW nameFirst nameLast   salary      resid  \n",
        "0  0.050501  104.050008     Bobby    Abreu  9000000  16.510691  \n",
        "3  0.010745   83.404437   Edgardo  Alfonzo  4112500  10.674691  \n",
        "5 -0.031390   58.526131      Chad    Allen   240000 -14.466879  \n",
        "7  0.004503   90.800847   Roberto   Alomar  5466667  18.071102  \n",
        "9  0.000737   92.104556    Moises     Alou  5135000  13.800993  "
       ]
      }
     ],
     "prompt_number": 32
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "Y = sub_players.resid.values\n",
      "X = np.log(sub_players[[\"salary\"]])\n",
      "\n",
      "clf = sklearn.linear_model.LinearRegression()\n",
      "clf.fit(X,Y)\n",
      "\n",
      "sub_players['resid'] = Y - clf.predict(X)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 33
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sub_players = sub_players[sub_players.resid >= 0]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 34
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def salary_minimum(tdf):\n",
      "    return tdf[\"salary\"].min()\n",
      "\n",
      "minmum_salary = sub_players.groupby('POS').apply(salary_minimum)\n",
      "minmum_salary.sort(ascending = False)\n",
      "\n",
      "minmum_salary"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 35,
       "text": [
        "POS\n",
        "RF     1700000\n",
        "CF     1500000\n",
        "DH     1000000\n",
        "3B      432500\n",
        "1B      375000\n",
        "C       350000\n",
        "OF      315000\n",
        "SS      314750\n",
        "2B      275000\n",
        "LF      195000\n",
        "dtype: int64"
       ]
      }
     ],
     "prompt_number": 35
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "indexs = list(minmum_salary.index)\n",
      "indexs"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 36,
       "text": [
        "['RF', 'CF', 'DH', '3B', '1B', 'C', 'OF', 'SS', '2B', 'LF']"
       ]
      }
     ],
     "prompt_number": 36
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "million_dollars = 20*10**6\n",
      "million_dollars"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 37,
       "text": [
        "20000000"
       ]
      }
     ],
     "prompt_number": 37
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# indexes will contain the indexes of the players we chose\n",
      "indexes=[]\n",
      "    \n",
      "for i in range(len(indexs)):\n",
      "    \n",
      "    # you need to have at least this much left to not go over in the next picks\n",
      "    maxmoney = million_dollars - sum([minmum_salary[x] for x in indexs[:-1] ])\n",
      "    \n",
      "    \n",
      "    # consider only players in positions we have not selected\n",
      "    index = [True if val in indexs else False for val in sub_players.POS.values]\n",
      "    left = sub_players[index & (sub_players.salary <= million_dollars)]\n",
      "    \n",
      "    # pick the one that stands out the most from what is expected given his salary\n",
      "    j = left[\"resid\"].argmax()\n",
      "    indexes.append(j)\n",
      "    \n",
      "    # remove position we just filled from posleft\n",
      "    indexs.remove(left.loc[j].POS)\n",
      "    million_dollars = million_dollars - left.loc[j].salary\n",
      "\n",
      "\n",
      "print indexes   \n",
      "topPicks= sub_players.loc[indexes,:]\n",
      "topPicks=topPicks.sort([\"OPW\"],ascending=False)\n",
      "topPicks"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[81, 274, 236, 55, 611, 475, 582, 966, 872, 922]\n"
       ]
      },
      {
       "html": [
        "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
        "<table border=\"1\" class=\"dataframe\">\n",
        "  <thead>\n",
        "    <tr style=\"text-align: right;\">\n",
        "      <th></th>\n",
        "      <th>playerID</th>\n",
        "      <th>POS</th>\n",
        "      <th>minYear</th>\n",
        "      <th>maxYear</th>\n",
        "      <th>1B</th>\n",
        "      <th>2B</th>\n",
        "      <th>3B</th>\n",
        "      <th>HR</th>\n",
        "      <th>BB</th>\n",
        "      <th>OPW</th>\n",
        "      <th>nameFirst</th>\n",
        "      <th>nameLast</th>\n",
        "      <th>salary</th>\n",
        "      <th>resid</th>\n",
        "    </tr>\n",
        "  </thead>\n",
        "  <tbody>\n",
        "    <tr>\n",
        "      <th>81 </th>\n",
        "      <td> bondsba01</td>\n",
        "      <td> OF</td>\n",
        "      <td> 1986</td>\n",
        "      <td> 2007</td>\n",
        "      <td>-0.045184</td>\n",
        "      <td> 0.001342</td>\n",
        "      <td> 0.001377</td>\n",
        "      <td> 0.030717</td>\n",
        "      <td> 0.112071</td>\n",
        "      <td> 143.101202</td>\n",
        "      <td>  Barry</td>\n",
        "      <td>     Bonds</td>\n",
        "      <td> 8541667</td>\n",
        "      <td> 52.642833</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>582</th>\n",
        "      <td> martied01</td>\n",
        "      <td> DH</td>\n",
        "      <td> 1987</td>\n",
        "      <td> 2004</td>\n",
        "      <td> 0.000910</td>\n",
        "      <td> 0.011751</td>\n",
        "      <td>-0.003912</td>\n",
        "      <td> 0.004922</td>\n",
        "      <td> 0.052827</td>\n",
        "      <td> 113.934171</td>\n",
        "      <td>  Edgar</td>\n",
        "      <td>  Martinez</td>\n",
        "      <td> 3500000</td>\n",
        "      <td> 17.655966</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>274</th>\n",
        "      <td> ensbemo01</td>\n",
        "      <td> 3B</td>\n",
        "      <td> 2000</td>\n",
        "      <td> 2008</td>\n",
        "      <td>-0.033243</td>\n",
        "      <td>-0.003037</td>\n",
        "      <td>-0.000346</td>\n",
        "      <td> 0.026321</td>\n",
        "      <td> 0.047626</td>\n",
        "      <td> 108.584662</td>\n",
        "      <td> Morgan</td>\n",
        "      <td>   Ensberg</td>\n",
        "      <td>  450000</td>\n",
        "      <td> 48.943930</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>475</th>\n",
        "      <td> johnsni01</td>\n",
        "      <td> 1B</td>\n",
        "      <td> 2001</td>\n",
        "      <td> 2012</td>\n",
        "      <td>-0.030406</td>\n",
        "      <td> 0.018102</td>\n",
        "      <td>-0.002523</td>\n",
        "      <td>-0.000333</td>\n",
        "      <td> 0.072075</td>\n",
        "      <td> 107.537577</td>\n",
        "      <td>   Nick</td>\n",
        "      <td>   Johnson</td>\n",
        "      <td> 1450000</td>\n",
        "      <td> 23.763780</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>236</th>\n",
        "      <td> delluda01</td>\n",
        "      <td> LF</td>\n",
        "      <td> 1997</td>\n",
        "      <td> 2009</td>\n",
        "      <td>-0.050673</td>\n",
        "      <td>-0.018869</td>\n",
        "      <td> 0.004528</td>\n",
        "      <td> 0.024153</td>\n",
        "      <td> 0.057238</td>\n",
        "      <td> 100.483979</td>\n",
        "      <td>  David</td>\n",
        "      <td>  Dellucci</td>\n",
        "      <td>  812500</td>\n",
        "      <td> 34.667273</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>922</th>\n",
        "      <td> werthja01</td>\n",
        "      <td> RF</td>\n",
        "      <td> 2002</td>\n",
        "      <td> 2013</td>\n",
        "      <td>-0.015169</td>\n",
        "      <td>-0.000742</td>\n",
        "      <td>-0.003539</td>\n",
        "      <td> 0.012239</td>\n",
        "      <td> 0.032909</td>\n",
        "      <td>  95.991832</td>\n",
        "      <td> Jayson</td>\n",
        "      <td>     Werth</td>\n",
        "      <td> 1700000</td>\n",
        "      <td>  9.562527</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>55 </th>\n",
        "      <td> bellhma01</td>\n",
        "      <td> 2B</td>\n",
        "      <td> 1997</td>\n",
        "      <td> 2007</td>\n",
        "      <td>-0.039044</td>\n",
        "      <td> 0.002241</td>\n",
        "      <td> 0.001326</td>\n",
        "      <td> 0.005377</td>\n",
        "      <td> 0.046554</td>\n",
        "      <td>  91.598047</td>\n",
        "      <td>   Mark</td>\n",
        "      <td>  Bellhorn</td>\n",
        "      <td>  477500</td>\n",
        "      <td> 30.412329</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>872</th>\n",
        "      <td> torrean02</td>\n",
        "      <td> CF</td>\n",
        "      <td> 2002</td>\n",
        "      <td> 2013</td>\n",
        "      <td>-0.038587</td>\n",
        "      <td> 0.025363</td>\n",
        "      <td> 0.009017</td>\n",
        "      <td>-0.003139</td>\n",
        "      <td> 0.006371</td>\n",
        "      <td>  83.881250</td>\n",
        "      <td> Andres</td>\n",
        "      <td>    Torres</td>\n",
        "      <td> 1500000</td>\n",
        "      <td> 13.450094</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>966</th>\n",
        "      <td>  zaungr01</td>\n",
        "      <td>  C</td>\n",
        "      <td> 1995</td>\n",
        "      <td> 2010</td>\n",
        "      <td>-0.008357</td>\n",
        "      <td>-0.016634</td>\n",
        "      <td>-0.003284</td>\n",
        "      <td>-0.010903</td>\n",
        "      <td> 0.052494</td>\n",
        "      <td>  82.532772</td>\n",
        "      <td>  Gregg</td>\n",
        "      <td>      Zaun</td>\n",
        "      <td> 1000000</td>\n",
        "      <td> 15.380639</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>611</th>\n",
        "      <td> menecfr01</td>\n",
        "      <td> SS</td>\n",
        "      <td> 1999</td>\n",
        "      <td> 2005</td>\n",
        "      <td>-0.021680</td>\n",
        "      <td>-0.011214</td>\n",
        "      <td>-0.001739</td>\n",
        "      <td>-0.014485</td>\n",
        "      <td> 0.046071</td>\n",
        "      <td>  73.581041</td>\n",
        "      <td>  Frank</td>\n",
        "      <td> Menechino</td>\n",
        "      <td>  314750</td>\n",
        "      <td> 25.534135</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
        "</table>\n",
        "</div>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 38,
       "text": [
        "      playerID POS  minYear  maxYear        1B        2B        3B        HR  \\\n",
        "81   bondsba01  OF     1986     2007 -0.045184  0.001342  0.001377  0.030717   \n",
        "582  martied01  DH     1987     2004  0.000910  0.011751 -0.003912  0.004922   \n",
        "274  ensbemo01  3B     2000     2008 -0.033243 -0.003037 -0.000346  0.026321   \n",
        "475  johnsni01  1B     2001     2012 -0.030406  0.018102 -0.002523 -0.000333   \n",
        "236  delluda01  LF     1997     2009 -0.050673 -0.018869  0.004528  0.024153   \n",
        "922  werthja01  RF     2002     2013 -0.015169 -0.000742 -0.003539  0.012239   \n",
        "55   bellhma01  2B     1997     2007 -0.039044  0.002241  0.001326  0.005377   \n",
        "872  torrean02  CF     2002     2013 -0.038587  0.025363  0.009017 -0.003139   \n",
        "966   zaungr01   C     1995     2010 -0.008357 -0.016634 -0.003284 -0.010903   \n",
        "611  menecfr01  SS     1999     2005 -0.021680 -0.011214 -0.001739 -0.014485   \n",
        "\n",
        "           BB         OPW nameFirst   nameLast   salary      resid  \n",
        "81   0.112071  143.101202     Barry      Bonds  8541667  52.642833  \n",
        "582  0.052827  113.934171     Edgar   Martinez  3500000  17.655966  \n",
        "274  0.047626  108.584662    Morgan    Ensberg   450000  48.943930  \n",
        "475  0.072075  107.537577      Nick    Johnson  1450000  23.763780  \n",
        "236  0.057238  100.483979     David   Dellucci   812500  34.667273  \n",
        "922  0.032909   95.991832    Jayson      Werth  1700000   9.562527  \n",
        "55   0.046554   91.598047      Mark   Bellhorn   477500  30.412329  \n",
        "872  0.006371   83.881250    Andres     Torres  1500000  13.450094  \n",
        "966  0.052494   82.532772     Gregg       Zaun  1000000  15.380639  \n",
        "611  0.046071   73.581041     Frank  Menechino   314750  25.534135  "
       ]
      }
     ],
     "prompt_number": 38
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "topPicks['salary'].sum()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 39,
       "text": [
        "19746417"
       ]
      }
     ],
     "prompt_number": 39
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "round(topPicks['OPW'].mean()) # we expect 98 wins"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 40,
       "text": [
        "100.0"
       ]
      }
     ],
     "prompt_number": 40
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "#### Problem 1(m)\n",
      "What do these players outperform in? Singles, doubles, triples HR or BB?"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "### Your code here ###\n",
      "\n",
      "def round1000(x):\n",
      "    return np.round(x*1000)\n",
      "\n",
      "topPicks[[\"1B\",\"2B\",\"3B\", \"HR\",\"BB\"]] = topPicks[[\"1B\",\"2B\",\"3B\", \"HR\",\"BB\"]].apply(round1000)\n",
      "topPicks[[\"OPW\"]] = np.round(topPicks[[\"OPW\"]])\n",
      "topPicks[[\"nameFirst\",\"nameLast\",\"POS\",\"1B\",\"2B\",\"3B\", \"HR\",\"BB\",\"OPW\",\"salary\",\"minYear\",\"maxYear\"]]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
        "<table border=\"1\" class=\"dataframe\">\n",
        "  <thead>\n",
        "    <tr style=\"text-align: right;\">\n",
        "      <th></th>\n",
        "      <th>nameFirst</th>\n",
        "      <th>nameLast</th>\n",
        "      <th>POS</th>\n",
        "      <th>1B</th>\n",
        "      <th>2B</th>\n",
        "      <th>3B</th>\n",
        "      <th>HR</th>\n",
        "      <th>BB</th>\n",
        "      <th>OPW</th>\n",
        "      <th>salary</th>\n",
        "      <th>minYear</th>\n",
        "      <th>maxYear</th>\n",
        "    </tr>\n",
        "  </thead>\n",
        "  <tbody>\n",
        "    <tr>\n",
        "      <th>81 </th>\n",
        "      <td>  Barry</td>\n",
        "      <td>     Bonds</td>\n",
        "      <td> OF</td>\n",
        "      <td>-45</td>\n",
        "      <td>  1</td>\n",
        "      <td> 1</td>\n",
        "      <td> 31</td>\n",
        "      <td> 112</td>\n",
        "      <td> 143</td>\n",
        "      <td> 8541667</td>\n",
        "      <td> 1986</td>\n",
        "      <td> 2007</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>582</th>\n",
        "      <td>  Edgar</td>\n",
        "      <td>  Martinez</td>\n",
        "      <td> DH</td>\n",
        "      <td>  1</td>\n",
        "      <td> 12</td>\n",
        "      <td>-4</td>\n",
        "      <td>  5</td>\n",
        "      <td>  53</td>\n",
        "      <td> 114</td>\n",
        "      <td> 3500000</td>\n",
        "      <td> 1987</td>\n",
        "      <td> 2004</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>274</th>\n",
        "      <td> Morgan</td>\n",
        "      <td>   Ensberg</td>\n",
        "      <td> 3B</td>\n",
        "      <td>-33</td>\n",
        "      <td> -3</td>\n",
        "      <td> 0</td>\n",
        "      <td> 26</td>\n",
        "      <td>  48</td>\n",
        "      <td> 109</td>\n",
        "      <td>  450000</td>\n",
        "      <td> 2000</td>\n",
        "      <td> 2008</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>475</th>\n",
        "      <td>   Nick</td>\n",
        "      <td>   Johnson</td>\n",
        "      <td> 1B</td>\n",
        "      <td>-30</td>\n",
        "      <td> 18</td>\n",
        "      <td>-3</td>\n",
        "      <td>  0</td>\n",
        "      <td>  72</td>\n",
        "      <td> 108</td>\n",
        "      <td> 1450000</td>\n",
        "      <td> 2001</td>\n",
        "      <td> 2012</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>236</th>\n",
        "      <td>  David</td>\n",
        "      <td>  Dellucci</td>\n",
        "      <td> LF</td>\n",
        "      <td>-51</td>\n",
        "      <td>-19</td>\n",
        "      <td> 5</td>\n",
        "      <td> 24</td>\n",
        "      <td>  57</td>\n",
        "      <td> 100</td>\n",
        "      <td>  812500</td>\n",
        "      <td> 1997</td>\n",
        "      <td> 2009</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>922</th>\n",
        "      <td> Jayson</td>\n",
        "      <td>     Werth</td>\n",
        "      <td> RF</td>\n",
        "      <td>-15</td>\n",
        "      <td> -1</td>\n",
        "      <td>-4</td>\n",
        "      <td> 12</td>\n",
        "      <td>  33</td>\n",
        "      <td>  96</td>\n",
        "      <td> 1700000</td>\n",
        "      <td> 2002</td>\n",
        "      <td> 2013</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>55 </th>\n",
        "      <td>   Mark</td>\n",
        "      <td>  Bellhorn</td>\n",
        "      <td> 2B</td>\n",
        "      <td>-39</td>\n",
        "      <td>  2</td>\n",
        "      <td> 1</td>\n",
        "      <td>  5</td>\n",
        "      <td>  47</td>\n",
        "      <td>  92</td>\n",
        "      <td>  477500</td>\n",
        "      <td> 1997</td>\n",
        "      <td> 2007</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>872</th>\n",
        "      <td> Andres</td>\n",
        "      <td>    Torres</td>\n",
        "      <td> CF</td>\n",
        "      <td>-39</td>\n",
        "      <td> 25</td>\n",
        "      <td> 9</td>\n",
        "      <td> -3</td>\n",
        "      <td>   6</td>\n",
        "      <td>  84</td>\n",
        "      <td> 1500000</td>\n",
        "      <td> 2002</td>\n",
        "      <td> 2013</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>966</th>\n",
        "      <td>  Gregg</td>\n",
        "      <td>      Zaun</td>\n",
        "      <td>  C</td>\n",
        "      <td> -8</td>\n",
        "      <td>-17</td>\n",
        "      <td>-3</td>\n",
        "      <td>-11</td>\n",
        "      <td>  52</td>\n",
        "      <td>  83</td>\n",
        "      <td> 1000000</td>\n",
        "      <td> 1995</td>\n",
        "      <td> 2010</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>611</th>\n",
        "      <td>  Frank</td>\n",
        "      <td> Menechino</td>\n",
        "      <td> SS</td>\n",
        "      <td>-22</td>\n",
        "      <td>-11</td>\n",
        "      <td>-2</td>\n",
        "      <td>-14</td>\n",
        "      <td>  46</td>\n",
        "      <td>  74</td>\n",
        "      <td>  314750</td>\n",
        "      <td> 1999</td>\n",
        "      <td> 2005</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
        "</table>\n",
        "</div>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 41,
       "text": [
        "    nameFirst   nameLast POS  1B  2B  3B  HR   BB  OPW   salary  minYear  \\\n",
        "81      Barry      Bonds  OF -45   1   1  31  112  143  8541667     1986   \n",
        "582     Edgar   Martinez  DH   1  12  -4   5   53  114  3500000     1987   \n",
        "274    Morgan    Ensberg  3B -33  -3   0  26   48  109   450000     2000   \n",
        "475      Nick    Johnson  1B -30  18  -3   0   72  108  1450000     2001   \n",
        "236     David   Dellucci  LF -51 -19   5  24   57  100   812500     1997   \n",
        "922    Jayson      Werth  RF -15  -1  -4  12   33   96  1700000     2002   \n",
        "55       Mark   Bellhorn  2B -39   2   1   5   47   92   477500     1997   \n",
        "872    Andres     Torres  CF -39  25   9  -3    6   84  1500000     2002   \n",
        "966     Gregg       Zaun   C  -8 -17  -3 -11   52   83  1000000     1995   \n",
        "611     Frank  Menechino  SS -22 -11  -2 -14   46   74   314750     1999   \n",
        "\n",
        "     maxYear  \n",
        "81      2007  \n",
        "582     2004  \n",
        "274     2008  \n",
        "475     2012  \n",
        "236     2009  \n",
        "922     2013  \n",
        "55      2007  \n",
        "872     2013  \n",
        "966     2010  \n",
        "611     2005  "
       ]
      }
     ],
     "prompt_number": 41
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "** Your answer here: ** <br>\n",
      "Our best players out perform in BB. \n"
     ]
    }
   ],
   "metadata": {}
  }
 ]
}