Jimenez Evaluation.ipynb

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      "# Jimenez Evaluation\n",
      "\n",
      "Prepared by **Christopher J. Fonnesbeck**\n",
      "\n",
      "*February 6, 2014*\n",
      "\n",
      "> Pick any starting pitcher who entered this offseason as a free agent.  Be as specific as possible: how would you go about evaluating him?  What information would you use to determine his value?  If you were in charge of the Orioles, would you sign him?  For how much?\n",
      "\n",
      "I will consider Ubaldo Jimenez, who as of this writing was a free agent. He is a challenging player to evaluate due to his history in Major League Baseball. After beginning his career as one of the hardest-throwing pitchers in the league, he blossomed into one of baseball's best starters in 2010, when he added a two-seam fastball and a sinking split-finger fastball to his repertoire (see pitch selection chart at end of document). However, he regressed badly during the following two years after being traded from Colorado to Cleveland, and was widely considered one of the poorest regular starters in the league in 2012. But he bounced back strongly in 2013, regaining much of the value he had lost. This variability makes prediction difficult: will he continue pitching strongly in his thirties, or will he regress?\n",
      "\n",
      "My evaluation involves three primary considerations: (1) the probability he will produce some level future value as a starting pitcher; (2) the expected number of seasons over which he will produce this value; and (3) the probability he will miss significant time due to injury over the course of the contract.\n",
      "\n",
      "A reasonable approach to predicting future value is to compare his trajectory to pitchers that are similar to him who have pitched for a greater number of years. In the work outlined below, I obtained a set of pitchers to compare to Ubaldo Jimenez based on a set of selected characteristics. These included:\n",
      "\n",
      "- Strikeout rate\n",
      "- Home run rate\n",
      "- Walk rate\n",
      "- Strikeout to walk ratio\n",
      "- Games started\n",
      "- Complete games\n",
      "- WHIP\n",
      "\n",
      "Note that these metrics were used simply to select pitchers that are similar to Jimenez, and not necessarily to evaluate him. The selection was performed using a statitical methodology called ***clustering***, which groups individuals into clusters based on a statistical distance measure among the characteristics. This resulted in a set of 16 pitchers since 2000 who have averaged 15 or more starts per season with which we might project Jimenez in future years (see calculations below for the list of players). To improve the performance of the algorithm, one might also include PITCHf/x information to cluster based on pitch selection and velocity.\n",
      "\n",
      "In evaluating pitchers, I favor measures that are relatively independent of factors outside the control of the player. Thus, commonly-cited statistics such as wins, saves and ERA are not useful for individual evaluation, since they are to a large degree a function of externalities. Instead, metrics like home run rate, strikeout rate and walk rate are much more directly related to how well a pitcher is performing. Advanced context-independent metrics such as fielding-independent pitching (FIP) attempt to isolate pitching quality from the performance of the team as a whole, and are similarly useful for evaluation. Alternatively, statistics like batting average on balls in play (BABIP) estimate the contribution of a team's defensive performance (and sheer luck) to the opponent batting average, which can then be used to adjust standard metrics like ERA for the influence of externalities.\n",
      "\n",
      "In comparing Jimenez to other pitchers in this group, I plotted the trajectories of each pitcher from their first year in the league forward, for several key statistics. The red line in each plot is Jimenez, while the grey lines are those of the comparables. Additionally, I have included ***Gaussian process models*** of the comparable pitchers, which is a non-parametric regression that fits the trajectories of the pitchers to obtain a Bayesian prediction (dashed line) and associated 95% posterior interval (grey region). Seasons in which fewer than 15 games were pitched were excluded for all pitchers. For example, the figure below illustrates the seasonal variation in FIP (graphics for the other metrics can be found below.):\n",
      "\n",
      "![*Jimenez FIP (red) relative to comparables (grey)*](http://d.pr/i/eJ8b+)\n",
      "\n",
      "Jimenez' FIP values indicate that it is likely that his worst season (2012) was due in large part to his own performance, rather than to external factors. Note, however, that replacement-level 2011 season, came with a FIP that was similar to that of his best season. Note also that the fitted trend of FIP for his comparables nominally decreases in later years, but there is considerable uncertainty associated. Jimenez' **strikeout rate** is generally higher than his comparables, even in his down year, and shows no sign of declining; comparables generally show little regression in later years. **Walk rate** is high relative to others in the group, even in strong years. **Strikeout/walk rate** is average with respect to comparables, for which it shows a tendency to increase somewhat in later years. Though the **home run rate** has worsened for Jimenez (even in 2013), it is still average among comparables, and projects not to worsen. Finally, Jimenez' **WHIP** fluctuates more strongly than his walk rate, and his comparables' WHIP appears to decline over time.\n",
      "\n",
      "A compelling measure of a player's value to his team is some estimate of wins above replacement (WAR), since team wins are inarguably of fundamental value to any team. However, there is no single formula for WAR, which results in some ambiguity in its true relation to expected difference in wins relative to a replacement-level player. It is encouraging that the only two regularly published WAR estimates, FanGraphs (fWAR) and Baseball Reference (rWAR), generally correspond to one another. Jimenez' WAR accurately reflects the perceived variation in his performance, ranging fom a 7.5 in his 2010 peak season to replacement level or below in the subsequent two years.\n",
      "\n",
      "As important as a composite metric like WAR is for assigning value to a particular player, it is an emergent property of the entirety of a player's talents, and therefore, it alone is of limited use for evaluation. Specifically, it is imporant to determine which characteristics of a player's performance contribute most importantly to the additional wins that he adds. From the measures I have examined, two important patterns stand out: first, the player's strikeout rate appears to fluctuate closely with changes in WAR, while the walk rate, though worryingly high, stays relatively constant during good and poor seasons. The second, as noted earlier, with the exception of the 2011 season, FIP also tracks closely with WAR, indicating that poor seasons cannot realistically be attributed strongly to random chance.\n",
      "\n",
      "One worrying trend is the loss in velocity from his fastball over time:\n",
      "\n",
      "![*Jimenez fastball velocity (min, max, mean) by season*](http://d.pr/i/jizd+)\n",
      "\n",
      "Once the hardest in the league, his fastball no longer reaches 100 MPH, but is still very good. Here, it is the *trend* rather than the current state that may be concerning. One also has to consider that the drop in velocity coincided with the addition of a broader range of pitches to his repertoire, perhaps making him less reliant on throwing so hard.\n",
      "\n",
      "\n",
      "It is also relevant to consider the park effects of Camden Yards on expected performance. Baltimore plays in a hitter's park, with an average park factor of 117. This is appreciably larger than that of Cleveland's ball park, which could inflate his home run rate. However, it should be noted that Jimenez' home run rate in Colorado--an *extreme* hitter's park--was lower than it was in Cleveland.\n",
      "\n",
      "Regarding durability, Jimenez has started at least 30 games in each of his 6 full seasons in Major League Baseball. While this is no guarantee that he will continue to be healthy from 2014 onwards, it suggests that he is durable despite throwing hard with a moderately heavy annual workload. I am not an authority on mechanics, but Jiminez' recovery in performance in 2013 appears to be at least partly to due to a change in delivery. As the season progressed, he threw with a more upright stance and with increased leg drive. This results not only in increased wrist velocity but also decreased risk of shoulder injury (MacWilliams et al. 1998). To some degree, the likelihood of his continuing to pitch with the same effectiveness as in 2013 will depend on whether this biomechanical change is permanent or transient.\n",
      "\n",
      "\n",
      "Addressing the decision of whether or not to sign a pitcher depends not only on value, but on the anticipated cost of the player relative to his value, and on the needs of the team over the course of any contract that might be signed. If the current rotation includes Miguel Gonzalez, Chris Tillman, Bud Norris, Wei-Yin Chen and Kevin Gausman, this means there will be no high-value starters on the team (each projects to 2-3 WAR in 2014). Though Ubaldo Jimenez also projects to 2-3 WAR, he has shown the ability to add 1-2 additional wins in years that he pitches well (or conversely, fall to replacement level in years he does not). Hence, he provides a reasonable probability of adding front-end productivity while Baltimore's prospects (Gausman, Dylan Bundy, Eduardo Rodruiguez) continue to develop.\n",
      "\n",
      "Given that the Orioles would benefit from short-term help at the top of the rotation, I would recommend signing Ubaldo Jimenez. This recommendation is due to the potential upside, based on the evaluation of his strengths and on the trajectories of his comparables. The potential downside can be mitigated by signing the player to a short (*i.e.* 2-year) contract. Since Cleveland made him a qualifying offer, his signing will cost a first-round draft choice, thereby increasing the overall cost of his signing. \n",
      "\n",
      "Several starting pitchers have signed or been extended this offseason, and those who would be expected to provide similar value to Jimenez commanded contracts of 10-13 million dollars per year for contracts ranging from one year (Colon) to four (Garza). A 2-year contract in the range of 12-14 million annually would be on the higher end of market value, yet cap the total risk to the team below 30 million dollars. Moreover, the length of the contract might incentivize the player to play for another contract in the near future.\n",
      "\n",
      "**Positives:**\n",
      "\n",
      "* durability\n",
      "* improved mechanics\n",
      "* relatively young\n",
      "\n",
      "**Negatives:**\n",
      "\n",
      "* high variance in performance\n",
      "* slowing fastball\n",
      "\n",
      "\n",
      "### References\n",
      "\n",
      "+ MacWilliams, BA, T Choi, MK Perezous, EYS Chao and EG McFarland. 1998. *Characteristic Ground-Reaction Forces in Baseball Pitching*. 26(1), pp.66-71.\n",
      "\n",
      "---"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Deriving Comparables"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%matplotlib inline\n",
      "import numpy as np\n",
      "import pandas as pd\n",
      "import matplotlib as mpl\n",
      "plt = mpl.pyplot\n",
      "import seaborn as sb"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1,
     "trusted": true
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Load standard pitching statistics."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "pitchers = pd.read_csv(\"../Datasets/baseball/Pitching.csv\")"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2,
     "trusted": true
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "pitchers.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>stint</th>\n",
        "      <th>teamID</th>\n",
        "      <th>lgID</th>\n",
        "      <th>W</th>\n",
        "      <th>L</th>\n",
        "      <th>G</th>\n",
        "      <th>GS</th>\n",
        "      <th>CG</th>\n",
        "      <th>SHO</th>\n",
        "      <th>SV</th>\n",
        "      <th>IPouts</th>\n",
        "      <th>H</th>\n",
        "      <th>ER</th>\n",
        "      <th>HR</th>\n",
        "      <th>BB</th>\n",
        "      <th>SO</th>\n",
        "      <th>BAOpp</th>\n",
        "      <th>ERA</th>\n",
        "      <th></th>\n",
        "    </tr>\n",
        "  </thead>\n",
        "  <tbody>\n",
        "    <tr>\n",
        "      <th>0</th>\n",
        "      <td> bechtge01</td>\n",
        "      <td> 1871</td>\n",
        "      <td> 1</td>\n",
        "      <td> PH1</td>\n",
        "      <td> NaN</td>\n",
        "      <td>  1</td>\n",
        "      <td>  2</td>\n",
        "      <td>  3</td>\n",
        "      <td>  3</td>\n",
        "      <td>  2</td>\n",
        "      <td> 0</td>\n",
        "      <td> 0</td>\n",
        "      <td>  78</td>\n",
        "      <td>  43</td>\n",
        "      <td>  23</td>\n",
        "      <td> 0</td>\n",
        "      <td> 11</td>\n",
        "      <td>  1</td>\n",
        "      <td>NaN</td>\n",
        "      <td>  7.96</td>\n",
        "      <td>...</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1</th>\n",
        "      <td> brainas01</td>\n",
        "      <td> 1871</td>\n",
        "      <td> 1</td>\n",
        "      <td> WS3</td>\n",
        "      <td> NaN</td>\n",
        "      <td> 12</td>\n",
        "      <td> 15</td>\n",
        "      <td> 30</td>\n",
        "      <td> 30</td>\n",
        "      <td> 30</td>\n",
        "      <td> 0</td>\n",
        "      <td> 0</td>\n",
        "      <td> 792</td>\n",
        "      <td> 361</td>\n",
        "      <td> 132</td>\n",
        "      <td> 4</td>\n",
        "      <td> 37</td>\n",
        "      <td> 13</td>\n",
        "      <td>NaN</td>\n",
        "      <td>  4.50</td>\n",
        "      <td>...</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>2</th>\n",
        "      <td> fergubo01</td>\n",
        "      <td> 1871</td>\n",
        "      <td> 1</td>\n",
        "      <td> NY2</td>\n",
        "      <td> NaN</td>\n",
        "      <td>  0</td>\n",
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        "      <td>  0</td>\n",
        "      <td>  0</td>\n",
        "      <td> 0</td>\n",
        "      <td> 0</td>\n",
        "      <td>   3</td>\n",
        "      <td>   8</td>\n",
        "      <td>   3</td>\n",
        "      <td> 0</td>\n",
        "      <td>  0</td>\n",
        "      <td>  0</td>\n",
        "      <td>NaN</td>\n",
        "      <td> 27.00</td>\n",
        "      <td>...</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>3</th>\n",
        "      <td> fishech01</td>\n",
        "      <td> 1871</td>\n",
        "      <td> 1</td>\n",
        "      <td> RC1</td>\n",
        "      <td> NaN</td>\n",
        "      <td>  4</td>\n",
        "      <td> 16</td>\n",
        "      <td> 24</td>\n",
        "      <td> 24</td>\n",
        "      <td> 22</td>\n",
        "      <td> 1</td>\n",
        "      <td> 0</td>\n",
        "      <td> 639</td>\n",
        "      <td> 295</td>\n",
        "      <td> 103</td>\n",
        "      <td> 3</td>\n",
        "      <td> 31</td>\n",
        "      <td> 15</td>\n",
        "      <td>NaN</td>\n",
        "      <td>  4.35</td>\n",
        "      <td>...</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>4</th>\n",
        "      <td> fleetfr01</td>\n",
        "      <td> 1871</td>\n",
        "      <td> 1</td>\n",
        "      <td> NY2</td>\n",
        "      <td> NaN</td>\n",
        "      <td>  0</td>\n",
        "      <td>  1</td>\n",
        "      <td>  1</td>\n",
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        "      <td> 0</td>\n",
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        "      <td> 10.00</td>\n",
        "      <td>...</td>\n",
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        "  </tbody>\n",
        "</table>\n",
        "<p>5 rows \u00d7 30 columns</p>\n",
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       "text": [
        "    playerID  yearID  stint teamID lgID   W   L   G  GS  CG  SHO  SV  IPouts  \\\n",
        "0  bechtge01    1871      1    PH1  NaN   1   2   3   3   2    0   0      78   \n",
        "1  brainas01    1871      1    WS3  NaN  12  15  30  30  30    0   0     792   \n",
        "2  fergubo01    1871      1    NY2  NaN   0   0   1   0   0    0   0       3   \n",
        "3  fishech01    1871      1    RC1  NaN   4  16  24  24  22    1   0     639   \n",
        "4  fleetfr01    1871      1    NY2  NaN   0   1   1   1   1    0   0      27   \n",
        "\n",
        "     H   ER  HR  BB  SO  BAOpp    ERA      \n",
        "0   43   23   0  11   1    NaN   7.96 ...  \n",
        "1  361  132   4  37  13    NaN   4.50 ...  \n",
        "2    8    3   0   0   0    NaN  27.00 ...  \n",
        "3  295  103   3  31  15    NaN   4.35 ...  \n",
        "4   20   10   0   3   0    NaN  10.00 ...  \n",
        "\n",
        "[5 rows x 30 columns]"
       ]
      }
     ],
     "prompt_number": 3,
     "trusted": true
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Extract pitchers since 2000:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "pitchers2000 = pitchers[pitchers.yearID>=2000]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 4,
     "trusted": true
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Extract pitchers having at least 6 years to compare as potential comps:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "atleast_6 = pitchers2000.groupby('playerID').playerID.count() >= 6 \n",
      "potential_comps = pitchers2000[pitchers2000.playerID.isin(atleast_6.index[atleast_6].values)]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 5,
     "trusted": true
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Extract pitchers averaging at least 20 starts"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "starts_15 = potential_comps.groupby('playerID').apply(lambda x: x.GS.mean()) > 20\n",
      "potential_comps = potential_comps[potential_comps.playerID.isin(starts_15.index[starts_15].values)]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 6,
     "trusted": true
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "To obtain comparables, I used several standard metrics calculated for each pitcher (filtered according to the criteria above), then applied a **clustering algorithm** to objectively extract pitchers that are close to Jimenez according to these measures. Note that the selection of comparables will be dependent on the metrics that are used in the clustering procedure, and in practice one might choose a different set, depending on the desired characteristics for similarity."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Transform `yearID` to center at first seasons"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "potential_comps['year'] = potential_comps.groupby('playerID')['yearID'].transform(lambda x: x - x.min())"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 7,
     "trusted": true
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Calculate rates"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Total batters faced\n",
      "TBF = potential_comps.IPouts + potential_comps.BB + potential_comps.HBP + potential_comps.H\n",
      "\n",
      "# Strikeout rate\n",
      "potential_comps['Krate'] = potential_comps.SO.astype(float) / TBF\n",
      "\n",
      "# Home run rate\n",
      "potential_comps['HRrate'] = potential_comps.HR.astype(float) / TBF\n",
      "\n",
      "# Walk rate\n",
      "potential_comps['BBrate'] = potential_comps.BB.astype(float) / TBF\n",
      "\n",
      "# Strikeout:walk ratio\n",
      "potential_comps['KtoBB'] = potential_comps.SO.astype(float) / potential_comps.BB\n",
      "\n",
      "# WHIP\n",
      "potential_comps['WHIP'] = (potential_comps.BB.astype(float) + potential_comps.H) / (potential_comps.IPouts/3.)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 8,
     "trusted": true
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Calculate fielding-independent pitching (FIP):\n",
      "\n",
      "    FIP = ((13*HR)+(3*(BB+HBP))-(2*K))/IP + constant"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Import constants for each season\n",
      "constants = pd.read_csv(\"constants.csv\", index_col=0)\n",
      "cFIP = constants.cFIP\n",
      "\n",
      "potential_comps['FIP'] = ((13.*potential_comps.HR + 3*(potential_comps.BB + potential_comps.HBP) - 2*potential_comps.SO) /\n",
      "                          potential_comps.IPouts/3.) + cFIP[potential_comps.yearID].values"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 9,
     "trusted": true
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We will select comparables based on the first 6 years of service, therefore drop years >6 before calculating features for clustering."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "comp_stats = potential_comps[potential_comps.year<=6].groupby('playerID').apply(lambda x: (x.Krate.mean(), x.HRrate.mean(), \n",
      "                                                     x.BBrate.mean(), x.KtoBB.mean(), x.GS.mean(), x.CG.sum(), x.WHIP.mean()))\n",
      "comp_stats.head()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 10,
       "text": [
        "playerID\n",
        "anderbr02    (0.104109363771, 0.0392228809739, 0.0488916813...\n",
        "appieke01    (0.128362760437, 0.028149658298, 0.09551802700...\n",
        "arroybr01    (0.157561409718, 0.020576281093, 0.07891219350...\n",
        "baileho02    (0.17299518789, 0.0268215841456, 0.08413451786...\n",
        "bakersc02    (0.181597540651, 0.0298544189507, 0.0542977121...\n",
        "dtype: object"
       ]
      }
     ],
     "prompt_number": 10,
     "trusted": true
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "X = pd.DataFrame(dict(comp_stats)).T.dropna()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 11,
     "trusted": true
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Use affinity propagation (a clustering method) to sort pitchers into groups. We can then extract the pitchers that share the group ID."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from sklearn.cluster import AffinityPropagation\n",
      "from sklearn import metrics\n",
      " \n",
      "af = AffinityPropagation(preference=-50).fit(X.values)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 12,
     "trusted": true
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "cluster_centers_indices = af.cluster_centers_indices_\n",
      "labels = af.labels_\n",
      "\n",
      "n_clusters_ = len(cluster_centers_indices)\n",
      "\n",
      "print('Estimated number of clusters: %d' % n_clusters_)\n",
      "print(\"Silhouette Coefficient: %0.3f\"\n",
      "      % metrics.silhouette_score(X, labels, metric='sqeuclidean'))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Estimated number of clusters: 12\n",
        "Silhouette Coefficient: 0.525"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n"
       ]
      }
     ],
     "prompt_number": 13,
     "trusted": true
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "X['labels'] = labels\n",
      "comps = X[X.labels==X.ix['jimenub01']['labels']]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 14,
     "trusted": true
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Match `playerID` values to names."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "master = pd.read_csv(\"../Datasets/baseball/Master.csv\")\n",
      "comp_names = master[master.playerID.isin(comps.index)][['nameFirst', 'nameLast']]\n",
      "comp_names['playerID'] = comps.index.values\n",
      "comp_names"
     ],
     "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>playerID</th>\n",
        "    </tr>\n",
        "  </thead>\n",
        "  <tbody>\n",
        "    <tr>\n",
        "      <th>291  </th>\n",
        "      <td>   Brian</td>\n",
        "      <td>   Anderson</td>\n",
        "      <td> anderbr02</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>569  </th>\n",
        "      <td>   Homer</td>\n",
        "      <td>     Bailey</td>\n",
        "      <td> baileho02</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1925 </th>\n",
        "      <td>   Kevin</td>\n",
        "      <td>      Brown</td>\n",
        "      <td> brownke01</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>2266 </th>\n",
        "      <td>  Daniel</td>\n",
        "      <td>    Cabrera</td>\n",
        "      <td> cabreda01</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>2475 </th>\n",
        "      <td> Roberto</td>\n",
        "      <td>  Hernandez</td>\n",
        "      <td> carmofa01</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>3234 </th>\n",
        "      <td>   Aaron</td>\n",
        "      <td>       Cook</td>\n",
        "      <td>  cookaa01</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>3829 </th>\n",
        "      <td>    Doug</td>\n",
        "      <td>      Davis</td>\n",
        "      <td> davisdo02</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>5159 </th>\n",
        "      <td>    Doug</td>\n",
        "      <td>     Fister</td>\n",
        "      <td> fistedo01</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>8064 </th>\n",
        "      <td>  Ubaldo</td>\n",
        "      <td>    Jimenez</td>\n",
        "      <td> jimenub01</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>9314 </th>\n",
        "      <td>   Cliff</td>\n",
        "      <td>        Lee</td>\n",
        "      <td>   leecl02</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>9643 </th>\n",
        "      <td>    Kyle</td>\n",
        "      <td>      Lohse</td>\n",
        "      <td> lohseky01</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>10315</th>\n",
        "      <td>  Justin</td>\n",
        "      <td>  Masterson</td>\n",
        "      <td> masteju01</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>13000</th>\n",
        "      <td>    Joel</td>\n",
        "      <td>    Pineiro</td>\n",
        "      <td> pineijo01</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>14451</th>\n",
        "      <td>   Johan</td>\n",
        "      <td>    Santana</td>\n",
        "      <td> santajo01</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>14493</th>\n",
        "      <td>     Joe</td>\n",
        "      <td>   Saunders</td>\n",
        "      <td> saundjo01</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>17000</th>\n",
        "      <td>    Adam</td>\n",
        "      <td> Wainwright</td>\n",
        "      <td> wainwad01</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
        "</table>\n",
        "<p>16 rows \u00d7 3 columns</p>\n",
        "</div>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 15,
       "text": [
        "      nameFirst    nameLast   playerID\n",
        "291       Brian    Anderson  anderbr02\n",
        "569       Homer      Bailey  baileho02\n",
        "1925      Kevin       Brown  brownke01\n",
        "2266     Daniel     Cabrera  cabreda01\n",
        "2475    Roberto   Hernandez  carmofa01\n",
        "3234      Aaron        Cook   cookaa01\n",
        "3829       Doug       Davis  davisdo02\n",
        "5159       Doug      Fister  fistedo01\n",
        "8064     Ubaldo     Jimenez  jimenub01\n",
        "9314      Cliff         Lee    leecl02\n",
        "9643       Kyle       Lohse  lohseky01\n",
        "10315    Justin   Masterson  masteju01\n",
        "13000      Joel     Pineiro  pineijo01\n",
        "14451     Johan     Santana  santajo01\n",
        "14493       Joe    Saunders  saundjo01\n",
        "17000      Adam  Wainwright  wainwad01\n",
        "\n",
        "[16 rows x 3 columns]"
       ]
      }
     ],
     "prompt_number": 15,
     "trusted": true
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "comp_data = comp_names.merge(potential_comps, on='playerID')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 16,
     "trusted": true
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Extract Jimenez' data"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "jimenez_index = comp_data.playerID=='jimenub01'\n",
      "jimenez_data = comp_data[jimenez_index]\n",
      "comp_data = comp_data[jimenez_index-True]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 17,
     "trusted": true
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Plot trajectories of metrics for comparables. \n",
      "\n",
      "We can compare pitchers based on a number of metrics, including several of interest that were not used to identify the comps. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from sklearn import gaussian_process\n",
      "from pymc.gp.cov_funs import matern\n",
      "from pymc import gp\n",
      "\n",
      "def plot_comps(stat, V=1., diff_degree=2, amp=0.4, scale=10, rank_limit=1000):\n",
      "    \n",
      "    # Mean and covariance of Gaussian Process\n",
      "    M = gp.Mean(lambda *args, **kwargs: comp_data[stat].mean())\n",
      "    C = gp.Covariance(eval_fun=matern.euclidean, diff_degree=diff_degree, \n",
      "                  amp=amp, scale=scale, rank_limit=rank_limit)\n",
      "    \n",
      "    # Data\n",
      "    obs_x = comp_data.year\n",
      "    data = comp_data[stat]\n",
      "\n",
      "    # Update GP with observations\n",
      "    gp.observe(M=M, C=C, obs_mesh=obs_x, obs_V=V, obs_vals=data)\n",
      "    gp.plot_envelope(M, C, mesh=np.linspace(0,12))\n",
      "    \n",
      "    axes = plt.gca()\n",
      "    # Plot comparables\n",
      "    comp_data[comp_data.GS>=15].groupby('playerID').plot(axes=axes, x='year', y=stat, color='grey', alpha=0.4, grid=False)\n",
      "    # Plot Jiminez\n",
      "    jimenez_data[jimenez_data.GS>=15].plot(axes=axes, x='year', y=stat, color='red', grid=False)\n",
      "    axes.set_xlabel('Year')\n",
      "    axes.set_ylabel(stat)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 18,
     "trusted": true
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "**FIP**\n",
      "\n",
      "Jimenez' FIP bounced around in the past, but was generally high in years where his performance was poor."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plot_comps('FIP', V=0.5, diff_degree=4, amp=2, scale=5)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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cBs/zyGQyIwcM4qHOw3sgXmgkEpmLpw8MNuxyuUyFV8jah/u3d6LdbqPT6SAU\nCiGRSIz87cRzyuUmK34kBXW5XG7X0LthGKhUKhBFEen0eCkhYtyJkI3jOPB4PNT4TzIcqNfr0WK+\neWkKMMZjP6IkR4Ej66HH43EYhgZd19Hv9+nJXZIkhEIhBAKBA+O1t9stdLsdpNMZSFIQjsOh/74P\nIP6iX4Lv85+D/sr/vvA1DOaUn0WlUkKptA5VVTZapXb+IlmWudGeFxsx5pZlQlU1aJpKf0aNtx+h\nUGQjT+mHz+cbeT8G1dQVhELhbavGR3tPyUQwA7Lc37UafBxI/s5xnBGDCAwMfavVooIos6DrOvVC\n55kn5DgO8XgclUoFsixTr1iSJLTbbTiOs+X7S/5uWZYRi8U2RR9s26aGftJOhng8Dk3T6EFoOyzL\nQrVahcfj2aTPvhMcx8Hv98Pv9yORSFDjLssyut3uRMY9HA5DVVUaobicBJL2m16vB13Xsby8zIz5\nAjk0HvqlOXSiUNXv96HrOgRBQDAYnGpTWiSi6EMisQSfL4Dw7bfB8//9O5rf+h6whx7CYHrXOkTR\nh+PHT+4Yslxbu4hOp4OVlRWYpkk9b+IFC4JAPW9J8m/0+Pp23aBd18Ujj5yDbVs4c+ZKeDwCOM7d\nqHo1YNvmxmYtL6z3lLRMbeWBV6tVGIaBbDY700ZPNNA9Hs+mQ8O8qNVq0HUduVwOPM/DNE0Ui8Ut\nPU/btmmfdyKR2DI0TnrQV1ZWpvrbSTRiaWlpy+vbto1KpQLXdZHJZOZiSIc9d1VVYdv2iHEXRXHL\n1962bRSLRTr4hbF4TNNEqVSikSHG+EzqoR8ag/7Hf/wnbiazjMc//vGbbjMMA/1+H7Isw3EcSJJE\ne2APitcuCAIyvR6Wb7wRym/dAeUdv7Wnz69pKlZXL8C2baysHEc4PGh/Mk2ThsxbrQbW11cRDkcQ\nCAQ3jLefet2S5N92o9wNngdUVcHPfvZTBIMBxOMx9Pv9PcvpkeKxaDS6yWsmbVizhmIXYbi2wrIs\nFIvFkVas9fV16sUO369arcK27W37vMm1IpHITNEEEnrPZrMjaTAi6Uqq/Bdx2CbGnRTV7WbcZ2m7\nY0wGC7XPxpE16E984pPcUqmIT37yk9vmCl3XhSzLkGUZmqZRcYtQKDT3/tZpOf4nf4Lk//k/aD3w\nPTjJ+YzhHBdNU/Hoo+fRbrc2Njof9YZ5nker1UQgEMTp02ep5z0Ng95sZyNsbmwcuLowDGNf8piW\nZaFcLsMhGdRRAAAgAElEQVTr9W7K3c5SrT2M67qoVqswTXNhhmuYdruNbreLbDYLr9eLZrMJVVWx\nsjJQ8yMDVjiOQzqd3nY99XodmqZRb39ayOtI8uPAYy17mqZheXl5onz3tLiuC13Xac6dqOgNh+U5\njtv2AMKYL6Q2Y5zOCcZmjqxB/+53v+e+6EUvxFOe8hT83u/93q73N02Teu2k55V47ft5ShTabVz3\nkpeg+cIXQv7DP0IwGMZWPeyzYhjGhuetbPxXg21bG+1Bg9+Fw1GcPHkawWAIrVYDjUYdZ88+buKN\nl+exofo00FzWNBX9fm/bNpd5hbfHgXgIlmVt+XzEoM2yFpKjVpRBG9xebFyO46BUKtFDCgl753I5\nmKaJer0OURSRSqW2/bsMw0CpVKIKcbNyaei9Xq9DURSkUql9qWreybj7fD40m02IorhrMSFjOlio\nfXaOrEFfWyu6Dzzw7Yk9O9Lf2u/3oaoqFbYYyDsu3mPYiuW778bKRz+K//y7v4N+6hRCoTCCwRBE\nUYIg7DwsglR5E8Uly7I2/VvXNep5ezyekZC53z/Q0e73e1hbWwXPc0illlEqrSOVWt5yYMgwxPse\nVJnrGwenLnRdH/vv38qbWxQkPzzsIbquS4VCNE2j08OmhVSP73UIl4SO0+k0fD4f1tbWIIoidF1H\nIBDA0tLSjodXElHI5XJzS00Rz5cI3myXV99rtjLugxZLDel0GktLSwcmPXcUYKH2+XCkDfqswjJE\nclCWZViWRfWqL1XfWjScpuEJv/IrUK+6Cuf+5E82+qcd6kH4/QHwvADX5WCa9ojRvjTnzHGAIHg2\nNKcH/xVFHzXiO4V+DWPQ2ra+fhHRaBxPfOKTRza1YeNtWcZGpbtClclmgeS05+UdbgUxePF4HJFI\nhKZkOp0OTNOk/c0nT56c2hCTVretqsf3ArJpZjIZPPLIIzTsHovFdjRQ5PWf9yHEtm2cP38euq7j\nxIkTm6RqDwKu68IwDCiKgkqlMqJjT9TkmHGfDRZqnw9Htm1tHng8HrrxapqGfr+PdruNdrtNvfZ5\nfPiIkAPxAoYNNvl/7lWvwpP/9E8h//M/o37NNSOPJ0ITHo8H0WgUkhRAMBiC1yvC4xHB8wI8nseM\n+LSbjyiKiEQiqFQ8cF0bpdIq0ukUXHeQ/9Y0lRYazhu/349QKEQnd8075zwYutFEIBBAJBLZKPpr\nwTRNOu2L4zj4fD4aGk4kEhMd7EgLVCgU2hdjDgzaxorFIlZXV2GaJpU63ekzMSzxOu+IAhnnSkRR\nDiLkfff5fIhEIvS1UxQFvV5v41DtpyI7zLhPhmEYaLfbiEQizJjvMYfaQ3/wwQfR6XTwtKc9berr\n2rZNw6+Teu39fh+maW5puC+F47gNBajBDw/gGW97GyAI+MFHPwrB66Wb4E7PK4oiDZsLggc8P6oq\n9djbSaQj3SFv2t2QdhyE7XVdw7lz5zYKhYBGo7GhDpfak0KhgR7+QCjlUpGXeVwXGBi8TqcDXdfh\n8/kQj8chCAKKxSKi0Sii0ShkWUar1YLruojH42OFiIlICimm269Nn3jEsizjxIkTY8nMksjFvL0n\nVVVRq9VoSuywFJ1pmoZKpYJYLAZJkmhY3rIsZtwnhITaHcdBJpM5sIe6w8Jl5aF/5jOfwQ033DDT\nNYikZiQSoaI1xGsnXuRWX2TXddHrDQq/iDH1XmKUh/9/qw926Z3vxFVveQuO/du/ofW85421XsMw\ndhRZcRxnI1S++2eAFKfF4zG6/lqthlKpRKdvLRKe57G0tIRKpYJOpzM3EZZmswlN0yBJEqrVKs3V\nk7+n2WyC4zga6g8Gg3REKRFgWVpa2tYQ2baNWq0Gj8eDZDK5b5u8aZqoVqvw+XzweDxwHAeCIEDT\ntG3fO+KdTzKoRFxfh5HLEZHwLTEMA/V6HT6fD0tLS3BdF8VikWrDH2QkSUIkEqGz0+PxOOLx+EjO\nvd/v0/obZty3p9sd1NMwY74/HGoPfdIJU+Ni2zZkWaYeuMfjoe1v8/Y2zr797fCfP4///MIX4M6h\ntY54vLtJa27Xe23bNhqNBlRVpR7sojcuIvgyD4+x1WqhWCzSeduxWGxERZD0XZO/7VJIGN1xnA21\nvNAmxbvhvPV+eZ+apqFWq9EBK2TdZGpaLpfb8nEktznuMBf/T3+Kx7/mNbjwP/8nGi996Zb3IWI6\ngiCMKIHtRZ3EvBjMLxjsL1vNTic5d0VRYJomeJ6nnvulc+ovV+YxqpYxyoHy0PP5/AcBPAuABeD1\nhULh/NBtzwXw2wBCAP6mUCh8fNLrL+pLJAgCIpHIiNfe7XbpCT4UCs3tS7z+trfhmle+EqlCAdVX\nv3rm60WjUdRqNVSr1W2NOpE5JRvSMIIgIJVKodPpoNPpwDAMLC0tLbRokOS4G43G1BWxRBGtWCzC\n7/cjm81uMsbAwKDxPL+tgSGPbbfbaDab1Fv3er1wXRf1en2mUajzQJZlNBoN+Hw+JJNJOtuAyGty\nHAfLsjatz3EcdLvdiXQZsp/4BDjXRfYTn0DjRS8CLrkmmanO8zzS6fTIe0e+KyQicJBD7xzHIZlM\nolwuo91ubzJIoijS+oRh4y7LMjPueKx1k9QpMfaHhcVE8vn89QBOFQqF6wH8IYAPDN3GA/gggDwG\nBv938/n8zL0ti5gmREKIx44dQyKRoOHW9fV1qp89C9qZM6i/5CXIfvzjEDqdmdfr9/uRSqWosMhW\nEZh2uw3XdbftDeU4DrFYDOl0Grquo1wuz0VLfTvINCzHcdBqtSZ6rOM4aLfbWFtbQ6VSQSQSwZVX\nXolwOLxpYyVdDuFweMdDA8/zSCQSWF5epi12nU6HhvKTyeS+CRV1Oh2qE59Op+lBi+M4JBIJ2p5F\nitMufazjOGMX8EmPPILY176G2stfDt/6OhJf/vLI7UQFznXdkbUME4/HwfM8Go3GgZ8NLooiotEo\nDRvvdL9YLIZcLodsNotwOEzny1er1T1c8cGh2+3Sw//leKA5KCzMoBcKhW8CeNXGP68B0B66zQHw\nlEKh0ABwHIAIYCaL4bou7rzzTnzoQx9ayMZBvLpsNotsNotAIIBut4t2u737g3eh+OY3g7MsZD8+\ncZBiS4hRJ2HZ4deDVPdHo9FdPSbirfI8j3K5jH5/91GQ0+L1ehGPx9Hv96Eoyq73d10X3W4XxWIR\nnU6Hjjw9efLkttGE3bzzS5EkiW7Y5XIZ6+vrNDqz1xAPqN1uIxqNbpm7J4OKiAc5jGVZ6PV6iEQi\nY3vKmbvvhrm0hNV3vhPt669H9n//b2Cj4JOowFmWNTJT/VLI4Yh87uYBEdWZ9PA3DpFIhHY+jHNY\nHzbu5Ds3zuf3KGEYBjqdDn3tGPvHQqsWCoWCnc/nPwvgfQDuvuQ2J5/PvxzAfwD4LIDxZ2BuAcdx\nuO666/CZz3wG99xzzyyX2hVRFJFIJBCLxWiYcxasZBKV174WqUIB4traXNa4lVF3XZdOmhrXqHk8\nHmQyGQSDQTQajYV6WmRqXrPZ3HZACxGFKRaLNG0QDodpLnk7wzKud34pPM9DFEUq0EOKJvfS2ySe\nMAn/7xTSjMfj8Hg8tGqf0Ol0wPP82H3h4oZHXnn1q+H6fCi98Y2QLl5E/L776OFC13WkUqldoxXD\noXfLssb7o3eApIK63e7cD5kkWmTb9sSHdRJyv/S1P8qwUPvBYuFliIVC4VYA1wH4XD6fFy657e8B\npACcBvCyWZ/r1ltvxete9zo6IGPRhMNhqqM96/NVXv1qWLEYVv7iL+a0ulGjXq/X0el0YFnWplnY\nu0E2uaWlJciyjHK5PJeNeStIGqBer296TRVFQalUQqPRgCiKyOVyCAQC6PV6iEajO3rOxKBNWpyl\n6zoajQai0SjOnj2LSCSCbreLUqk080FuHIgOvWEYYynaeTweJBIJmt8FHhteFIlExj7MZD71Kdih\nEOovfzkAQLn2WnSf/nRkP/5xtIY6AcYtYpxX6F3XdXS7XVqwSNIg84REi3q9HlRVneixsVgMtm2j\n1+vNdU0HFRZqP1gsMof+wnw+//sb/+wBkLAhWp7P56V8Pv8v+XzeXygUdAAagLkoXPz6r/863vWu\nd+3Jh4sYOjJ0ZBYcvx/Ft7wFia9+FcEf/nBOK3zMqPf7fRoynjb/GwqFsLy8TPu8J93sxkEQBCwt\nLY2EaDVNQ7lcplXdmUyG9n43Gg1IkrRjXtiyLMiyPJFBAwbV27VaDaIoUhnVWCxGe+bL5TJardbC\nJsaRqmHXdbG8vDx2qJ8UMdZqNQCDmgmPxzN+VKZex9KXvoTKrbfCGSqaLL3xjfCfP4/w176GRCIx\nkSjNPELvxBskgkiJRIKGx8l433lB2lUbjcZE43xFUUQoFKJpoKMMC7UfPBbpoX8ZQCKfz/8LgI8B\nuA3Ay/L5/K8VCgUNwF8B+Md8Pn8fgIcAfHoeTzpuD/a8IOFr4v3OQuPFL4Z69iyO3XUXMMcIgyRJ\nEAQBlmXBNM2ZPCSfz4dMJgNRFFGtVtHpdOYeDSFhdFJ8SCIu6XSaarKTinMAu/aCE+98Ek1xUvzI\n8/wm4RhRFJHJZGjKpVQqzd1LVFWVtoKR13tcBEGg9Qjtdhuqqu6qHjfM8qc/DVcUUcvnR35fvvJK\n1K65Btf8/d8jPIU+O3lfiWLfpHS7XViWRb1BUpnOcRxqtdpcD1bksO667sS5enK4nEd9zaxsJ3Q1\nKyzUfjA51H3o40JERhbFvEZwAkDk3/4NV77tbTj3R3+E9nOeM5f1Eb3xcDiMfr8Pv98/syCK67q0\ntc3v98+1tc00TbRaLZTLZQiCQLXWh9dLhq7sNt2M9J3HYrGx88fDE9p2G4VqmibNJ4dCIRpanoVe\nr0clcZPJ5FTX6/V6uHDhAoCBxz6uEp/QbuO6F78Y1Ve8AsXf+A36e6ICd/zBB/HUO+7Az+66C93r\nr594XaSgzePx7KqVMAyZ3LVVj7NpmiiXywtR7SPfnUk17yft9583JGqoKMpCJsqR8b17NRb3cmXS\nPvQjL+Xzla98BW9961sXmlMnHhHpTZ2F7n/9r+g+7WlY+fM/B+aQpyY958FgEIlEAslkEqqqbpmj\nnoRFtLbZto1ms4lSqQTDMLCysoJQKATTNEc2aUVRaB51t4PapN458TxIzno3jXmv14vl5WWaty4W\ni1OnIog3SPThU6nU1IcD0vetqio8nvH1/tOf+xw4x0H11lvp70gLpCRJwE03oX/ddch+7GNTRZGI\nOqCmaWOnqXbzBr1eL/1cz7vynRRqtlqtiTxdUl+ziEr87SAFo+VyGaVSCaqqIhwOI5lMzvV5SEEi\nC7UfPA6NQT937uGpipCe+MQn4v3vf//Cw/DD8qEzhf44Dmu/+Zvwra4i9cUvzryuVqsFjuOoVxMI\nBOjmN4+K9Xm0tpFe8vX1dciyjGg0ilwuRyu6u90uDWkTj5gMXdkJ0zQnzp23221a8DXuZkVkZLPZ\nLLxeL6rVKur1+kQGgBitbreLeDw+ceHipZAUiyiK0DRtrLXw/T7Sf/d3qL/0pbCWlgAMIhykjiCZ\nTILjeZTe8AaEfvQjhB94YKq1SZKEcDiMdrs9Vui93+9D1/UdXxO/349EIoFerzf3gjRSqNloNMZ+\nDPnO7UUbm2VZaLVaWF9fR6PRAMdxSKVSdOrePEWhhg9X+zWQiLE9h8agezwDnfFJc2+ZTAbHjh1b\n0KpGIcIznRkFYtSrrkLj5puR+5u/AT9DW46qDqalXfqlJrOyFUWZi1GftrWN9JKvr6+j2+0iHA4j\nl8shGo1SA0y8gEajQY0LKZzbDdJ3Pq533uv1qEGdZgqZx+PB8vIylpaWoKoqSqUSrTTfCdu2UalU\noCgKksnkXEaO9vt9CIJAC+HGyeemvvAF8KqK8mteA+CxzRvASLSg+6xnQb766pl0E8hncrfPimVZ\naLfbY01CDIfDNEc/z5oGQRCQSCSgqupEB1a/37+wNjbXdam07vr6Ovr9PgKBAHK5HJaXl0fkjucJ\nGT28nzMMGNtzaAz6YCIYh2q1urCWqVnxer2IRqPo9Xozh5+Lb30reE1D5u67p3q84zhoNptUbORS\ngsEgbUObh1EnRUSJRGLX1jYSGiRqe2QjIpPQtrqu4zi4cOECLMsaK688qXdOwrXhcHhmgxoKhZDL\n5WgFdq1W29ZDJjroJF8/j3GmjuOg0+kgGo1CEAQEAgH0+/0dP5OcpmH5b/8WzZtvhpnJABgccDRN\n21wfwXEov+ENCH/vewh973tTrZGE3nVd39GjJoN0xtUGj8fj8Pl8Ux3+d4KMV261WhPtP/NuYyMO\nQ7FYRLVahW3bWFpawsrKChKJxNzHEA8zHGrfL6VExs4cGoPe7Xboh5V8kKeh3W7jIx/5yMIOBUSJ\na9bedHN5GZVXvQrLn/0svBujQCeBtM1sJ+8KDIx6Mpmcm1EHBl7Spa1tZLQsMNpLTpTYdppsBgwO\nSj6fD91uF36/f6zNZJLcOZkUJknS3IZKEE38ZDIJXddRLBY3eXe6rqNSqQDAXIuLut0uHMehBWIe\nj4fqJWxH8h/+AZ52G+XbbgPw2EzrcDi8Zbtc+4YboJ49O5OXvlvoXZZlqKqKRCIxdsqEVL6Ttr15\nVr5P00s/rzY2XddRr9exvr6OTqdDu03IzIJFTzYjXSXEaWEcTA6NQU+nl6GqKgKBAG0pmsYA/fjH\nP8Y999yDO+64Y+69q8BjmtpkqMsslG+7DXYggJW//MuJHkcqXKPR6K4n9mFPfR4COcBjrW1erxel\nUgnnzp3DhQsXcOHChZFe8mQyOZZHYRgGNE1DJBKBpmm7HsYm8c4ty0K1Wl3YKNRgMIhsNgu/349G\no0EjTIqioFKp0DD9vDwr27Zp+sLr9UKSJGiaRseBbpUC4EwTmXvuQesXfxH6iRPjtSRt5NIj3/kO\nAj/60dTr3S70Too5ybjSSSCHqVn2ia2YpqAPmL6NzXEc2hZZLpeh6zpisRhWVlaQTCb3tCCNtOUy\nAZmDzaEx6LFYDMFgEL1ej048mqZS+5nPfCY++MEP4v7778cPfvCDhaxVkiQEg0G02+2ZTuVOKITS\nm96ExD//M/w//elYjxnejMcNHYdCISwtLaHf78/NqJOJdaZpQtM0qKpKPYt0Oj32ZkQ2Za/Xi5Mn\nT1IxmZ3W2Ol0RvLH2+E4Dmq1Gh03uygvRxAEJJNJpFIpGIaB8+fPY3V1FZIkYXl5ea5FS+12GxzH\n0fdekiToug6fz0ertS/1WhP/9/9CrFRQev3rATyWJyViOtvRuukmaCdPDirep2S70DvJO+8UYdoJ\nUvmu6/pcK83J7PR2uz12Wk0QBESj0V3THgTDMNBsNrG+vo5ms0lljXO5HCKRyEInH24FUedjofaD\nz6Ex6MCg6Mzj8aDX69Girp3CiNvx7Gc/G//4j/+In//5n1/AKgfE43FwHDfzZlJ72cugHz+OYx/6\n0FhtQiR/P+lJet5GnfQtx2IxXHHFFTh9+jROnToFwzBozng3yOGEhI89Hs+uHtKwd77T3z88CjWV\nSu3JJun3+yFJEizLopMB55n6IRKvJHdOnpNMYIvFYnSEKsW2kfnkJ9H+hV+AdsUV0HWd5t93PXQJ\nAkq3347YN7859oFzK4aNpGmatJhzq5oKgq7r0HV9x8+p3++nEq7zrHyPxWLweDwThd53a2NzXRey\nLKNSqaBUKkFRFITDYaysrCCdTu/bWFbyHWSh9sPBoTLoPM8jmUzCsixarEPUsCZlVgGY3RAEAbFY\njOYBp8bjwdrb3obIv/87Ivffv+NdDcOgAjfThOOGjfoslbmyLNO+5XQ6TcOmkUgEy8vLVJ98t9el\n2+1CVdWRHDtRG9vOQ9rOOyeGvtVqoVKpYG1tbU9HoZJogCzLOH78OE6dOkUFibrd7lyiIp1OZ5PE\nq9frpf3oXq+XatGTg0T8vvsgra6i9PrXw3Ec1Ot1+Hy+saM7zec/H/rKysyTAsn0v1qtRusrtqp/\nME0T1WoV5XIZ5XIZq6urtCaDeMDDr+Vw5fu8pIpJoaZpmmN3tGzXxkaq+NfX12nEMZlM0paz/Z4h\nTwbqsFD74WB/Py1TQCadNRoN+Hw+xGIxtNvtsUKsO+G6LgzDmGteKhQK0dx0Lpeb+gvRueEG9J78\nZBz78Ifx42c8A9jiS27bNqrVKjiOg2EYsG17Kq+TbKKkXWnSkGev10Oz2aS5+Uv/Zp/Ph2w2i3q9\njmq1img0img0uul+mqah3W4jEolsyqHGYjFomoZGozGigDbsnSuKAsMw6A8JMwuCQA2WJEl7kock\n7w0ZNUqKzLLZLDqdDlqtFu19n/ZwQQzFVq85yaMDg6JNcmBLLS0h84lPoPu0p0G59lq0NnTLJ1Fw\ng8eD0u2349Tv/z6khx+GdsUVU62fhN7PnTsHj8eDM2fOjNxOqrtJO14ymYTH44FhGNRbJzUrHMdB\nFEX6Q0bK1ut1WtsxK+QzRJQSfT4fPUyIorjl6zfcxgYMDr6KooDneQSDwZnmLCyC4UE4B2ldjO0R\n3vve9+73Gsai2+29V5YHX1hRFGFZFu0Z5jgOnU4HoihO/WX98Ic/jG9/+9t45jOfOc9lQxRFGu6b\nWn6W46CeOYPsJz4Bc3kZyuMfP3Kz67qoVqtwHAe5XA6qqsIwjKlboERRhCAI6HQ6cBxn7KEgxDiF\nw+EdRUDIBkYeo+s6/H4/zdcSA+jz+bY0UBzHwefz0VwvCVcOV5KT6nqPx0OjA/F4nNZiSJK0J96P\nYRj0vVleXh75DHAcRzd5on7nui48Hs/E+fx6vU77pbd63Xu9HoLBIDweD31vs9/9LnKf/zwe/d3f\nRSceR6vVQiKRmHjeu3b2LJbuvRe+Ugntm26a6LHDkJGlRIVQEATa4liv12EYBp0FT0baktoA0m7o\n9/vh9Xrhui40TYMsy+j3+7BtG7Iso9vtwufzgef5mWsmfD4fPbCrqkrHufZ6PZimCcdxIAjCyOea\nDNyRZRlerxexWAxLS0sIBAJ7nhvfCbKnkDQX8873B78/gHg89r5x73/oPHRCIpGgp+7l5WXYto16\nvb6rtvd23HTTTTh16tTc10kmQ3W7XQSDwakPHMq116L53Oci91d/hebznjcyBYtIlZLWp6WlJVSr\nVfR6vamjFuRxpEZhN0+91Wqh2+0iGo2ONayBbNpENKZUKtHK3a2GrriuC9M0R7xuTdPQbDZpftIw\nDCSTScTjcXoo2U+IxK4gCFheXt72AEGiFp1OB91ulxYPklTFbgcPRVGg6/q2nrUkSeA4Dpqmwev1\nDopLu11kP/EJ9K+7Dp2f+zk0ymWazpgU1+tF+bbbcPyP/gjFN70J+hTfI5KrJXl+MrKW5NVDodCu\nqmc8z0OSpJHvPzGihmHA6/WiXq/jkUceQTgchsfjgSiK8Pl81Jsf5zMzfFggvdkcxyGTyUAQBKiq\nSusAgMFnnQxJIcWqZILefn9Gt4OE2sedAcA4GBxKDx14zEsjPbfDlbJ+v3/iL0o6nV5YWImc5MkA\nj2lRrr4ay/fcA/A8+k99KoBBnrnb7dJTPjDIm5L2pVlO/j6fj3pzrutu6bm5rotms4ler4d4PD5x\n4YzX60UgEICmadTDMU0T8XgclmWh3+9Tz5/Mp3Ych+aDBUGAx+OBJEl0RrrX6114X+5ukKEePp9v\nrI2b4ziaN/Z6vfRvJ7K3l3p7BFLcJ4ritgcpjuPo60YiI8kf/hAnPv1p/PTtb0d1Q/xklkp/9Yor\nkPqHf4C30UDn2c+e+PGdTgeqqiKdTtN2R/JdTqfTCIfDU62N53navke8eJJaIy2wiqLQ15oYacuy\n4LoueJ6nBo1EBcnnHRikf6LRKD10kANFMBgEz/N0Lr2maeA4Dl6vF36/H7quj7wfBwld1+nh6iCu\n73LisvHQgc359FQqhUqlgmq1ikwmM3NI1bKsuYRlSW96tVpFv9+f2qgbKyuo5fNYvuce1G65Bb1g\nEK1WC5FIZNM1Sd9xo9HA8vLy1KfsSz31YeEVYkxI4do0f5frunRj6/V6qNVq8Pv9cByHbsaiKCIQ\nCND/HzaOoVAIq6ur6Ha7OHHixIHwJtrtNjqdDkKh0MSa7IIgIBQKIRQKwbZtqKoKRVHQbrfRarU2\nee7kALTbAA6/309D+hzH4finPoXumTP4yenTEPp9pNNpKsby4IMPwrZtJJNJPOEJTxi5TrFYRLFY\nxFM3DpQEg+exduutOPXRj6L0xjfCmEBumXi5pOak1+vRPHQikZjrQZtMGiSRnXg8Dtd1YVkW9eR1\nXYeiKHBdl/4QA0887OE+cFJ/02w2kUwm6QGBfK5JqoVU8BNt/fX1dWiahnA4TA8C+/35vXTmPONw\ncWg9dMJwPp3k0kixSSAQmNrjePTRR3H77bfj7NmzWFlZmXX5I14XOb1Pg3zNNUh/4QsQajU8dNVV\nkCRpJMdFNmxSGESqcGcZH0tyjsOeOqnaJpXi45zkSdicaGIPe979fp8KB5H8diaTQTweRyAQgM/n\n29Lz5nmejomc9+Y/KWQzJFoJpL5jWniehyiKtGDqUs9dVVVagHhpZMQ0Tayvr+NnP/sZarUaMpkM\ner0eJElC9Mc/xspHP4q/vPpq8NddR7UBAODb3/423vWud+ErX/kKut0ufumXfmnkut/5znfwpS99\nadPv//Vf/xWv+MAH8CbXxUPf+hYCr3jFyO3tdpsa0Utfs1qtRj1WkifPZrMwDAOqqiIUCs3V0Pl8\nPtq+R+puBEGAKIrw+/3U0yYHKtIex/M8PB4PNf6macK2bXAch0AgQNvjLMuiHSORSARer5cq9pEo\nDNHSIDUgJPdOXoetojF7QbvdhqZpSKfT+15hz5jcQz/0Bh0YGCsyujQcDlPtak3Tph5SwHEcHnjg\nAXz84x9HJpPBVVddNeufAJ/Ph16vB9u2J1a/IriSBIfnkfv0p1G+/nrErrxy5ItfrVahKAotDgIG\nYYYWAzkAACAASURBVPlZi8CGjTrRpjZNc6Rqe2SdG17LVsZbVVW4rkvzuZFIBJZlwe/34/Tp04hG\no1Ttjuf5HSvRyf38fj80TZvpsDQLRACHHHBm6bjYiq2Me7fbRbVaxerqKoLB4Igh+Na3voXbb78d\n9957L8rlMn75l38Z/X4fHMfhcXfdBcOy8PVbbkHu2DFapCgIAnK5HG655Ra89rWvxY033rjptT95\n8iRuuummTa+xJEk4/bjHwbUsPO/HP0bjxS+GMxSx+ad/+id8+ctfxg033DDyuIceegirq6u0cHG4\n55ocSEk6Yp4QwZ1er0fTUqRwrtls0sMrOVyQEbkkUgSAVtb3+32aLxdFEel0mr6e20Hy/aT9lmgH\nmKZJjbuiKLS9cJIRuNPCQu0Hj0kNOrfIOeHzZG2t6FYqpW1vJ9WjpF2K6GRLkkQ1rSfFsix85CMf\nwfOf/3xcffXVsyyfQtq6Lq14HhfXdVFfX8d/e/ObYZw9i/Mf/vDI7cOFWESMpVwuw3VdZDKZmY1d\nq9WiKmcnT56Ez+ejxnv4h3geAGiofPhneB2NRgOyLCOTyVAPm+TmSURjOz3vWq1GCwLL5TK8Xu9k\nbVdzgMjH2raNVCo1V+PTbrfx1a9+FcViEZIk4c1vfjOAwQGiWCyiXC7jnnvuwZ133glN0+C6LvVA\nL168iEwmQ7UA6vU6/A8+iF/4zd/ET979bvzk6U9HOp1Gq9WihXuzwvf7uO6XfxnN5z8fq+9+98jf\noWkaMhuDX0zTRL1exze+8Q3cf//9ePDBB/G6170Or3zlK0euRw6Bw5+NeWHbNsrlMkzTpHUcAKgX\nPY6Yi+M40HWdfu5Jrzs5qO5WBFutVmGa5khbq23b0DSNKiySKIAkSVScaN5DWMjsBZ7nZ0rRMeZL\nIpHE6dMnx34zjoSHDgxyj6SAi7QqiaJIRTSm8Yh5nscznvGMXfOTk0DmUyuKMlUosdVqQdF1iCdO\n4Pg996D/cz8HYyglQIrMSLuOz+dDKBSixYOTtiQNY5omnTZFwqNkShmJiBCDEgqFEI1GEY/HaS+5\nz+fb5GkQ731paWlkbSSM6fF40O12oSgKLdIjGIaBVquFWCxGIxJkKMte6Vzruo5qtQpgtgEr9Xod\nH/vYx/D0pz995PeVSgXveMc7UK1W4ff7ceONNwIArf6+4oorcPPNN9O8OwnLG4ZBQ8fkuwEAZz/8\nYYimie+84Q0Ix2K02rvT6dCD1yy4oghe15H+3OdQf8lLaDcGMZKkn5zMfs9kMrj66quRTCZxzTXX\nIJfLjVzvgQceoLUs8wy9k9SFpmlotVowDIMO0yFdE+M8Fyl0I4VwZFAKaZEzDIPWgmyF1+vdFIki\n0RgStSDfg2HvXZZl6r0LgjDz60IOXMQJYBwMLquiuEsJhUK0lYnkw0jRnCAIc5ukRfLU00AKfcrl\nMm3zGhfyZU4kEpBvvhny5z+PY3fdhZ98+tPAkPfq9XqRyWSoeEs8Hkc8Hkez2aR9z+NAjLZhGFAU\nhU6vCofDVCUrGo3S3PV2ghrbQQqJiDHaCiK2Ua/XUS6XsbS0NNLDTjZ6YFRFjlS9LxJFUWiFOZGP\nJWNrLz0Edjod/M7v/A7tSf/iF784crsoijh37tym5zh+/Djuv//+kU2WbOyxWGzEUOxWUBerVLDy\nrW/he7ffDkGSaFU8+Uy02+0RPYBpqb7ylVj+zGeQuecerL3jHQAeG5lLtA1IuoWE2LeTYb7vvvvw\n/Oc/n37exmmJ3A7XdWnBGqk6J/UHJJU0bkeI4zgwTXPkh+TOo9EoIpEINerVapV2ZQSDwZHvyPA0\ntu3C9OS7FYlE4DgO9dxVVUWv16MdP+R9nNR7Jx0mpN2TcXg5Mh46YTifHgwGR3K/8/DcVFXFW97y\nFjzpSU+aenMhG/8kbWWapqFer9OCGnActFOnkL37bugrK1Af97iR+5O8KJmNTcRKtivKI6FDRVHQ\n6/WoEZBlGbIs095oMneZbMSaptFNaRJj7jgOnTa2W0pEEAQEg0FYlkUNAs/zaLVadP41wefz0fd/\nVo/OcZxNj7csC5///OfxwAMP4Ic//CGuvfbaES14VVVx88034/Ubg06G/4avf/3reNzjHoenPvWp\neNKTnjRyu8/nwwte8IJNa+A4btN7RbT2d5oOt1XO/cq//mt463X8cz6PUCwGjuNozp1Es4DZCigB\nwPX5wCsKUoUC6i97GWSAyt4GAgEkEgmau97tQHvjjTfi+PHjAEDH5wqCgLe//e34/ve/D47jkM1m\nd/wOGYaBTqeDZrMJWZapLDM5HEqSRPcIoiRIIH3spK+82+2i3W6j3W7TQk7btuneQr7PpAYgHA7D\n5/PRwl1S/T5c4EnEp8aprSERgUu9d8uyaIcA8d5d193Ve3cchx44Ju3IYCyeyzaHPsyl+XTgMeGT\ncSuyt0PTNNx777245ZZbZjYWpVKJjs/cCaJ9vlV++My73oXgT36CH33xi3C32YhJ3p6EY30+Hy08\nG855A49tGKSq3HVdtNvtES90mE6ng3a7Tftxx4UUkE0qxdnr9agut9/vx/Hjxze9D+T9J21JmqZt\nMlKu6+KTn/wkrUy+4447Rq5j2zauv/563H///SMG1bZtvOIVr8Dx48dhGAbuuuuukfW7rotvfvOb\nuP766xeyOeq6TiMVk7QJiqUSnvDSl+L7v/Ir+NELXoBUKkWrt4khIpGYXC43c9hVaLdx3YtehEdf\n8hL8Rz4Pn89HD1+kqn03QzyM67oolUrgOA6pVAp/9md/hm984xuo1Wq47777Nn2nHcehaSfDMOih\nMBgMbvJCSVtarVajU8V4nqdqbwBG5soTfXzy/+NGNEzTpL3uwCDPHg6H6WGq1Wohm81O7SUT7514\n8Jb1/7P35mGS1dX5+Htr39eu3vcZdhz3JYBERIGviKKElgQxgnsSH5Sv+iWoUQkKLiE/CMElIO5L\nEQVccFcgEhMDJAbZhpme6bW69vXeurfqLr8/qs9nblVXVdfa3TPT7/PU00tV3Xtrufd8zjnveV+Z\nta4aqb0RT2VkZKTnfflddI92e+jHZEAHjgh70IWPRooEQUAoFOqql9wrUBm72SKDMllVVZkSlR7W\nhQWcNjeH1Xe/G2tXXrnh+ZRh5PN5JBIJNhZDs6+1ZDV975BKyjabDQMDAw0vXDR33WpQp4tXKBTq\niNtQKBRw8OBBOBwOjI2N4cEHH0Q0GkUymcTVV1/NesKZTAaDg4M455xz8OCDD26ozpx//vksi/ry\nl7+8Iejfe++9eO1rX8uCGymYCYLAuAFbjbW1NaiqipGRkbYWDOOf/jT8P/kJfvbFL6JsszGdBirL\nk3gNz/NwuVwYGxvrOKhTVWjqn/4J07/4Bf4rHIZ1ZATAke98uwsSTdNQLBYRiUTYHL7D4WB6/vQY\n4jQ89dRTOPnkk9kYGp3vtSVyvYgMUFkwaprGrhH64N2rBZqiKKx9pigKE70hT4pekBMBsBHRTCZT\nldwQRFFENBrdtu/yLjZHuwH9mOqh61HbT7dYLAgGg0widmhoqOt+UTQaZX7n//Zv/4Z9+/axPr3+\n5Kffa38Clex7aWmJBUz9YzRNY1rnAwMDVVKS9LMQDGL1ooswdNddWDzvPMh+f5VEKhFnOI6D1+ut\ncn9rtiqnBZHD4Wha2gXAWg+1Xtz10Mx0ZTNcd911uO6661AsFhEIBFi2981vfhNLS0sIBoN4xzve\nAY/HA4/Hw+a0P/GJ+hWrn/3sZ033d/HFF7PfaSyNyFOdjh12g80kXhvBlEhg4N57sf+SSzAwM4No\nNApRFOH1ejf03DmOQyqVYspnFDhbIV7V9smjV1yBPT/7GaZ/8ANE3vUuxi+gIFsLRVEgy3Ldm6Io\nbJqC+r1WqxXDw8Os3FwoFCDLMp555hn813/9F1760peyYyIyJ4EUBonASdk2x3HsvHa5XH2RZiV/\ndOqzk6ASvT6Xy9WTsTF9BYEsUOncpMWp1Wrt+YjlLrYPx2yGDhwZxQDARrYo41UUBUNDQ12VmXK5\nHGPtfvzjH0epVMLFF1/MmMgA2Mq/0U9FUZBKpdiFRX8fCeRQWa7e8wHAks3i/L/+ayy+4hX4w9vf\nvsFtSp95k/FJLBaDx+PB9PT0hgs1ZdDtKp1Rpt5oxU92oY1Gy+644w488cQTWFhYwO23384yL8In\nP/lJXHXVVczvndj78XgcTqeTOXARZFlGJBJh6mCdgiw7KXPbKga9HlRy7iSDG/yHf8DwPffgP7/7\nXdjHxhCPx6Eoyob3V78fmunXe46TYJF+QUk3IuopisICtslkwsmf/zxGf/Ur/PYb30BKliEIAnzr\n/XtFUaputE3giGSryWRiGTIZyySTSRgMBvb58zwPVVXZYw0GAyO46Uvjzz77LGRZxote9KKmi/ly\nuYxoNLqlI5BETKPv2fj4OJM27gWo5Ujcl91S+9GB3QxdB/JPX1tbQzqdRjAYhMFgwODgYJVEbKcn\nDQUtv9+PW2+9FbfddhuefPJJzM3NtbUd8msOBoMsWBCxZWhoqGEZWx/co1deiZkvfhH8VVehVCdI\nE4xGIzNciEQiWF5exvj4OHs8BWVyJ2sHPp8PmqYxe0h9UCeZWKBSzTjzzDMxsl6GJRw8eBCyLOOM\nM86oe/wf/vCHmQMUZTAej2cDC57KqyaTCX6/H8lkEna7vaOsRxRFxOPxTQ1W+g2SeK0tm26KVAoj\n99yDxQsvhH19vNFmsyGVStVldXNcxet7bW2NVWeoHA+gSg6VlP+IHEafi9FohCiKkGUZj517LsZ/\n9CO4vvpVPP6KV8BisTAfe3I8MxgMjJxHNzI0oUqTHrSIJlIlWZnSwpVMV2pd6+6//3786Ec/QigU\nwt///d9vkK8lmM1mDAwMIBaLIZVKtf+edwCSfnW5XFhYWGDmSvo+ezfw+Xxs9t/n8zHvhd1gfmzh\nmM7QCbX9dOAI0Ywu1L1SFyMGdjvQNK2qklAul7G27n4VCoVa2gYnijj9kkvAn3oq5j/72Zaes7Ky\nglgshsHBQQwNDSGXy7ETvZueWjqdRiQSQSQSwUknnYTx8XGWIQwNDeFzn/scXvWqV+FlL3tZW9tt\nRgijVgqVkvUe60TAGxkZYQGZmPDNrCF5nmdlyYGBgW1zxlJVlQnLtFtp8Nx8M2bvvhv/e999UNfl\nXWVZxsrKStPWAXEFRkdH2evWNA2KorAedDabZT1nmnfXZ++UIT/nttsQ+u1v8dPPfx6h6WkmtUrb\npFvt383ukySJ6U20qqKmaRoef/xx3H///bjyyis3rXTQdWOre8xk/uJ2uyEIAuuzezyervTeiYhL\nNrnt8jB2sfU4boVlmkGv905jLyS9SPrJtfOhnaJ2G5qm4a677sKpp57aMLvTy1xS37yVca4qmEyQ\nvV6MfOUrKOzb15I5htvthiRJLCsnk49uL16f//zn8eUvfxkLCwswm82YmZlhAjAulwtnn302xtsw\n7yCkUik2x1/7vjTzWLfZbCgUCuxzprZDqVRqOCpEY05OpxOhUGhb3dvIca3d4yjGYjjthhsQ/z//\nB3ndSBy5gGmaVvXaKWCXSiU23UAscZLuJbcxWiTRGBr14j0eD3w+H3w+HzMNSgwPY/ruu2EfGUH5\nRS+qeg1Usq/N1mkxoC+Z6xUHSfO/HVEVjuMwNDSEs846a8OCsFwu4yMf+Qj+9E//lC02LBYLOx9p\n6mMrYLFYUCgUYDabWVVIkiQmsASgI5IeWejqfS92A/rOxo4Slpmbm/s0gDMByACuCofD87r7LgTw\nXgBWAL8Jh8PX9/NY9P7p1E+nUaxYLMYy+F5/wVdWVpiudjNQD315eRler7ejqkHqNa/BwA9+gL3v\nex+W3/c+xN/0JqDJ6+G4ioezPjNvp6T88MMPo1Ao4Pzzz6/6/ytf+UqceuqpmJ2dhaIoWFpaQiAQ\n6GqhIEkSc3Vr9Blx3EaPdep5k0c8BUeO4+D3+5FOp6vIQnrJ2Va93fsJssElRbdWIcsyfN/5DkzF\nIpK6mXgingGVSgrHcVXkM33FjuM4ZuhCVqM8z7OZ5Va+L6VSCXGXC2uvfjXGvv1tpC67rOF45XYi\nHo/D6/VuCNr6UnW7I5adgkhz6XQabrebLZZEUWQjqOTm53a7W64ckRjN6OgoI4xuRTthF52DuCWt\nom9px9zc3FkApsPh8FkAPgPgU7r7TABuAnBpOBw+B8CL5+bmXtivYwGO9NNlWWY9XgDMrYzneWQy\nmZ7vd3x8HF/60pc2BKFEIsE8lQmqqjKDjY56tQYDnr3tNiTe+EZMfu5zmL32WhgKjasaqqoyVTWv\n18tY4/rjUhQFBw4cwOOPP77h+ZqmYXl5ecP/n/e85+Hcc8+tCpJWq7WrxRJJk7bSB7fb7WwsKxqN\nssqM2+1GNBoFz/PMCcvj8bC5dhLZoPu3O5gDYG55rS6GSCAoMj+PPffdh8grX4kVkwmRSARLS0tY\nXl7G2toaY4UX1r8ftnXluFAohJGREUxMTGDv3r1swoGY5CQu1IpEKI2KmkwmJN/xDpjSaQzcd193\nb0ifMDo6imuvvXbD/x977DHcfffdSKVSTK9/K0Dys7XXqlAohNHRUTgcDuRyOaysrCCRSGzgGdSC\nJgyobRMIBJhr3y52Fsj8KhqN1lWPbIa+ZejhcPi3c3Nzv1v/81QA+mipAHhlOBymyGEC0Btd1iao\n9U+nshspqqVSKRiNxp73y+oFsi996Uu4//778ZrXvAZXXnklnE4n61lSf7eT0SjNYsHShz6EwvOf\nj6kbbsApV1yB+ZtuQrHGLY7KzrIsY3JykpXciQFbLpexuLiIq6++GjzP47nPfS7uvPPOqm2cddZZ\nOOusszYcA40JGQwGzM7Oguf5ukS5VkHZ+Wbjc3qQYA8p3kmSBLfbzURmVFVFOp1mZV3iU5BwyU7Q\nKSDCGTlxAUdEUGpHuvS/F4tFTN9/P2y5HJ55wxugqiorU+uZ4JFIhJXGG8Hv9yMWi8FoNDJltVY/\ng3w+j1KphOHhYZSsVqRf/WoMf+1rSLzhDdCOEonRxcVFhMNhfOtb38L73vc+nH322VvCfKcKErkn\n6q8FVCGhMVRi+tM8ez1TmXQ6DUVR2LG7XC7mzWA2m3fE9/14hqqq7LpPnhg2m63tiZa+k+Lm5ua+\nDeB1AM4Nh8P/Uef+9wI4PxwOv7bZdrohxdUikUhAEIQNDk7US25X9KITxGIx3HPPPfj+97+P66+/\nHsPDw4xZTgzXmZmZrnq31oUFzF57LWwLC1j64AeRuPhiYD3bIk3xwcFBZDIZ3HnnnXjzm98Mu90O\nq9XK5nZ//etfY9++fTjttNM2zY5pUcTz/AaHNOq/tqsoR++VLMsdk3hIICefz8NisUCSJBiNRrjd\nbkbyisfjMBgMmJiYYKzidrXpewHqY9NnJIoi/H4/+19thkgBmqo6mqYhHYvhte9/P4r79uHQTTc1\n3Fc0GgWATS8akiS1pYgGVBYjkUiEqfUBgO3gQZz2pjdh4brrkHjjG1ve1nZDFEU89NBD2Lt3L2Py\nU6m6Hf33TlDPja0WpFFPZjBmsxlut5tJPBeLRcRiMQQCgaqZc70X/Va1E3ZxBKqqMmEnspS2Wq1w\nOp1M+2FHKsXNzc3NAvg1gD3hcFhZ/x8H4NMA9gK4LBwON60Z9TKg15tPJ5CV51ZlaYIgIBaLweFw\nMBKcLMu47rrr8Ja3vAWnn3561ePJupTGsDYLOJwoYvwzn8HgD36A305P4wvPfS7m1nuqg4ODMJvN\nEEURn/jEJ3DdddcxYxGj0ciCHD2uGSRJQiKRgKqq8Pv9dRdEnYzEEbO9W8neRCKBhYUFAGD2kxMT\nE2zmmEakOI6r+tyNRmOVWhgxqusxr7v5u/Y+InFSD1UftPU3/edPM+Tjv/oVnn/LLXjyW9/aoPGv\nB+mSj697ovcS0WiULcL025790IfgePpp/PH73weOQlcvPfPd7Xbj0ksvxS233IIxneNhL0EyxptV\nUgjUZxcEgc3qC4IAk8lUt7KgvxYODQ1t2yTH8QJSPKQgTtUzCuK1bawdM4c+Nzf3GgBnhMPhjwDI\nA7ABMKNSbgeAz6///mfhcFjt13HUQ735dEIgEGCqYN3YYbYCRVGYTrq+nGw0GvGqV70KLpcLpVKp\nqopw2WWXQZIkAJV5bn3wUVUVF1xwAe6//372xdBsNix+9KP4u1/8AjcvLODGRAJPv+IV8PzJn7DH\n2Gw23HjjjQDA1PVGRkYwPDyMeDzOAmq9BY6macjlcqzH3Sz4+3w+ZqqiaRr8fv+mC5JMJsPMKDoF\nz/NMMpR6+bIsY3FxEYIgwGw2M1Uwcq+y2WyQZRmSJG3IjPWiJzSCVTuyVSvAUqsCWHs/UHnvSTSH\nZGubZWb13itZknDyPfcg8/KXNw3mQOVzpxGwXi5eyc1scHBww0IhctVVOPXNb0bgpz9F6rVNi3I7\nEvpSNVA5H2stX+k97dbkBmjNjU0Pmmcvl8vI5/OMI9GITGowGBAKhRCNRpFIJLZMSOd4gqZpzDJb\nEARmzkNqmb2sjPQtQ5+bmzMAuA3ASQAKAG4HEADgAvDI+u0h3VNuCYfD9zbaXi8zdEK9+XTgiAMR\nCbv0oxSlaRobnapX7tKbUZAQDAA88sgj7Itx/vnnbzj5vvGNb+DSSy/dsBARRRHio4/iJZ/7HBzx\nOBavvbbuBbVWzY0EYYrF4oZ5XP3sN40rtXIxIKbuZkp03WbnNHK0uLgIg8GAPXv2wG63s8+9VCrB\n6XSy4+Y4jtmN+ta9wun/lDXTDDYJntD5Q2Im+lsr2Q5Jk+ZyOciyzFTONE3D8PBwy4GWdLlP/MMf\ncPr11+PpL38Z/L59mz5veXkZTqezZ9bCiqJgdXW1qTrfnve/H7aFBTxx993AUZgR6kvV9SSk//jH\nP+I973kPzjrrLJx33nk455xzutofvadkstIOiGi7GYFRFEXEYjF2Tu6iO5CML6l9KorCdBPqGQQ1\nwo4sufcC/QjoQON+uqIoiEaj7MLa61JUrRRjPVBAq+19tQvqIVutVgw5nZj+9KcR/MlPkHj967H4\nwQ9uGCOq7bnRTHIul2MnPI29AKhSZ2sVFFSpH1kvqJNEbye9c0mSkEwmkc1mwXEcpqenqzImcpir\nt1CgsbXN2i6klEbboiBPqmoU5PXz03qjFwrkiqLA6XTC4/FA0zTs378fZrMZJ554YkulcBIMMRoM\nOOeaayB7vXj2C19o6X1KJpOQJGlDltkpWnFSc/zxjzjlrW/F/A03IH3BBT3Z71aDStX1rg+xWAz3\n3nsvHnzwQZx44on42Mc+1vX+euHGthlood3t9eZ4hj6Iy7LMXP6oOtgudgN6m2jWTyc1OYPBsOG+\nbtCOAhUpdulVztrdFxlisLK+piF4332Y/MxnIE5NYf6mmyBNTVU9r57WMx13uVxmX9RgMNjxYoeU\n2KqObR2UcbabndMoXj6fh8FgQKlUwsDAQFtEvM2qJ5s9l1y89De9DSeJt9BEhV6Cs1AoIBqNguM4\nOJ3OlkqgVEE5ZX4eJ/3f/4v9t9+O/Ete0tLx8jyPRCLRlbsaoRX3QMLev/kbWGIxPPmd7wDbKNrT\nDZrZGusfU/u+3nvvvXA6nXj1q1/d8r660fJvB60uZndxBOVymQVxujYSx6nbcd12A/rReSb1EI3m\n0wEwIgn11Hux+JEkiZWbWyG5UDm49thaQT6fr++YxnFIXnwxnr7rLhhEEadccQX8P//5hv2aTCYk\nEgn2uikz4HkeiqLA5/N1VbkgQ5Visbjh/aWefDu9c0EQsLq6yka9KCi2OyrHcVwVMbCd2WOO49i8\nvN/vx9DQECYmJlgFqFgsgud5aJoGo9GIYrGItbU1RKNRpNNp5kQ3OjoKSZI2/d4JggCe5+H3+TD2\n1a+icPrpyL/4xS0fL1UtyIGvU5DJUKua+Wtvexvs8/PwPfBAV/vdTphMJgwMDLBzutFjasHzfN2y\n9vLyMkRRrLsdGmOjXmy/QC52iUQC5XK5b/vZblB1TRAEZLNZJBIJ1mZtBURajUQiWF1dZRM0g4OD\nGBsbQzAY7Eqmt1Mc9xk6oVE/HTjSX6qXSbYDWtHTjHSr26Fja1aerwX5gdPYUKN9GQoFTN1wAwK/\n/CVil16K5fe/n80IS5KEaDTKXJ9obtvn8yGTyUBRlIZkuXZAAd1qtSIUCqFUKiEajbZsU0rBRBAE\n2O12BAIB5HK5rt2kSFOfTtROPndZlpHP55lYj9vtZu+nPpOnkj353pvNZva+UO+0dv/Ed7BarZhZ\nWMBJ7343Dtx8M7Jnn93WMdIMfqu+AfXQSSXpxHe+E0aex1Pf+EZTRcOdjl5pvl9xxRU4cOAATjvt\nNHz0ox/FVE3VDGhtjK1bULsROPqZ7zTuSdwX+l2vimgwGFh7rFmSQkqJZGNMEzFOp7Pu7H8vsFty\n7wKN+unAkXKi2+3uiDRCtq10wW73JGk0BlQL+sKRTWVLpWZNQygcxvg//iOKJ5yA+ZtuQml9DCeV\nSiESiTAlMb/fz2xoG5HlOgG5mpnNZja6tVnvnAhl5MPu9/vhdDoZB6AXx0VBtV2yEK3gC4UCOI6D\n2+1uSaZT07Sq10wlcZfLtYEQRW2BkZERnPze98KUSuGpb32r7RJ2NptFLperct1rB43mnDeD+/e/\nx4l/9Vc48I//iOzLX972fncSiBPj9Xo7bs0dPnwYTz75JJ566im85z3v2bCYffjhh/H85z+fjTPq\nKyHNPjeDwQCHw9HWZ9uLxexWodY0SB+49dW1et4A9L9GIKEmnueZZDRJITscjr57POyYsbWjEfX0\n3glkQkFqcu32ZKn33CnBLhAIIBKJIJPJwOv1QlEUxmDV/x6PxyEIAiYnJ1s/Ro5D/E1vAn/66Zi9\n9lqccvnlOPzxjyP6spex8rDBYGDBHDgy7kJKbOVyuS3v9FrYbDYMDg5iZWUFhUIBs7OzTbdVywKL\nOgAAIABJREFULpcZocvlcrGVtaqqSCaTTDWrW9jtdvj9fqRSKSbY0QzkQkZzwF6vF263u+UTv/Y1\nO51O9v2hzwCotFOKxSJCoRDcTz0Fz+9/j/lPfrKjfrTNZkMmk+lo1EovKdquGFP+xS9GYd8+jNxx\nB7JnnXVUZ+k+n4/p7nezjTPOOANnnHHGBtvYcrmMH//4xzjllFNYBk3tuMXFxabVO2rvOJ1OuFyu\nlipWZCEbj8eZO9t2Q1XVqmxbH7wpMaWWl9lsZoY6FLhbPQdJ8IWCOKm2BQIBJviyU7GbodeAhBz0\nalB6kDhKO9kIPae2hEwry9qgXPs3/V4oFCAIQpUUKIEc5IBKqdxisXS0eDDmcpj+2Mfg+7d/w7MX\nXYQDb3873IEA4vF4w/eEiHdkdtPNF355eRmZTAaBQKBuuY9G0XK53LqSUqDqQkZVg05JhI1AZKHB\nwcG6Qa9UKjEJTiK7uVyunq3gieXs8/ngcDgQiUTY57HnmmtgO3y44zEwTdOwsrLCFkbtIJ1OI5/P\nd9za8Pz2tzjhfe/D/ttuQ75NO93jDaRJoR9jK5VKuOiiiwAA09PT+Nd//deq58iyjEwmA6PRiEKh\nAFVV2eKrlax9O5jv+rK4Pmjr+9u1gk90a8d9Tw8SfOF5vkq1jcbMtiuI9zRDn5ubOw/ALID7wuFw\n/6NpE1itNoRCgyiVJPA83zJ5oV000nsn+Hy+Kt13CtCNgjHP80ilUnA4HMjn88hms+wx9RZT9awk\nLRYLU31KJpOM6UpBXC9aAhzp1cdisbZd2ySHAw9/6EOYmJ3F6V//OkYOH8b8jTdCXs9SHQ7HhkyA\nlMwSiQTW1tYQCoU6Gq0RRRGKomBiYoKZEwwODrLATKNosizD7XZvmHsnglgwGOxpMAcqZCFy3dJr\nE+htLU0mE7MS7XWJkkba0uk0+276/X7YDhyA76GHcPijH+14ppvKiMVisa2ATq/d5/N1zFPInXkm\n+FNOwcidd+4G9E1A55TejS0UCuE73/kOnn322bqEusOHD+Nv//Zvcffdd8Pn8zFTnsXFRezfvx9e\nrxejo6M4sYEIkdvtZkI6JpOpZ8x3IqXVZtyyLFdNhFDAJgEWCuK9CLAk+EJBnFTbvF4vnE5nz68h\nW4GGGfrc3NzfA/hLAH8A8HIAV4fD4a9u4bFVIR7Pa0ClKsdxgKoqUJQ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P1TbqwRcKBUiS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\nBrokSTnw/4GRbjNH+aGEAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x106facb10>"
       ]
      }
     ],
     "prompt_number": 19,
     "trusted": true
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "**Strikeout Rate**"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plot_comps('Krate', V=0.1, diff_degree=5, amp=2, scale=5)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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VIgDa6HQpYMPQ/aWCRqOG41gEgwqO4xCLxVal3DfL4K9mPMVikUwmw+7de+e9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\nRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x1081c7c90>"
       ]
      }
     ],
     "prompt_number": 20,
     "trusted": true
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "**Walk Rate**"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plot_comps('BBrate', V=0.05, diff_degree=7, amp=5, scale=5)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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/AMICwMK6EwCmCdeRIwg++CCCDz8M33/+JyTDQGnPHpHAVzz77GU3S+lZ3L9T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\ngIiIyBxSACAiIjKHFACIiIjMof8PwA2QFhULO0cAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x1085f2fd0>"
       ]
      }
     ],
     "prompt_number": 21,
     "trusted": true
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "**Strikeout/Walk ratio**"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plot_comps('KtoBB', V=100, diff_degree=1.5, amp=7, scale=5)\n",
      "plt.ylim(0,10);"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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VALcBvBqDAP5NAFuzHBQh19XtdtBs1lEslpHPFxY9nKXH8z34/YGRqxU7O3u4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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10817c490>"
       ]
      }
     ],
     "prompt_number": 22,
     "trusted": true
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "**Home Run Rate**"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plot_comps('HRrate', V=0.01, diff_degree=15, amp=10, scale=5)\n",
      "plt.ylim(0, 0.1)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 23,
       "text": [
        "(0, 0.1)"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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ikQg8z+O/24VCAaFQCLOzs3v++zQuXNcFALo46wIF+h6xfdJ6vQ7XdTExMYF0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\npVD7M1zozgAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x1085e0a90>"
       ]
      }
     ],
     "prompt_number": 23,
     "trusted": true
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "**WHIP**"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plot_comps('WHIP', V=2, diff_degree=7, amp=5, scale=5)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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qyo7jIBAIIBaL0XqLrXC5XAgGgzTnvFbgZVkGsHOBN02Tbj5b00TkbyE1Ai6X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       "text": [
        "<matplotlib.figure.Figure at 0x1097c8c90>"
       ]
      }
     ],
     "prompt_number": 24,
     "trusted": true
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Value Analysis"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "jimenez_val = pd.read_csv(\"./jimenez_value.csv\")"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 25,
     "trusted": true
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "jimenez_val"
     ],
     "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>Year</th>\n",
        "      <th>Age</th>\n",
        "      <th>Tm</th>\n",
        "      <th>Lg</th>\n",
        "      <th>IP</th>\n",
        "      <th>G</th>\n",
        "      <th>GS</th>\n",
        "      <th>R</th>\n",
        "      <th>RA9</th>\n",
        "      <th>RA9opp</th>\n",
        "      <th>RA9def</th>\n",
        "      <th>RA9role</th>\n",
        "      <th>PPFp</th>\n",
        "      <th>RA9avg</th>\n",
        "      <th>RAA</th>\n",
        "      <th>WAA</th>\n",
        "      <th>gmLI</th>\n",
        "      <th>WAAadj</th>\n",
        "      <th>WAR</th>\n",
        "      <th>RAR</th>\n",
        "      <th></th>\n",
        "    </tr>\n",
        "  </thead>\n",
        "  <tbody>\n",
        "    <tr>\n",
        "      <th>0</th>\n",
        "      <td> 2006</td>\n",
        "      <td> 22</td>\n",
        "      <td> COL</td>\n",
        "      <td> NL</td>\n",
        "      <td>   7.2</td>\n",
        "      <td>  2</td>\n",
        "      <td>  1</td>\n",
        "      <td>   4</td>\n",
        "      <td> 4.70</td>\n",
        "      <td> 4.46</td>\n",
        "      <td> 0.10</td>\n",
        "      <td> 0.11</td>\n",
        "      <td> 108.0</td>\n",
        "      <td> 4.83</td>\n",
        "      <td>  0</td>\n",
        "      <td> 0.0</td>\n",
        "      <td>  0</td>\n",
        "      <td>-0.0</td>\n",
        "      <td> 0.1</td>\n",
        "      <td>  1</td>\n",
        "      <td>...</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1</th>\n",
        "      <td> 2007</td>\n",
        "      <td> 23</td>\n",
        "      <td> COL</td>\n",
        "      <td> NL</td>\n",
        "      <td>  82.0</td>\n",
        "      <td> 15</td>\n",
        "      <td> 15</td>\n",
        "      <td>  46</td>\n",
        "      <td> 5.05</td>\n",
        "      <td> 4.64</td>\n",
        "      <td> 0.08</td>\n",
        "      <td> 0.19</td>\n",
        "      <td> 108.8</td>\n",
        "      <td> 5.17</td>\n",
        "      <td>  1</td>\n",
        "      <td> 0.2</td>\n",
        "      <td>NaN</td>\n",
        "      <td>-0.1</td>\n",
        "      <td> 0.8</td>\n",
        "      <td>  8</td>\n",
        "      <td>...</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>2</th>\n",
        "      <td> 2008</td>\n",
        "      <td> 24</td>\n",
        "      <td> COL</td>\n",
        "      <td> NL</td>\n",
        "      <td> 198.2</td>\n",
        "      <td> 34</td>\n",
        "      <td> 34</td>\n",
        "      <td>  97</td>\n",
        "      <td> 4.39</td>\n",
        "      <td> 4.54</td>\n",
        "      <td>-0.18</td>\n",
        "      <td> 0.18</td>\n",
        "      <td> 107.9</td>\n",
        "      <td> 5.29</td>\n",
        "      <td> 21</td>\n",
        "      <td> 2.2</td>\n",
        "      <td>NaN</td>\n",
        "      <td>-0.1</td>\n",
        "      <td> 3.8</td>\n",
        "      <td> 37</td>\n",
        "      <td>...</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>3</th>\n",
        "      <td> 2009</td>\n",
        "      <td> 25</td>\n",
        "      <td> COL</td>\n",
        "      <td> NL</td>\n",
        "      <td> 218.0</td>\n",
        "      <td> 33</td>\n",
        "      <td> 33</td>\n",
        "      <td>  87</td>\n",
        "      <td> 3.59</td>\n",
        "      <td> 4.41</td>\n",
        "      <td> 0.04</td>\n",
        "      <td> 0.17</td>\n",
        "      <td> 110.6</td>\n",
        "      <td> 5.03</td>\n",
        "      <td> 34</td>\n",
        "      <td> 3.9</td>\n",
        "      <td>NaN</td>\n",
        "      <td>-0.2</td>\n",
        "      <td> 5.6</td>\n",
        "      <td> 53</td>\n",
        "      <td>...</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>4</th>\n",
        "      <td> 2010</td>\n",
        "      <td> 26</td>\n",
        "      <td> COL</td>\n",
        "      <td> NL</td>\n",
        "      <td> 221.2</td>\n",
        "      <td> 33</td>\n",
        "      <td> 33</td>\n",
        "      <td>  73</td>\n",
        "      <td> 2.96</td>\n",
        "      <td> 4.44</td>\n",
        "      <td> 0.16</td>\n",
        "      <td> 0.17</td>\n",
        "      <td> 112.5</td>\n",
        "      <td> 5.00</td>\n",
        "      <td> 49</td>\n",
        "      <td> 5.8</td>\n",
        "      <td>NaN</td>\n",
        "      <td>-0.2</td>\n",
        "      <td> 7.5</td>\n",
        "      <td> 69</td>\n",
        "      <td>...</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>5</th>\n",
        "      <td> 2011</td>\n",
        "      <td> 27</td>\n",
        "      <td> COL</td>\n",
        "      <td> NL</td>\n",
        "      <td> 123.0</td>\n",
        "      <td> 21</td>\n",
        "      <td> 21</td>\n",
        "      <td>  68</td>\n",
        "      <td> 4.98</td>\n",
        "      <td> 4.19</td>\n",
        "      <td> 0.12</td>\n",
        "      <td> 0.16</td>\n",
        "      <td> 117.5</td>\n",
        "      <td> 4.97</td>\n",
        "      <td> -1</td>\n",
        "      <td>-0.1</td>\n",
        "      <td>NaN</td>\n",
        "      <td>-0.1</td>\n",
        "      <td> 0.9</td>\n",
        "      <td> 10</td>\n",
        "      <td>...</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>6</th>\n",
        "      <td> 2011</td>\n",
        "      <td> 27</td>\n",
        "      <td> CLE</td>\n",
        "      <td> AL</td>\n",
        "      <td>  65.1</td>\n",
        "      <td> 11</td>\n",
        "      <td> 11</td>\n",
        "      <td>  43</td>\n",
        "      <td> 5.92</td>\n",
        "      <td> 4.49</td>\n",
        "      <td>-0.10</td>\n",
        "      <td> 0.16</td>\n",
        "      <td>  99.5</td>\n",
        "      <td> 4.73</td>\n",
        "      <td> -9</td>\n",
        "      <td>-0.9</td>\n",
        "      <td>NaN</td>\n",
        "      <td>-0.0</td>\n",
        "      <td>-0.2</td>\n",
        "      <td> -2</td>\n",
        "      <td>...</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>7</th>\n",
        "      <td> 2012</td>\n",
        "      <td> 28</td>\n",
        "      <td> CLE</td>\n",
        "      <td> AL</td>\n",
        "      <td> 176.2</td>\n",
        "      <td> 31</td>\n",
        "      <td> 31</td>\n",
        "      <td> 116</td>\n",
        "      <td> 5.91</td>\n",
        "      <td> 4.48</td>\n",
        "      <td>-0.24</td>\n",
        "      <td> 0.17</td>\n",
        "      <td>  96.5</td>\n",
        "      <td> 4.72</td>\n",
        "      <td>-24</td>\n",
        "      <td>-2.3</td>\n",
        "      <td>NaN</td>\n",
        "      <td>-0.1</td>\n",
        "      <td>-0.6</td>\n",
        "      <td> -5</td>\n",
        "      <td>...</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>8</th>\n",
        "      <td> 2013</td>\n",
        "      <td> 29</td>\n",
        "      <td> CLE</td>\n",
        "      <td> AL</td>\n",
        "      <td> 182.2</td>\n",
        "      <td> 32</td>\n",
        "      <td> 32</td>\n",
        "      <td>  75</td>\n",
        "      <td> 3.70</td>\n",
        "      <td> 4.12</td>\n",
        "      <td>-0.20</td>\n",
        "      <td> 0.16</td>\n",
        "      <td>  96.4</td>\n",
        "      <td> 4.32</td>\n",
        "      <td> 10</td>\n",
        "      <td> 1.1</td>\n",
        "      <td>NaN</td>\n",
        "      <td>-0.1</td>\n",
        "      <td> 2.7</td>\n",
        "      <td> 30</td>\n",
        "      <td>...</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
        "</table>\n",
        "<p>9 rows \u00d7 24 columns</p>\n",
        "</div>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 26,
       "text": [
        "   Year  Age   Tm  Lg     IP   G  GS    R   RA9  RA9opp  RA9def  RA9role  \\\n",
        "0  2006   22  COL  NL    7.2   2   1    4  4.70    4.46    0.10     0.11   \n",
        "1  2007   23  COL  NL   82.0  15  15   46  5.05    4.64    0.08     0.19   \n",
        "2  2008   24  COL  NL  198.2  34  34   97  4.39    4.54   -0.18     0.18   \n",
        "3  2009   25  COL  NL  218.0  33  33   87  3.59    4.41    0.04     0.17   \n",
        "4  2010   26  COL  NL  221.2  33  33   73  2.96    4.44    0.16     0.17   \n",
        "5  2011   27  COL  NL  123.0  21  21   68  4.98    4.19    0.12     0.16   \n",
        "6  2011   27  CLE  AL   65.1  11  11   43  5.92    4.49   -0.10     0.16   \n",
        "7  2012   28  CLE  AL  176.2  31  31  116  5.91    4.48   -0.24     0.17   \n",
        "8  2013   29  CLE  AL  182.2  32  32   75  3.70    4.12   -0.20     0.16   \n",
        "\n",
        "    PPFp  RA9avg  RAA  WAA  gmLI  WAAadj  WAR  RAR      \n",
        "0  108.0    4.83    0  0.0     0    -0.0  0.1    1 ...  \n",
        "1  108.8    5.17    1  0.2   NaN    -0.1  0.8    8 ...  \n",
        "2  107.9    5.29   21  2.2   NaN    -0.1  3.8   37 ...  \n",
        "3  110.6    5.03   34  3.9   NaN    -0.2  5.6   53 ...  \n",
        "4  112.5    5.00   49  5.8   NaN    -0.2  7.5   69 ...  \n",
        "5  117.5    4.97   -1 -0.1   NaN    -0.1  0.9   10 ...  \n",
        "6   99.5    4.73   -9 -0.9   NaN    -0.0 -0.2   -2 ...  \n",
        "7   96.5    4.72  -24 -2.3   NaN    -0.1 -0.6   -5 ...  \n",
        "8   96.4    4.32   10  1.1   NaN    -0.1  2.7   30 ...  \n",
        "\n",
        "[9 rows x 24 columns]"
       ]
      }
     ],
     "prompt_number": 26,
     "trusted": true
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "jimenez_val.columns"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 27,
       "text": [
        "Index([u'Year', u'Age', u'Tm', u'Lg', u'IP', u'G', u'GS', u'R', u'RA9', u'RA9opp', u'RA9def', u'RA9role', u'PPFp', u'RA9avg', u'RAA', u'WAA', u'gmLI', u'WAAadj', u'WAR', u'RAR', u'waaWL%', u'162WL%', u'Salary', u'Awards'], dtype='object')"
       ]
      }
     ],
     "prompt_number": 27,
     "trusted": true
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "PITCHf/x"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import pymysql\n",
      "\n",
      "con = pymysql.connect(host='127.0.0.1', port=3306, user='root', passwd='', db='pitchfx')\n",
      "cur = con.cursor()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 28,
     "trusted": true
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Query fastballs from database"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "query = \"\"\"\n",
      "SELECT p.`end_speed`, g.`date` FROM `games` g JOIN `atbats` ab USING(`game_id`) \n",
      "JOIN `pitches` p USING(`ab_id`)\n",
      "WHERE ab.`pitcher`=434622 AND p.`end_speed` > 0 AND p.`pitch_type`='FA'\n",
      "\"\"\"\n",
      "\n",
      "cur.execute(query)\n",
      "result = cur.fetchall()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 29,
     "trusted": true
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "pitches = pd.DataFrame(np.transpose(result).T, columns=['velocity', 'date'])\n",
      "pitches.velocity = pitches.velocity.astype('float')\n",
      "pitches.date = pd.to_datetime(pitches.date)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 30,
     "trusted": true
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Create time series of boxplots of fastball speed"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import matplotlib.ticker as mticker\n",
      "\n",
      "plt.figure(figsize=(16,5))\n",
      "sb.set(style=\"nogrid\")\n",
      "ax = sb.boxplot(pitches.velocity, groupby=pitches.date)\n",
      "ax.set(ylim=(75, 95), \n",
      "       xticks=ax.get_xticks()[::12],\n",
      "       xticklabels=pitches.date.map(pd.Timestamp.date).unique()[::12])\n",
      "sb.despine()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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6oHQrn56BXq1aXr2OjdQFqz39/bpp+7bAYwPH/elerQtKp3v19Pdr1TIWBuJs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\nYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x1081bd290>"
       ]
      }
     ],
     "prompt_number": 31,
     "trusted": true
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Summarized data\n",
      "\n",
      "Import summarized PITCH f/x data"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "pitchfx = pd.read_csv('jimenez_pitchfx.txt', sep='\\t')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 32,
     "trusted": true
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "pitchfx.tail()"
     ],
     "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>Season</th>\n",
        "      <th>Pitch</th>\n",
        "      <th>Pitches</th>\n",
        "      <th>AB</th>\n",
        "      <th>PA</th>\n",
        "      <th>H</th>\n",
        "      <th>1B</th>\n",
        "      <th>2B</th>\n",
        "      <th>3B</th>\n",
        "      <th>HR</th>\n",
        "      <th>BB</th>\n",
        "      <th>IBB</th>\n",
        "      <th>SO</th>\n",
        "      <th>HBP</th>\n",
        "      <th>SF</th>\n",
        "      <th>SH</th>\n",
        "      <th>GDP</th>\n",
        "      <th>AVG</th>\n",
        "      <th>min-Vel</th>\n",
        "      <th>max-Vel</th>\n",
        "      <th></th>\n",
        "    </tr>\n",
        "  </thead>\n",
        "  <tbody>\n",
        "    <tr>\n",
        "      <th>37</th>\n",
        "      <td> 2013</td>\n",
        "      <td> CH</td>\n",
        "      <td> 596</td>\n",
        "      <td> 153</td>\n",
        "      <td> 164</td>\n",
        "      <td> 32</td>\n",
        "      <td> 23</td>\n",
        "      <td> 4</td>\n",
        "      <td> 0</td>\n",
        "      <td> 5</td>\n",
        "      <td> 10</td>\n",
        "      <td> 0</td>\n",
        "      <td> 39</td>\n",
        "      <td> 0</td>\n",
        "      <td> 0</td>\n",
        "      <td> 1</td>\n",
        "      <td> 2</td>\n",
        "      <td> 0.209</td>\n",
        "      <td> 75.7</td>\n",
        "      <td> 89.0</td>\n",
        "      <td>...</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>38</th>\n",
        "      <td> 2013</td>\n",
        "      <td> FT</td>\n",
        "      <td> 480</td>\n",
        "      <td>  94</td>\n",
        "      <td> 119</td>\n",
        "      <td> 29</td>\n",
        "      <td> 21</td>\n",
        "      <td> 6</td>\n",
        "      <td> 0</td>\n",
        "      <td> 2</td>\n",
        "      <td> 23</td>\n",
        "      <td> 0</td>\n",
        "      <td> 15</td>\n",
        "      <td> 1</td>\n",
        "      <td> 1</td>\n",
        "      <td> 0</td>\n",
        "      <td> 3</td>\n",
        "      <td> 0.309</td>\n",
        "      <td> 86.2</td>\n",
        "      <td> 95.9</td>\n",
        "      <td>...</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>39</th>\n",
        "      <td> 2013</td>\n",
        "      <td> FS</td>\n",
        "      <td> 125</td>\n",
        "      <td>  25</td>\n",
        "      <td>  28</td>\n",
        "      <td>  8</td>\n",
        "      <td>  6</td>\n",
        "      <td> 2</td>\n",
        "      <td> 0</td>\n",
        "      <td> 0</td>\n",
        "      <td>  1</td>\n",
        "      <td> 0</td>\n",
        "      <td>  8</td>\n",
        "      <td> 0</td>\n",
        "      <td> 2</td>\n",
        "      <td> 0</td>\n",
        "      <td> 0</td>\n",
        "      <td> 0.320</td>\n",
        "      <td> 79.4</td>\n",
        "      <td> 87.4</td>\n",
        "      <td>...</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>40</th>\n",
        "      <td> 2013</td>\n",
        "      <td> CU</td>\n",
        "      <td> 118</td>\n",
        "      <td>  29</td>\n",
        "      <td>  32</td>\n",
        "      <td>  5</td>\n",
        "      <td>  4</td>\n",
        "      <td> 1</td>\n",
        "      <td> 0</td>\n",
        "      <td> 0</td>\n",
        "      <td>  2</td>\n",
        "      <td> 0</td>\n",
        "      <td> 10</td>\n",
        "      <td> 0</td>\n",
        "      <td> 1</td>\n",
        "      <td> 0</td>\n",
        "      <td> 1</td>\n",
        "      <td> 0.172</td>\n",
        "      <td> 70.7</td>\n",
        "      <td> 84.8</td>\n",
        "      <td>...</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>41</th>\n",
        "      <td> 2013</td>\n",
        "      <td> FC</td>\n",
        "      <td>  59</td>\n",
        "      <td>  15</td>\n",
        "      <td>  19</td>\n",
        "      <td>  4</td>\n",
        "      <td>  4</td>\n",
        "      <td> 0</td>\n",
        "      <td> 0</td>\n",
        "      <td> 0</td>\n",
        "      <td>  2</td>\n",
        "      <td> 0</td>\n",
        "      <td>  3</td>\n",
        "      <td> 0</td>\n",
        "      <td> 2</td>\n",
        "      <td> 0</td>\n",
        "      <td> 0</td>\n",
        "      <td> 0.267</td>\n",
        "      <td> 86.5</td>\n",
        "      <td> 93.8</td>\n",
        "      <td>...</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
        "</table>\n",
        "<p>5 rows \u00d7 21 columns</p>\n",
        "</div>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 33,
       "text": [
        "    Season Pitch  Pitches   AB   PA   H  1B  2B  3B  HR  BB  IBB  SO  HBP  SF  \\\n",
        "37    2013    CH      596  153  164  32  23   4   0   5  10    0  39    0   0   \n",
        "38    2013    FT      480   94  119  29  21   6   0   2  23    0  15    1   1   \n",
        "39    2013    FS      125   25   28   8   6   2   0   0   1    0   8    0   2   \n",
        "40    2013    CU      118   29   32   5   4   1   0   0   2    0  10    0   1   \n",
        "41    2013    FC       59   15   19   4   4   0   0   0   2    0   3    0   2   \n",
        "\n",
        "    SH  GDP    AVG  min-Vel  max-Vel      \n",
        "37   1    2  0.209     75.7     89.0 ...  \n",
        "38   0    3  0.309     86.2     95.9 ...  \n",
        "39   0    0  0.320     79.4     87.4 ...  \n",
        "40   0    1  0.172     70.7     84.8 ...  \n",
        "41   0    0  0.267     86.5     93.8 ...  \n",
        "\n",
        "[5 rows x 21 columns]"
       ]
      }
     ],
     "prompt_number": 33,
     "trusted": true
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Weighted On-base Average (wOBA)"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Group pitches by year\n",
      "all_pitches = pitchfx.groupby('Season').sum()\n",
      "constants = constants.ix[all_pitches.index]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 34,
     "trusted": true
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#wOBA = (c1\u00d7uBB + c2\u00d7HBP + c3\u00d71B + c4\u00d72B + c5\u00d73B + c6\u00d7HR) / (AB + BB \u2013 IBB + SF + HBP)\n",
      "wOBA = constants.wBB*all_pitches.BB + constants.wHBP*all_pitches.HBP + constants.w1B*all_pitches['1B']\n",
      "wOBA += constants.w2B*all_pitches['2B'] + constants.w3B*all_pitches['3B'] + constants.wHR*all_pitches.HR\n",
      "wOBA /= all_pitches.AB + all_pitches.BB - all_pitches.IBB + all_pitches.SF + all_pitches.HBP\n",
      "ax = wOBA.plot(grid=False)\n",
      "ax.set(xticklabels=wOBA.index.values.astype(str), \n",
      "       yticklabels=[str.format('{0:.3f}', val) for val in ax.get_yticks()],\n",
      "       ylabel='wOBA', xlabel='Season');"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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UCkRE/MCcFXv503/WMqJfLA9/fyhhob7c2qZpi27XglH9Y5n9+W6qqmucjtOoqBSIiDRh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\nSUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x1093d4290>"
       ]
      }
     ],
     "prompt_number": 35,
     "trusted": true
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Range of fastball velocity"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fastballs = pitchfx[pitchfx.Pitch=='FA']\n",
      "velocity = fastballs[['min-Vel','max-Vel', 'Vel']].values.T\n",
      "#plt.plot(fastballs.Season.values, fastballs.Vel, 'bo')\n",
      "yerr = np.abs(fastballs[['min-Vel','max-Vel']].values.T - fastballs.Vel.values)\n",
      "plt.errorbar(x=range(7), y=fastballs.Vel.values, yerr=yerr)\n",
      "plt.gca().set(xticks=range(7), \n",
      "              xticklabels=fastballs.Season.values.astype(str),\n",
      "              xlim=(-0.5, 6.5),\n",
      "              ylabel='Velocity',\n",
      "              xlabel='Season');"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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SJGWYQS5JUoYZ5JIkZZhBLklShhnkkiRlmEEuSVKGGeSSJGWYQS5JUoYZ5JIk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\n5JIkZdj/Bz0TvrlBgb2FAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x1093cc390>"
       ]
      }
     ],
     "prompt_number": 36,
     "trusted": true
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Pitch selection"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "pitch_crosstab = pd.crosstab(rows=pitchfx.Season, cols=pitchfx.Pitch, \n",
      "            values=pitchfx.Pitches, aggfunc=sum)\n",
      "pitch_crosstab.div(pitch_crosstab.sum(axis=1), axis=0).plot(kind='bar', stacked=True, grid=False)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 37,
       "text": [
        "<matplotlib.axes._subplots.AxesSubplot at 0x108601510>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x109823ed0>"
       ]
      }
     ],
     "prompt_number": 37,
     "trusted": true
    }
   ],
   "metadata": {}
  }
 ]
}