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<?xml version="1.0" encoding="utf-8"?>
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<meta name="author" content="Kenny Shirley" />
<title>Visualizing and Modeling Baseball Hall of Fame Voting</title>
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<div class="slide titlepage">
<h1 class="title">Visualizing and Modeling Baseball Hall of Fame Voting</h1>
<p class="author">
Kenny Shirley
</p>
<p class="date">NYC Sports Analytics Meetup, August 19, 2014</p>
</div>
<div id="welcome-to-att-labs-at-33-thomas-street-in-nyc" class="slide section level1">
<h1>Welcome to AT&T Labs at 33 Thomas Street in NYC!</h1>
<p><img src='figures/33thomas.jpg' height=500></p>
<p>Built for machines; safe, secure, and habitable by humans.</p>
</div>
<div id="about-me" class="slide section level1">
<h1>About Me</h1>
<ul>
<li>Long-time (~ 10 years) sports statistics researcher/hobbyist</li>
<li>Undergrad thesis on the Markov model for baseball</li>
<li>In statistics grad school, co-authored "Bayesball", a relatively early (Bayesian) model for fielding that used location information about all batted balls.
<ul>
<li>Our method was called SAFE = Spatial Aggregate Fielding Evaluation (Annals of Applied Statistics, 2009)</li>
</ul></li>
<li>I've also dabbled with some basketball and football statistics...</li>
</ul>
</div>
<div id="todays-outline" class="slide section level1">
<h1>Today's Outline</h1>
<ol class='incremental'>
<li>
Introduction: Baseball Hall of Fame voting is awful
</li>
<li>
But... if you can't beat 'em, join 'em
</li>
<li>
Part 1: Visualize the data
</li>
<li>
Part 2: Model the outcome
</li>
</ol>
<p><img src='figures/halloffamebuilding.jpg' width=700></p>
</div>
<div id="collaborators" class="slide section level1">
<h1>Collaborators</h1>
<p>Joint work with:</p>
<p>Carlos Scheidegger (University of Arizona)</p>
<p>
<img src='figures/cscheid.jpg' width='100'>
</p>
<p>and</p>
<p>Carson Sievert (Iowa State University)</p>
<p><img src='figures/sievert.png' width='100'></p>
</div>
<div id="introduction-baseball-hall-of-fame-voting-is-awful" class="slide section level1">
<h1>Introduction: Baseball Hall of Fame Voting is Awful</h1>
</div>
<div id="first-the-rules" class="slide section level1">
<h1>First, the rules:</h1>
<ol class='incremental'>
<li>
A player can appear on the ballot after having played for at least 10 years and having been retired for at least 5 years.
</li>
<li>
A committee chooses who appears on the ballot, and they are... "generous"
</li>
</ol>
</div>
<div id="jeff-cirillo" class="slide section level1">
<h1>Jeff Cirillo</h1>
<p><img src='figures/cirillo.jpg'></p>
<p>Jeff Cirillo, 3B, 1994 - 2007: .296 BA, 112 HR, 32 WAR, 2 All-Star Teams, 2013 HOF ballot</p>
</div>
<div id="jeromy-burnitz" class="slide section level1">
<h1>Jeromy Burnitz</h1>
<p><img src='figures/burnitz.jpg'></p>
<p>Jeromy Burnitz, OF, 1993 - 2006: .253 BA, 315 HR, 17.4 WAR, 1 All-Star Team, 2012 HOF ballot</p>
</div>
<div id="dan-plesac" class="slide section level1">
<h1>Dan Plesac</h1>
<p><img src='figures/plesac.jpg'></p>
<p>Dan Plesac, P, 1986 - 2003: 65 - 71 Win-Loss, 3.64 ERA, 17.2 WAR, 3 All-Star Teams, 2009 HOF ballot</p>
</div>
<div id="these-are-just-a-few-players-who-have-appeared-on-the-ballot" class="slide section level1">
<h1>These are just a few players who have appeared on the ballot</h1>
<ol class='incremental'>
<li>
... and these are just some of the former Brewers!
</li>
<li>
None of them received a single HOF vote, thankfully.
</li>
<li>
Unlike:
</li>
<li>
<pre><code>## Name Year WAR Votes NumBallots
## 1 Jacque Jones 2014 11.5 1 571
## 2 David Segui 2010 7.8 1 539
## 3 Shawon Dunston 2008 9.1 1 543
## 4 Walt Weiss 2006 14.6 1 520
## 5 Randy Myers 2004 14.2 1 506
## 6 Cecil Fielder 2004 14.7 1 506
## 7 Mark Davis 2003 6.8 1 496
## 8 Jim Deshaies 2001 10.2 1 515
## 9 Steve Bedrosian 2001 13.2 1 515
## 10 Ray Knight 1994 10.9 1 456</code></pre>
</li>
</ol>
</div>
<div id="more-rules" class="slide section level1">
<h1>More Rules:</h1>
<ul>
<li>About 625 members (as of 2014) of the Baseball Writers Association of America (BBWAA) receive a ballot, and 570 of them voted last year.</li>
<li>Ballots are due by 12/31, and results are announced in the first week of January.</li>
<li>A player must be selected on at least 75% of the returned ballots to be inducted into the HOF that year.</li>
<li>In 1967 they started to enforce the rule that if you appear on less than 5% of ballots, you are permanently removed from future ballots.</li>
<li>A player may appear on a maximum of 15 ballots (i.e. consecutive years) before being permanently removed.</li>
<li>In a given year, each voter may vote for as few as 0 players, and as many as 10 players (where an average year's ballot contains about 40 players).</li>
</ul>
</div>
<div id="some-statistics" class="slide section level1">
<h1>Some Statistics</h1>
<ol class='incremental'>
<li>
1936 was the first year of Hall of Fame voting
</li>
<li>
Five players were elected:
</li>
<li>
<pre><code>## Year Name Pos NumBallots Votes Percentage
## 1 1936 Ty Cobb OF 226 222 98.20%
## 2 1936 Honus Wagner SS 226 215 95.10%
## 3 1936 Babe Ruth OF 226 215 95.10%
## 4 1936 Christy Mathewson P 226 205 90.70%
## 5 1936 Walter Johnson P 226 189 83.60%</code></pre>
</li>
<li>
From 1936 - 2014, 1089 unique players have appeared on the ballot
</li>
<li>
115 have been elected, 47 on their first ballot appearance (<em>not</em> Lou Gehrig, Cy Young, Warren Spahn)
</li>
<li>
Famously, no player has been unanimously elected.
</li>
<li>
We consider 1967 to be the first year of 'modern' HOF voting (when the 5% rule was established)
</li>
</ol>
</div>
<div id="some-problems" class="slide section level1">
<h1>Some Problems</h1>
<ol class='incremental' style='list-style-type:none'>
<li>
<p>Does it really take 15 years to decide?</p>
</li>
<li>
<p>The so-called 'morals' clause, rule 5 out of 9:</p>
<blockquote>
<p>Voting: Voting shall be based upon the player's record, playing ability, integrity, sportsmanship, character, and contributions to the team(s) on which the player played.</p>
</blockquote>
<blockquote>
<p>(from http://baseballhall.org/hall-famers/rules-election/BBWAA)</p>
</blockquote>
</li>
<li>
<p>The voters don't actively cover baseball!</p>
<blockquote>
<p>Q: Does that mean some Hall of Fame voters don’t even cover baseball any more?</p>
</blockquote>
<blockquote>
<p>A: Yes. The BBWAA trusts that its voters take their responsibility seriously, and even those honorary members who are no longer covering baseball do their due diligence to produce a thoughtful ballot.</p>
</blockquote>
<blockquote>
<p>(from http://bbwaa.com/voting-faq/)</p>
</blockquote>
</li>
</ol>
</div>
<div id="some-responses" class="slide section level1">
<h1>Some Responses</h1>
<ul>
<li>Will Leitch: "Voter Fraud" 11/14/2013, sportsonearth.com</li>
</ul>
<blockquote>
<p>Stupid things are called out as stupid, and people try to figure out how to correct them. It's encouraging. It's kinda nice. And then there is Baseball Hall of Fame voting.</p>
</blockquote>
<ul>
<li>Jonathan Mahler: "Kill The HOF Character Clause, For The Sake Of The Writers", 1/10/2013, deadspin.com</li>
<li>Deadspin offered to buy a vote in 2013, and mainstream journalist Dan Le Batard (Miami Herald) gave his vote to the website (for no money). He was banned for life from voting on future HOF ballots.</li>
<li>Last month the BBWAA announced that they will only allow players to appear up to 10 times on the ballot, rather than 15. (with Mattingly, Trammell, and Smith grandfathered in to the 15-year clock)</li>
</ul>
</div>
<div id="my-thoughts" class="slide section level1">
<h1>My Thoughts</h1>
<ul>
<li>In a nutshell: the voting process is a phenomenon unto itself. It is not a yes-or-no question!</li>
<li>We might as well embrace this, and study it.</li>
<li>(Hasn't baseball always been famous for embracing the 'human element' of the game?)</li>
</ul>
</div>
<div id="part-1-visualize-the-data" class="slide section level1">
<h1>Part 1: Visualize the data</h1>
</div>
<div id="getting-the-data" class="slide section level1">
<h1>Getting the data</h1>
<ul>
<li>Baseball Reference has it all! Fantastic website.</li>
</ul>
<p><img src='figures/baseballreference.png' width=500></p>
<ul>
<li>Career statistics and voting percentages for each player, each year, from 1936-2014.</li>
<li>We did a bit of web scraping to download and parse each year's ballot.</li>
</ul>
</div>
<div id="a-few-plots-in-r" class="slide section level1">
<h1>A few plots in R</h1>
<p>We were really interested in the trajectories of voting percentages of players who had appeared on the ballot multiple times.</p>
<pre class="sourceCode r"><code class="sourceCode r">dat <-<span class="st"> </span><span class="kw">read.csv</span>(<span class="dt">file=</span><span class="st">"HOFregression_updated.csv"</span>, <span class="dt">as.is=</span><span class="ot">TRUE</span>)
<span class="kw">par</span>(<span class="dt">mfrow=</span><span class="kw">c</span>(<span class="dv">1</span>, <span class="dv">2</span>))
sel <-<span class="st"> </span>dat[, <span class="st">"Name"</span>] ==<span class="st"> "Alan Trammell"</span>
<span class="kw">plot</span>(dat[sel, <span class="st">"Year"</span>], dat[sel, <span class="st">"p"</span>], <span class="dt">ylim=</span><span class="kw">c</span>(<span class="dv">0</span>, <span class="dv">1</span>), <span class="dt">las=</span><span class="dv">1</span>, <span class="dt">pch=</span><span class="dv">19</span>, <span class="dt">xlab=</span><span class="st">"Year"</span>,
<span class="dt">ylab=</span><span class="st">"Voting Proportion"</span>)
<span class="kw">lines</span>(dat[sel, <span class="st">"Year"</span>], dat[sel, <span class="st">"p"</span>])
<span class="kw">title</span>(<span class="dt">main=</span><span class="st">"Alan Trammell"</span>)
<span class="kw">abline</span>(<span class="dt">h =</span> <span class="fl">0.05</span>, <span class="dt">col=</span><span class="dv">2</span>, <span class="dt">lwd=</span><span class="dv">2</span>)
<span class="kw">abline</span>(<span class="dt">h =</span> <span class="fl">0.75</span>, <span class="dt">col=</span><span class="dv">3</span>, <span class="dt">lwd=</span><span class="dv">2</span>)
sel <-<span class="st"> </span>dat[, <span class="st">"Name"</span>] ==<span class="st"> "Bert Blyleven"</span>
<span class="kw">plot</span>(dat[sel, <span class="st">"Year"</span>], dat[sel, <span class="st">"p"</span>], <span class="dt">ylim=</span><span class="kw">c</span>(<span class="dv">0</span>, <span class="dv">1</span>), <span class="dt">las=</span><span class="dv">1</span>, <span class="dt">pch=</span><span class="dv">19</span>, <span class="dt">xlab=</span><span class="st">"Year"</span>,
<span class="dt">ylab=</span><span class="st">"Voting Proportion"</span>)
<span class="kw">lines</span>(dat[sel, <span class="st">"Year"</span>], dat[sel, <span class="st">"p"</span>])
<span class="kw">title</span>(<span class="dt">main=</span><span class="st">"Bert Blyleven"</span>)
<span class="kw">abline</span>(<span class="dt">h =</span> <span class="fl">0.05</span>, <span class="dt">col=</span><span class="dv">2</span>, <span class="dt">lwd=</span><span class="dv">2</span>)
<span class="kw">abline</span>(<span class="dt">h =</span> <span class="fl">0.75</span>, <span class="dt">col=</span><span class="dv">3</span>, <span class="dt">lwd=</span><span class="dv">2</span>)</code></pre>
</div>
<div id="a-few-plots-in-r-1" class="slide section level1">
<h1>A few plots in R</h1>
<p>We were really interested in the trajectories of voting percentages of players who had appeared on the ballot multiple times.</p>
<div class="figure">
<img src="figure/edaplots2-1.png" alt="plot of chunk edaplots2" /><p class="caption">plot of chunk edaplots2</p>
</div>
<p>How did these guys end up with such different voting trajectories?</p>
</div>
<div id="we-built-an-interactive-plot-using-d3" class="slide section level1">
<h1>We built an interactive plot using D3</h1>
<ul>
<li>Link: http://cscheid.net/static/mlb-hall-of-fame-voting</li>
<li>Two main parts of the visualization:
<ul>
<li>Brushable plot of voting % vs. year</li>
<li>Linked histograms for each statistical category</li>
</ul></li>
</ul>
</div>
<div id="lots-of-interesting-trivia-was-uncovered-here" class="slide section level1">
<h1>Lots of interesting trivia was uncovered here:</h1>
<ul>
<li>Lefty Grove vs. Orval Grove</li>
<li>Runoff Elections</li>
<li>Dips in voting percentages for most players when a group of strong first-ballot players appears (1999, 2007)</li>
<li>Edd Roush's 19 ballots</li>
<li>Minnie Minoso and Jose Rijo's comebacks</li>
<li>Warren Spahn's early vote</li>
<li>HR > 400</li>
<li>OPS > .850</li>
</ul>
</div>
<div id="part-2-model-the-data-and-make-predictions" class="slide section level1">
<h1>Part 2: Model the data and make predictions</h1>
</div>
<div id="the-obvious-next-question-is-can-we-predict-next-years-vote" class="slide section level1">
<h1>The obvious next question is: Can we predict next year's vote?</h1>
<ul>
<li>Others have worked on this, of course:
<ul>
<li>JAWS: Jay Jaffe's 'Jaffe WAR Scoring System', an average of WAR and 'peak' WAR, normalized for position</li>
<li>Bill James has a few systems. Hall of Fame Monitor, for example, as described on baseball-reference.com (leader glossary section):
<pre style='white-space: pre-wrap'>
[1] For Batting Average, 2.5 points for each season over .300, 5.0 for over .350, 15 for over .400. Seasons are not double-counted. I require 100 games in a season to qualify for this bonus.
[2] For hits, 5 points for each season of 200 or more hits.
[3] 3 points for each season of 100 RBI's and 3 points for each season of 100 runs.
[4] 10 points for 50 home runs, 4 points for 40 HR, and 2 points for 30 HR.
[5] 2 points for 45 doubles and 1 point for 35 doubles.
[6] 8 points for each MVP award and 3 for each AllStar Game, and 1 point for a Rookie of the Year award.
[7] 2 points for a gold glove at C, SS, or 2B, and 1 point for any other gold glove.
[8] 6 points if they were the regular SS or C on a WS winning team, 5 points for 2B or CF, 3 for 3B, 2 for LF or RF, and 1 for 1B. I don't have the OF distribution, so I give 3 points for OF (requires at least 82 games as the position).
...
[19] ...
</pre></li>
<li>Michael Freiman's paper in JQAS a few years back. Random Forests for 0/1 induction into HOF.</li>
<li>Mills and Salaga, 2011 JQAS paper using random forests as well.</li>
</ul></li>
<li>Most of these focus on the yes/no question of induction, rather than predicting voting percentages.</li>
</ul>
</div>
<div id="what-predictors-should-we-use" class="slide section level1">
<h1>What predictors should we use?</h1>
<ul>
<li>Career Statstics? (including position, of course)</li>
<li>Awards? (Rookie of the Year, MVP, All-star appearnaces, Gold glove awards, etc.)</li>
<li>Measures of post-season success?</li>
<li>Measures of popularity with the press/public?</li>
<li>We used the first two, and the third should be easy to incorporate in future work. The fourth is a little tougher. (Some type of meta-analysis on newspaper articles, perhaps?)</li>
</ul>
</div>
<div id="what-data-do-we-use" class="slide section level1">
<h1>What data do we use?</h1>
<ul>
<li>I'll talk about making predictions last year (ballots were due 12/31/13, and results were announced January, 2014), and I'll finish by presenting my 2015 predictions.</li>
<li>We discarded anybody whose first year of eligibility was before 1967.</li>
<li>Through the 2013 vote, this gave us a historical data set of:
<ul>
<li>406 position players</li>
<li>229 pitchers</li>
<li><span class="math"> = 635</span> total unique players</li>
<li>and 1458 total data points, or voting outcomes (for an average of 2.3 years on the ballot per person)</li>
</ul></li>
<li>We'll test the accuracy of our model by making one-year-ahead (out-of-sample) predictions, starting in 1997, and going through 2014.</li>
</ul>
</div>
<div id="our-methodology" class="slide section level1">
<h1>Our methodology:</h1>
<ul>
<li>For each year, we fit a different model to the historical data from three different subsets of players:
<ul>
<li>First-ballot batters</li>
<li>First-ballot pitchers</li>
<li>Returning ballot players</li>
</ul></li>
<li>Career statistics are basically all we have for the first two groups.</li>
<li>For the third group, we have their previous HOF voting percentages, of course. (which should make our job much easier)</li>
</ul>
</div>
<div id="modeling" class="slide section level1">
<h1>Modeling:</h1>
<ul>
<li>All the models we fit were logistic regression models: assume the <span class="math"><em>n</em></span> voters in a given year act independently, and model the number of 'yes' votes as a binomial random variable: <br /><span class="math"><em>y</em><sub><em>i</em><em>t</em></sub> ∼ Binom(<em>n</em><sub><em>t</em></sub>, <em>p</em><sub><em>i</em><em>t</em></sub>), </span><br /> where
<ul>
<li><span class="math"><em>y</em><sub><em>i</em><em>t</em></sub></span> is the number of 'yes' votes for player <span class="math"><em>i</em></span> in year <span class="math"><em>t</em></span></li>
<li><span class="math"><em>n</em><sub><em>t</em></sub></span> is the number of ballots returned in year <span class="math"><em>t</em></span>, and</li>
<li><span class="math"><em>p</em><sub><em>i</em><em>t</em></sub></span> is the probability of a given voter voting 'yes' for player <span class="math"><em>i</em></span> in year <span class="math"><em>t</em></span>.</li>
</ul></li>
<li>Next, model <span class="math"><em>p</em><sub><em>i</em><em>t</em></sub></span> as a linear function of the predictor variables: <br /><span class="math"><em>p</em><sub><em>i</em><em>t</em></sub> = <em>β</em><sub>0</sub> + <em>β</em><sub>1</sub><em>X</em><sub><em>i</em></sub><sup>HR</sup> + <em>β</em><sub>2</sub><em>X</em><sub><em>i</em></sub><sup>RBI</sup> + <em>β</em><sub>3</sub><em>X</em><sub><em>i</em></sub><sup>OBP</sup> + ...</span><br /> for batters, for instance.</li>
<li>An alternative would be to use something like random forests, support vector machines, or whatever. We tried random forests and got similar results, and logistic regression is easy and interpretable, so we chose it.</li>
<li>Given the estimated regression coefficients, <span class="math"><em>β</em><sub>0</sub>, <em>β</em><sub>1</sub>, ...</span>, and the predictors for the players on next year's ballot, we can easily compute an estimate of <span class="math"><em>p</em><sub><em>i</em><em>t</em></sub></span> for them.</li>
</ul>
</div>
<div id="baseline-model" class="slide section level1">
<h1>Baseline Model:</h1>
<pre class="sourceCode r"><code class="sourceCode r"><span class="co"># Group 1: batters</span>
var.names[[<span class="dv">1</span>]] <-<span class="st"> </span><span class="kw">c</span>(<span class="st">"Yrs"</span>, <span class="st">"G"</span>, <span class="st">"AB"</span>, <span class="st">"R"</span>, <span class="st">"H"</span>, <span class="st">"HR"</span>, <span class="st">"RBI"</span>, <span class="st">"SB"</span>, <span class="st">"BB"</span>,
<span class="st">"BA"</span>, <span class="st">"OBP"</span>, <span class="st">"SLG"</span>,
<span class="st">"posC"</span>, <span class="st">"pos1B"</span>, <span class="st">"pos2B"</span>, <span class="st">"pos3B"</span>, <span class="st">"posSS"</span>, <span class="st">"posLF"</span>, <span class="st">"posCF"</span>, <span class="st">"posRF"</span>)
<span class="co"># Group 2: pitchers</span>
var.names[[<span class="dv">2</span>]] <-<span class="st"> </span><span class="kw">c</span>(<span class="st">"Yrs"</span>, <span class="st">"W"</span>, <span class="st">"L"</span>, <span class="st">"G"</span>, <span class="st">"GS"</span>, <span class="st">"SV"</span>, <span class="st">"IP"</span>, <span class="st">"H"</span>, <span class="st">"HR"</span>, <span class="st">"BB"</span>, <span class="st">"SO"</span>,
<span class="st">"ERA"</span>, <span class="st">"WHIP"</span>)
<span class="co"># Group 3: returning players</span>
<span class="co"># Just use the previous year's voting percentage as the sole predictor</span>
var.names[[<span class="dv">3</span>]] <-<span class="st"> </span><span class="kw">c</span>(<span class="st">"prev1"</span>)</code></pre>
</div>
<div id="lets-head-back-in-time...-to-1996" class="slide section level1">
<h1>Let's head back in time... to 1996:</h1>
<p><img src='figures/backtothefuture.jpg' width='1000'></p>
</div>
<div id="example-first-ballot-batters-from-1967---1996-n-255" class="slide section level1">
<h1>Example: First-ballot batters from 1967 - 1996 (n = 255):</h1>
<pre class="sourceCode r"><code class="sourceCode r"><span class="co"># Fit the model using weak priors:</span>
fit <-<span class="st"> </span><span class="kw">bayesglm</span>(data[sel, <span class="st">"p"</span>] ~<span class="st"> </span>X.scale, <span class="dt">weights=</span>data[sel, <span class="st">"NumBallots"</span>],
<span class="dt">family=</span><span class="kw">binomial</span>(<span class="dt">link =</span> <span class="st">"logit"</span>),
<span class="dt">prior.mean=</span><span class="dv">0</span>, <span class="dt">prior.scale=</span><span class="fl">2.5</span>)</code></pre>
</div>
<div id="example-first-ballot-batters-from-1967---1996-n-255-1" class="slide section level1">
<h1>Example: First-ballot batters from 1967 - 1996 (n = 255):</h1>
<pre class="sourceCode r"><code class="sourceCode r">Coefficients:
<span class="st"> </span>Estimate Std. Error z value <span class="kw">Pr</span>(><span class="er">|</span>z|)
(Intercept) -<span class="fl">4.95399</span> <span class="fl">0.05830</span> -<span class="fl">84.972</span> <<span class="st"> </span><span class="fl">2e-16</span> **<span class="er">*</span>
X.scaleYrs <span class="fl">0.50693</span> <span class="fl">0.05896</span> <span class="fl">8.597</span> <<span class="st"> </span><span class="fl">2e-16</span> **<span class="er">*</span>
X.scaleG <span class="fl">1.02455</span> <span class="fl">0.19500</span> <span class="fl">5.254</span> <span class="fl">1.49e-07</span> **<span class="er">*</span>
X.scaleAB -<span class="fl">3.63447</span> <span class="fl">0.48990</span> -<span class="fl">7.419</span> <span class="fl">1.18e-13</span> **<span class="er">*</span>
X.scaleR <span class="fl">2.27816</span> <span class="fl">0.14228</span> <span class="fl">16.012</span> <<span class="st"> </span><span class="fl">2e-16</span> **<span class="er">*</span>
X.scaleH <span class="fl">3.09098</span> <span class="fl">0.51523</span> <span class="fl">5.999</span> <span class="fl">1.98e-09</span> **<span class="er">*</span>
X.scaleHR <span class="fl">1.02895</span> <span class="fl">0.11611</span> <span class="fl">8.862</span> <<span class="st"> </span><span class="fl">2e-16</span> **<span class="er">*</span>
X.scaleRBI -<span class="fl">0.96718</span> <span class="fl">0.11939</span> -<span class="fl">8.101</span> <span class="fl">5.44e-16</span> **<span class="er">*</span>
X.scaleSB <span class="fl">0.05451</span> <span class="fl">0.02301</span> <span class="fl">2.370</span> <span class="fl">0.0178</span> *<span class="st"> </span>
X.scaleBB <span class="fl">0.11784</span> <span class="fl">0.10958</span> <span class="fl">1.075</span> <span class="fl">0.2822</span>
X.scaleBA <span class="fl">0.36248</span> <span class="fl">0.14991</span> <span class="fl">2.418</span> <span class="fl">0.0156</span> *<span class="st"> </span>
X.scaleOBP -<span class="fl">0.87497</span> <span class="fl">0.12853</span> -<span class="fl">6.807</span> <span class="fl">9.93e-12</span> **<span class="er">*</span>
X.scaleSLG <span class="fl">0.66728</span> <span class="fl">0.12253</span> <span class="fl">5.446</span> <span class="fl">5.15e-08</span> **<span class="er">*</span>
X.scaleposC <span class="fl">1.23696</span> <span class="fl">0.08342</span> <span class="fl">14.828</span> <<span class="st"> </span><span class="fl">2e-16</span> **<span class="er">*</span>
X.scalepos1B <span class="fl">0.62907</span> <span class="fl">0.08655</span> <span class="fl">7.268</span> <span class="fl">3.65e-13</span> **<span class="er">*</span>
X.scalepos2B <span class="fl">0.69809</span> <span class="fl">0.07841</span> <span class="fl">8.903</span> <<span class="st"> </span><span class="fl">2e-16</span> **<span class="er">*</span>
X.scalepos3B <span class="fl">0.54610</span> <span class="fl">0.07735</span> <span class="fl">7.060</span> <span class="fl">1.66e-12</span> **<span class="er">*</span>
X.scaleposSS <span class="fl">0.98036</span> <span class="fl">0.07683</span> <span class="fl">12.759</span> <<span class="st"> </span><span class="fl">2e-16</span> **<span class="er">*</span>
X.scaleposLF <span class="fl">0.40763</span> <span class="fl">0.08836</span> <span class="fl">4.613</span> <span class="fl">3.97e-06</span> **<span class="er">*</span>
X.scaleposCF -<span class="fl">0.01915</span> <span class="fl">0.08636</span> -<span class="fl">0.222</span> <span class="fl">0.8245</span>
X.scaleposRF <span class="fl">0.49648</span> <span class="fl">0.08293</span> <span class="fl">5.987</span> <span class="fl">2.14e-09</span> **<span class="er">*</span>
---
Signif. codes:<span class="st"> </span><span class="dv">0</span> ‘**<span class="er">*</span>’ <span class="fl">0.001</span> ‘**’ <span class="fl">0.01</span> ‘*’ <span class="fl">0.05</span> ‘.’ <span class="fl">0.1</span> ‘ ’ <span class="dv">1</span></code></pre>
</div>
<div id="interpretation" class="slide section level1">
<h1>Interpretation?</h1>
<ul>
<li>Position coefficients are reasonable:
<ul>
<li>DH = 0, as it is the baseline position.</li>
<li>SS and C have the highest estimates.</li>
</ul></li>
<li>OBP has a negative coefficient? But SLG and BA are positive... (and of course, coefficients for correlated predictors in linear models can't be interpreted in isolation).</li>
</ul>
</div>
<div id="making-out-of-sample-predictions-for-1997" class="slide section level1">
<h1>Making out-of-sample predictions for 1997:</h1>
<pre>
Name Prediction Actual
1 Dave Parker 39.4 17.5
2 Dwight Evans 51.8 5.9
3 Ken Griffey 12.7 4.7
4 Garry Templeton 5.3 0.4
5 Terry Kennedy 0.5 0.2
6 Terry Puhl 0.2 0.2
</pre>
<ul>
<li>Pretty bad!</li>
<li>The RMSE here (for the percentage difference) is about 21%.</li>
<li>If we had just guessed the intercept for everybody we would have gotten a 25% RMSE.</li>
<li>But this is a tiny sample...</li>
</ul>
</div>
<div id="overall-results-for-baseline-model" class="slide section level1">
<h1>Overall Results for Baseline Model:</h1>
<ul>
<li>Pseudo-code:</li>
</ul>
<pre class="sourceCode r"><code class="sourceCode r">for (year in <span class="dv">1997</span>:<span class="dv">2014</span>) {
for (group in <span class="kw">c</span>(<span class="st">"batters"</span>, <span class="st">"pitchers"</span>, <span class="st">"returning"</span>)) {
train <-<span class="st"> </span>Year <<span class="st"> </span>year &<span class="st"> </span>Group ==<span class="st"> </span>group
test <-<span class="st"> </span>Year ==<span class="st"> </span>year &<span class="st"> </span>Group ==<span class="st"> </span>group
historical.fit <-<span class="st"> </span><span class="kw">glm</span>(y[train] ~<span class="st"> </span>data[train, ])
predict <-<span class="st"> </span><span class="kw">predict</span>(historical.fit, <span class="dt">newdata=</span>data[test, ])
}
}</code></pre>
<table>
<thead>
<tr class="header">
<th align="left">Group</th>
<th align="left">Baseline</th>
<th align="left"></th>
<th align="left"></th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td align="left">First-ballot Batters (n = 151)</td>
<td align="left">18.4%</td>
<td align="left"></td>
</tr>
<tr class="even">
<td align="left">First-ballot Pitchers (n = 85)</td>
<td align="left">9.7%</td>
<td align="left"></td>
</tr>
<tr class="odd">
<td align="left">Returning Players (n = 262)</td>
<td align="left">5.7%</td>
<td align="left"></td>
</tr>
<tr class="even">
<td align="left">Overall</td>
<td align="left">11.7%</td>
<td align="left"></td>
</tr>
</tbody>
</table>
</div>
<div id="lets-make-2014-predictions" class="slide section level1">
<h1>Let's make 2014 Predictions</h1>
<pre style='font-size:14px'>
Name Previous Predicted
1 Craig Biggio 68.2 77.0
2 Jack Morris 67.7 76.5
3 Jeff Bagwell 59.6 67.5
4 Mike Piazza 57.8 65.3
5 Tim Raines 52.2 58.0
6 Lee Smith 47.8 52.0
7 Curt Schilling 38.8 39.7
8 Frank Thomas 0.0 39.2
9 Jeff Kent 0.0 38.7
10 Roger Clemens 37.6 38.1
11 Greg Maddux 0.0 37.5
12 Barry Bonds 36.2 36.3
13 Edgar Martinez 35.9 35.9
14 Alan Trammell 33.6 33.0
15 Luis Gonzalez 0.0 23.0
16 Larry Walker 21.6 20.3
17 Fred McGriff 20.7 19.5
18 Mark McGwire 16.9 16.4
19 Mike Mussina 0.0 16.3
20 Tom Glavine 0.0 15.1
21 Don Mattingly 13.2 13.8
22 Sammy Sosa 12.5 13.3
23 Rafael Palmeiro 8.8 11.1
24 Moises Alou 0.0 10.5
25 Ray Durham 0.0 7.1
26 Armando Benitez 0.0 3.3
27 Sean Casey 0.0 0.9
28 Eric Gagne 0.0 0.8
29 Richie Sexson 0.0 0.6
30 Paul Lo Duca 0.0 0.5
31 J.T. Snow 0.0 0.4
32 Kenny Rogers 0.0 0.4
33 Hideo Nomo 0.0 0.2
34 Jacque Jones 0.0 0.1
35 Todd Jones 0.0 0.1
36 Mike Timlin 0.0 0.1
</pre>
<p><audio controls> <source src='figures/record-scratch-1.wav' type='audio/wav'> </audio></p>
</div>
<div id="residuals-for-baseline-model" class="slide section level1">
<h1>Residuals for Baseline Model</h1>
<p><img src='figures/fig_residuals_without2014.jpg' width=1200></p>
</div>
<div id="residual-analysis" class="slide section level1">
<h1>Residual Analysis:</h1>
<ul>
<li>Stats 101: Fit a model, look at the residuals, see if you can think of a variable to incorporate that would explain some of the residuals.
<pre>
Year Name Actual Predicted Residual
1 2002 Ozzie Smith 91.7 9.3 82.4
2 2001 Kirby Puckett 82.1 2.8 79.3
3 2005 Wade Boggs 91.9 57.1 34.8
4 2004 Paul Molitor 85.2 56.0 29.2
5 2010 Edgar Martinez 36.2 7.6 28.6
</pre>
<pre>
1 2011 Rafael Palmeiro 11.0 93.8 -82.8
2 2013 Barry Bonds 36.2 99.5 -63.3
3 2013 Roger Clemens 37.6 99.5 -61.9
4 2010 Fred McGriff 21.5 73.9 -52.4
5 2013 Julio Franco 1.1 52.3 -51.3
</pre></li>
<li>Let's try:
<ul>
<li>Awards, like All-Star teams and Gold Gloves, and...</li>
<li>Drugs! (i.e. steroid or HGH suspicion or suspension) Specifically, we can gather data on drug suspensions, and on being named in the Mitchell Report, as our proxy for suspected use.</li>
</ul></li>
</ul>
</div>
<div id="a-side-note..." class="slide section level1">
<h1>A side note...</h1>
<p>Don't google image search "Barry Bonds before vs. after" unless you have half an hour to kill...</p>
<p><img src='figures/bonds1.jpg' width=700></p>
</div>
<div id="a-side-note...-1" class="slide section level1">
<h1>A side note...</h1>
<p>Don't google image search "Barry Bonds before vs. after" unless you have half an hour to kill...</p>
<p><img src='figures/bonds2.jpg' width=700></p>
</div>
<div id="a-side-note...-2" class="slide section level1">
<h1>A side note...</h1>
<p>Don't google image search "Barry Bonds before vs. after" unless you have half an hour to kill...</p>
<p><img src='figures/bonds3.jpg' width=700></p>
<p>People have really put a lot of work into this sort of comparison</p>
<p>Related searches: McGwire, Clemens, Sosa.</p>
</div>
<div id="model-2-awards-drugs-batters-from-1967---2013" class="slide section level1">
<h1>Model 2 ('Awards + Drugs'), Batters from 1967 - 2013:</h1>
<pre style='font-size:14px'>
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) -5.06179 0.04106 -123.281 < 2e-16 ***
X.scaleYrs 0.45714 0.03482 13.127 < 2e-16 ***
X.scaleG 0.04859 0.14207 0.342 0.732324
X.scaleAB 1.19308 0.35354 3.375 0.000739 ***
X.scaleR 0.77132 0.08730 8.835 < 2e-16 ***
X.scaleH -0.45612 0.33860 -1.347 0.177963
X.scaleHR 0.23513 0.07811 3.010 0.002611 **
X.scaleRBI -0.25777 0.07589 -3.397 0.000682 ***
X.scaleSB 0.05965 0.01926 3.098 0.001950 **
X.scaleBB 0.19772 0.07434 2.660 0.007821 **
X.scaleBA 0.70078 0.09828 7.130 1.00e-12 ***
X.scaleOBP -0.34334 0.09172 -3.743 0.000182 ***
X.scaleSLG 0.44604 0.08467 5.268 1.38e-07 ***
X.scaleposC 0.15346 0.02416 6.351 2.14e-10 ***
X.scalepos1B 0.12147 0.02200 5.523 3.34e-08 ***
X.scalepos2B -0.11253 0.02412 -4.665 3.09e-06 ***
X.scalepos3B -0.05741 0.02361 -2.431 0.015055 *
X.scaleposSS 0.10689 0.02301 4.646 3.38e-06 ***
X.scaleposLF 0.03260 0.02365 1.379 0.168038
X.scaleposCF -0.20443 0.02516 -8.127 4.41e-16 ***
X.scaleposRF -0.17331 0.02406 -7.203 5.87e-13 ***
X.scaledrugs -0.91577 0.02574 -35.583 < 2e-16 ***
X.scaleAllStarpy 1.12873 0.01691 66.752 < 2e-16 ***
X.scalegold.gloves 0.20908 0.01136 18.411 < 2e-16 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
</pre>
<p>Nice -- the z-scores for the three new predictors are highly significant, and have signs that we expected.</p>
</div>
<div id="new-rmse-results" class="slide section level1">
<h1>New RMSE results:</h1>
<table>
<thead>
<tr class="header">
<th align="left">Group</th>
<th align="left">Baseline</th>
<th align="left">Awards + Drugs</th>
<th align="left"></th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td align="left">First-ballot Batters (n = 151)</td>
<td align="left">18.4%</td>
<td align="left">15.2%</td>
</tr>
<tr class="even">
<td align="left">First-ballot Pitchers (n = 85)</td>
<td align="left">9.7%</td>
<td align="left">8.6%</td>
</tr>
<tr class="odd">
<td align="left">Returning Players (n = 262)</td>
<td align="left">5.7%</td>
<td align="left">5.7%</td>
</tr>
<tr class="even">
<td align="left">Overall</td>
<td align="left">11.7%</td>
<td align="left">10.0%</td>
</tr>
</tbody>
</table>
</div>
<div id="updated-2014-predictions" class="slide section level1">
<h1>Updated 2014 predictions:</h1>
<pre style='font-size:14px'>
Name Previous Predicted
1 Greg Maddux 0.0 96.0
2 Craig Biggio 68.2 77.0
3 Jack Morris 67.7 76.5
4 Jeff Bagwell 59.6 67.5
5 Mike Piazza 57.8 65.3
6 Tim Raines 52.2 58.0
7 Mike Mussina 0.0 57.7
8 Lee Smith 47.8 52.0
9 Frank Thomas 0.0 51.0
10 Tom Glavine 0.0 50.5
11 Curt Schilling 38.8 39.7
12 Roger Clemens 37.6 38.1
13 Barry Bonds 36.2 36.3
14 Edgar Martinez 35.9 35.9
15 Alan Trammell 33.6 33.0
16 Luis Gonzalez 0.0 20.9
17 Larry Walker 21.6 20.3
18 Fred McGriff 20.7 19.5
19 Mark McGwire 16.9 16.4
20 Don Mattingly 13.2 13.8
21 Sammy Sosa 12.5 13.3
22 Moises Alou 0.0 13.1
23 Rafael Palmeiro 8.8 11.1
24 Jeff Kent 0.0 11.0
</pre>
</div>
<div id="residuals-for-awards-drugs-model" class="slide section level1">
<h1>Residuals for 'Awards + Drugs' Model</h1>
<p><img src='figures/fig_residuals_M2_without2014.jpg' width=1200> Whew. At least now the results are plausible. Maddux is a lock, and Glavine and Thomas are above 50% (just barely).</p>
</div>
<div id="residual-analysis-1" class="slide section level1">
<h1>Residual Analysis:</h1>
Top-5 and Bottom-5 residuals:
<pre>
Year Name Actual Predicted Residual
1 2001 Kirby Puckett 82.1 12.0 70.1
2 1999 Robin Yount 77.5 8.6 68.9
3 1999 George Brett 98.2 54.3 43.9
4 2004 Paul Molitor 85.2 50.3 34.9
5 2005 Wade Boggs 91.9 60.4 31.4
</pre>
<pre>
Year Name Actual Predicted Residual
1 2013 Barry Bonds 36.2 99.3 -63.1
2 2013 Roger Clemens 37.6 97.9 -60.3
3 2008 Tim Raines 24.3 81.7 -57.4
4 2007 Jose Canseco 1.1 38.6 -37.5
5 2007 Mark McGwire 23.5 58.7 -35.2
</pre>
<ul>
<li>Any thoughts?</li>
</ul>
</div>
<div id="residual-analysis-2" class="slide section level1">
<h1>Residual Analysis:</h1>
Top-5 and Bottom-5 residuals:
<pre>
Year Name Actual Predicted Residual
1 2001 Kirby Puckett 82.1 12.0 70.1
2 1999 Robin Yount 77.5 8.6 68.9
3 1999 George Brett 98.2 54.3 43.9
4 2004 Paul Molitor 85.2 50.3 34.9
5 2005 Wade Boggs 91.9 60.4 31.4
</pre>
<pre>
Year Name Actual Predicted Residual
1 2013 Barry Bonds 36.2 99.3 -63.1
2 2013 Roger Clemens 37.6 97.9 -60.3
3 2008 Tim Raines 24.3 81.7 -57.4
4 2007 Jose Canseco 1.1 38.6 -37.5
5 2007 Mark McGwire 23.5 58.7 -35.2
</pre>
<ul>
<li>Any thoughts?</li>
<li>We can try some milestones, like 3000 hits, and also a variable for 'Played for only one team entire career'.</li>
<li>Specifically, we'll add: Rookie of the Year, MVP, Cy Young, 3000 hits, 500 HR, 300 wins, 3000 strikeouts, and 'Oneteam' (there is a list available online for those with > 15 years of service. I cheated and included Puckett).</li>
</ul>
</div>
<div id="improving-the-model-for-returning-players" class="slide section level1">
<h1>Improving the model for returning players</h1>
<ul>
<li>Previous Year's voting percentage</li>
<li>Previous Year's voting percentage squared (to model a potentially quadratic relationship)</li>
<li>"Top 3 First Ballot": The mean voting percentage of the top 3 first-ballot players in a given year. This variable we expect to have a negative association with a returning player's voting percentage, as it did in 1999, for example, when first-timers George Brett, Nolan Ryan, and Robin Yount all received very high voting percentages, and most returning players received a lower voting percentage than their previous year.</li>
<li>"Top 5 Returning Ballot": The mean of the top five voting percentages from the previous year of players who are re-appearing on this year's ballot; this should also have a negative correlation with the current year's voting percentages.</li>
<li>Indicator of whether this is a player's second or final ballot (two years in which an extra bump often occurs)</li>
<li>Interaction between indicator of second ballot and previous year's percentage -- included specifically to capture the fact that first-ballot players who get between 60 and 75% of the vote percentage tend to increase a lot in their second year.</li>
<li>All of this based on EDA and residual plots</li>
</ul>
</div>
<div id="returning-player-updated-model" class="slide section level1">
<h1>Returning Player Updated Model</h1>
<ul>
<li>All the coefficients are statistically significant (so there's that, at least)</li>
<li>Do the predictions improve? Recall that the baseline RMSE for this group (n = 262) was 5.7%.
<pre>
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) -1.104016 0.004748 -232.535 < 2e-16 ***
X.scaleprev1 1.456224 0.018842 77.288 < 2e-16 ***
X.scaleprev1.squared -0.419837 0.017857 -23.510 < 2e-16 ***
X.scaletop3 -0.189887 0.004369 -43.460 < 2e-16 ***
X.scalereturn -0.016023 0.004591 -3.490 0.000482 ***
X.scaleballot2ndyear -0.071682 0.009175 -7.813 5.60e-15 ***
X.scaleballotfinal 0.026895 0.004286 6.276 3.48e-10 ***
X.scaleballot2nd.x.prev1 0.091116 0.008260 11.031 < 2e-16 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
</pre>
</li>
</ul>
</div>
<div id="new-rmse-results-1" class="slide section level1">
<h1>New RMSE results:</h1>
<table>
<thead>
<tr class="header">
<th align="left">Group</th>
<th align="left">Baseline</th>
<th align="left">Awards + Drugs</th>
<th align="left">Milestones, One-team, and 'Returning'</th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td align="left">First-ballot Batters (n = 151)</td>
<td align="left">18.4%</td>
<td align="left">15.2%</td>
<td align="left">13.5%</td>
</tr>
<tr class="even">
<td align="left">First-ballot Pitchers (n = 85)</td>
<td align="left">9.7%</td>
<td align="left">8.6%</td>
<td align="left">9.6%</td>
</tr>
<tr class="odd">
<td align="left">Returning Players (n = 262)</td>
<td align="left">5.7%</td>
<td align="left">5.7%</td>
<td align="left">4.6%</td>
</tr>
<tr class="even">
<td align="left">Overall</td>
<td align="left">11.7%</td>
<td align="left">10.0%</td>
<td align="left">9.1%</td>
</tr>
</tbody>
</table>
<p>Well, it's not great that the 1st-ballot pitchers RMSE went up (adding milestones, or rookie of the year, or something made the model perform worse for them), but we'll keep the effect in.</p>
</div>
<div id="one-more-change" class="slide section level1">
<h1>One more change:</h1>
<ul>
<li>Let's add in a few interaction effects between the 'drugs' variable and slugging variables, since you could argue that drug use is more damaging to one's reputation (and helpful to one's career) for sluggers.
<ul>
<li>Include drugs <span class="math"> × </span> SLG and drugs <span class="math"> × </span> HR.</li>
<li>Also let's include 'drugs' interaction with MVP awards and Cy Young Awards (to additionally 'downweight' Clemens and Bonds -- a little bit of snooping here...)</li>
</ul></li>
<li>With this change, our final 2014 predictions are:
<pre style='font-size:14px'>
Name Previous Predicted
1 Greg Maddux 0.0 97.4
2 Craig Biggio 68.2 73.7
3 Jack Morris 67.7 70.2
4 Frank Thomas 0.0 64.2
5 Mike Piazza 57.8 63.7
6 Jeff Bagwell 59.6 60.4
7 Tom Glavine 0.0 53.5
8 Tim Raines 52.2 52.7
9 Lee Smith 47.8 47.7
10 Mike Mussina 0.0 42.4
11 Curt Schilling 38.8 38.5
12 Roger Clemens 37.6 36.8
13 Barry Bonds 36.2 34.8
14 Edgar Martinez 35.9 33.1
15 Alan Trammell 33.6 30.4
16 Larry Walker 21.6 17.5
17 Fred McGriff 20.7 16.7
18 Mark McGwire 16.9 13.5
19 Don Mattingly 13.2 10.8
20 Luis Gonzalez 0.0 9.6
21 Sammy Sosa 12.5 9.4
22 Moises Alou 0.0 8.7
23 Rafael Palmeiro 8.8 8.2
24 Jeff Kent 0.0 5.1
</pre></li>
<li>These predictions looked decent at the time, although I thought Frank Thomas should have been a bit higher.</li>
</ul>
</div>
<div id="checking-the-2014-predictions-ouch" class="slide section level1">
<h1>Checking the 2014 Predictions (ouch!)</h1>
<p><img src='figures/fig_2014_intervals_updated.jpg' width=1050></p>
</div>
<div id="lessons-learned" class="slide section level1">
<h1>Lessons learned?</h1>
<ul>
<li>RMSE for 2014 was 9.9%, compared to 9.0% historically. Not terrible. But misleading since very low data points (< 2%, for example) are equally weighted in RMSE calculation. They're just not that interesting or important.</li>
<li>Postseason success might be a big factor. The data is a bit harder to gather.</li>
<li>Is there a teammate effect? (Maddux + Glavine?)</li>
<li>The predictions are dependent. We underestimated the first-ballot voting percentages in 2014, and thus, our model also overestimated the voting percentages of <em>every</em> returning player (because of the 'top-3' variable in the Group 3 = 'Returning' regression.)</li>
<li>Also, historical RMSE is fine to look at, but with Clemens/Bonds, there may have simply been no way for us to predict their voting percentages, since there were truly none like them before (in the modern era, or in any era when including the drugs variable).</li>
</ul>
</div>
<div id="predictions-drum-roll-please..." class="slide section level1">
<h1>2015 predictions (drum roll, please...)</h1>
<pre style='font-size:14px'>
Name Previous Predicted
1 Randy Johnson 0.0 99.8
2 Pedro Martinez 0.0 93.5
3 John Smoltz 0.0 72.4
4 Craig Biggio 74.8 69.2
5 Mike Piazza 62.2 59.2
6 Jeff Bagwell 54.3 51.3
7 Tim Raines 46.1 41.9
8 Roger Clemens 35.4 29.3
9 Barry Bonds 34.7 28.5
10 Lee Smith 29.9 23.4
11 Curt Schilling 29.2 22.6
12 Edgar Martinez 25.2 18.7
13 Alan Trammell 20.8 14.9
14 Mike Mussina 20.3 13.8
15 Jeff Kent 15.2 9.9
16 Fred McGriff 11.7 8.7
17 Mark McGwire 11.0 8.3
18 Larry Walker 10.2 7.8
19 Don Mattingly 8.2 7.8
20 Nomar Garciaparra 0.0 7.8
21 Gary Sheffield 0.0 7.6
22 Sammy Sosa 7.2 6.4
23 Troy Percival 0.0 5.3
24 Carlos Delgado 0.0 1.9
</pre>
</div>
<div id="predictions-drum-roll-please...-1" class="slide section level1">
<h1>2015 predictions (drum roll, please...)</h1>
<pre style='font-size:14px'>
Name Previous Predicted
1 Randy Johnson 0.0 99.8
2 Pedro Martinez 0.0 93.5
3 John Smoltz 0.0 72.4
4 Craig Biggio 74.8 69.2
5 Mike Piazza 62.2 59.2
6 Jeff Bagwell 54.3 51.3
7 Tim Raines 46.1 41.9
8 Roger Clemens 35.4 29.3
9 Barry Bonds 34.7 28.5
10 Lee Smith 29.9 23.4
11 Curt Schilling 29.2 22.6
12 Edgar Martinez 25.2 18.7
13 Alan Trammell 20.8 14.9
14 Mike Mussina 20.3 13.8
15 Jeff Kent 15.2 9.9
16 Fred McGriff 11.7 8.7
17 Mark McGwire 11.0 8.3
18 Larry Walker 10.2 7.8
19 Don Mattingly 8.2 7.8
20 Nomar Garciaparra 0.0 7.8
21 Gary Sheffield 0.0 7.6
22 Sammy Sosa 7.2 6.4
23 Troy Percival 0.0 5.3
24 Carlos Delgado 0.0 1.9
</pre>
<p><img src='figures/johnson-plaque.png' width=200></p>
</div>
<div id="predictions-drum-roll-please...-2" class="slide section level1">
<h1>2015 predictions (drum roll, please...)</h1>
<pre style='font-size:14px'>
Name Previous Predicted
1 Randy Johnson 0.0 99.8
2 Pedro Martinez 0.0 93.5
3 John Smoltz 0.0 72.4
4 Craig Biggio 74.8 69.2
5 Mike Piazza 62.2 59.2
6 Jeff Bagwell 54.3 51.3
7 Tim Raines 46.1 41.9
8 Roger Clemens 35.4 29.3
9 Barry Bonds 34.7 28.5
10 Lee Smith 29.9 23.4
11 Curt Schilling 29.2 22.6
12 Edgar Martinez 25.2 18.7
13 Alan Trammell 20.8 14.9
14 Mike Mussina 20.3 13.8
15 Jeff Kent 15.2 9.9
16 Fred McGriff 11.7 8.7
17 Mark McGwire 11.0 8.3
18 Larry Walker 10.2 7.8
19 Don Mattingly 8.2 7.8
20 Nomar Garciaparra 0.0 7.8
21 Gary Sheffield 0.0 7.6
22 Sammy Sosa 7.2 6.4
23 Troy Percival 0.0 5.3
24 Carlos Delgado 0.0 1.9
</pre>
<p><img src='figures/pedro-plaque.png' width=200></p>
</div>
<div id="predictions-drum-roll-please...-3" class="slide section level1">
<h1>2015 predictions (drum roll, please...)</h1>
<pre style='font-size:14px'>
Name Previous Predicted
1 Randy Johnson 0.0 99.8
2 Pedro Martinez 0.0 93.5
3 John Smoltz 0.0 72.4
4 Craig Biggio 74.8 69.2
5 Mike Piazza 62.2 59.2
6 Jeff Bagwell 54.3 51.3
7 Tim Raines 46.1 41.9
8 Roger Clemens 35.4 29.3
9 Barry Bonds 34.7 28.5
10 Lee Smith 29.9 23.4
11 Curt Schilling 29.2 22.6
12 Edgar Martinez 25.2 18.7
13 Alan Trammell 20.8 14.9
14 Mike Mussina 20.3 13.8