At any point, feel free to scroll down to the bottom to see some of the tables of pitcher clusters.

Clustering Pitches

Clustering individual pitches using data from PITCHf/x is a fairly simple task. All you need to do is pick out the important attributes that you believe define a pitch (velocity, movement, etc.) and use a clustering algorithm, such as K-Means clustering.

With K-Means clustering, you decide what K (the number of clusters) should be. For my analysis, I chose K to be 500 (rather arbitrarily). Different pitch clusters can represent the same type of pitch (i.e. fastball) but with varying attributes. For example, clusters 50 and 100 might both correspond to fastballs, but cluster 50 might be a typical Chris Young fastball whereas cluster 100 might be a typical Aroldis Chapman fastball.

One important point to remember is that you, the analyst, must decide what the clusters represent. By looking at attributes of the pitches in a given cluster, you might identity the cluster as “lefty changeups” or “submariner fastballs” (which is actually a category you will discover).

The Problem of Clustering Pitchers

We can identify every pitch that a pitcher throws as belonging to a cluster from 1 to 500. Therefore, we know the distribution of pitch clusters for a given pitcher. The difficult problem, however, is how do we compare two pitchers using this information? Let’s say we have two pitchers:

• Pitcher A’s pitches are 50% from cluster 1 and 50% from cluster 200.
• Pitcher B’s pitches are 33% from cluster 1, 33% from cluster 300, and 33% from cluster 139.

The question remains, are Pitcher A and Pitcher B similar pitchers?

The problem of clustering pitchers is a more complicated one than clustering pitches because we now have a collection of pitches instead of just individual pitches to compare. In order to cluster pitchers, I use a model that is typically used for topic modeling called Latent Dirichlet Allocation (LDA).

An Aside on LDA

In LDA for topic modeling, our data is a collection of documents.

Let’s imagine that our collection of documents is articles from the New York Times. There are global topics that govern how these articles are generated. For example, if you think of a newspaper, the topics might be sports, finance, health, politics, etc. Additionally, each article can be a mixture of these topics. We might imagine there is an article in the sports section titled, “Yankees payroll exceeds $300 million”, which our algorithm may discover is 50% about sports and 50% about finance.

Similar to what is mentioned above, the analyst must figure out what the topics actually are. You do not tell the algorithm that there is a sports topic. You discover that the topic is sports by observing that the most probable words are “baseball”, “Jeter”, “LeBron”, “touchdown”, etc. The algorithm will tell you that a particular document is 50% about topic 1 and 50% about topic 20, but you must ultimately infer what topics 1 and topics 20 are.

I am harping on this point mainly just to mention that there is no magic to these clustering algorithms. An algorithm can cluster data, but it cannot tell you what these clusters mean.

Relevance of LDA to Pitchers

Anyway, how can this model be used to analyze pitchers? We just need to use our imagination. Instead of a collection of documents, we now have a collection of pitcher seasons. Whereas each document is made up of a collection of words, each pitcher season is made up of a collection of pitches. We have already discretized each pitch using K-Means clustering in order to create our own “dictionary” of pitches. In our baseball model, we imagine that each pitcher is a mixture of repertoires, whereas in topic modeling, each document was a mixture of topics. We can then cluster pitchers together by figuring out who has the most similar repertoires.

Nitty Gritty Details

If you are not interested in getting into the nitty gritty details, feel free to skip ahead to the next section to just see the cluster groupings.

• Data used is from 2007-2014.
• The dictionary of pitches (500 clusters) was created by running K-Means using all of the pitches from 2014. The choice of 2014 is arbitrary, but I used just one year’s worth of data because I thought it might be a sufficient amount and it was much quicker to run K-Means.
• The PITCHf/x attributes that were used to cluster pitches were start_speed, pfx_x/pfx_z (horizontal/vertical movement), px/pz (horizontal/vertical location), vx0/vz0 (components of velocity).
• For each pitcher from 2007-2014, each pitch was assigned to its closest cluster (determined by distance to the cluster center). I filtered out pitcher seasons in which the pitcher threw fewer than 500 pitches.
• I then ran LDA on pitcher seasons, choosing the number of repertoires (topics) to be 5.
• I used the method from this paper to get a vector representation of each pitcher season. I could have used the inferred repertoire proportions as my vector representations, but for various reasons, this did not produce as nice of clusters.
• Finally, I ran K-Means (K=100) on these vectors to get clusters of pitchers.
• Whereas in topic modeling, it is often interesting to interpret what the global topics actually are, I am not really interested in what the global “repertoires” are for the model. I am really using LDA as a dimensionality reduction technique to produce smaller vectors (5 vs. 500) that can be clustered together.

Some Observations

The actual clusters along with some relevant FanGraphs statistics are provided below. Each table is sortable. For brevity, I have only included clusters in which there are 10 or fewer pitchers. Only the first cluster shown (cluster 3) has more than 10 pitchers, which I simply included to demonstrate that a cluster could be quite big.

• As is probably expected, clusters are almost always entirely righties or lefties even though this is not an input to the model.
• Guys with similar numbers of batters faced cluster together. This is by design, as the way I determined the repertoire proportions accounts for the number of times a particular pitch is thrown.
• Sometimes weird clusters can form, such as Cluster 37, which contains both Chapman and Wakefield. Cluster 37 is mostly cohesive with hard-throwing left-handers and I believe Wakefield ends up here simply because he did not fit well into any cluster.
• This is not to say that the algorithm cannot find clusters of knuckleballers. Cluster 14 is all R.A. Dickey from years 2011-2014.
• There are also other clusters that contain exclusively one (or almost one) pitcher. Cluster 8 is 5 Kershaw years and one Hamels year. Cluster 68 is 5 Verlander years. I believe these clusters form partially because their stuff is so good. There are other pitchers who fall into almost exclusively one cluster but who are joined by many other pitchers. Another factor is that they might be able to repeat their mechanics so well that they remain in the same cluster because they are always throwing the same pitch types.
• Clusters of individual pitchers also happens if a pitcher has an incredibly unique style. Justin Masterson has his own cluster because he is such an extreme ground-ball pitcher. Josh Collmenter does as well due to the extreme rise he generates on his “fastball”.
• Cluster 29 contains just Kershaw’s 2014 season and J.A. Happ’s 2009 season. If you do a Ctrl-F for J.A. Happ, he finds himself in some pretty flattering clusters. This is especially interesting because from 2007-2014, he does not have particularly good seasons, but he has been quite good the last two years. This is not to suggest that these clusters can uncover hidden gems, but it’s not fully out of the realm of possibility.
• Most clusters produce quite similar ground-ball percentages. One of the factors that goes into clustering pitches (and therefore pitchers) is horizontal and vertical movement, which play a huge factor in a pitcher’s ability to produce ground-balls.
• Submarine pitchers always end up together. Check out Clusters 9, 60, and 92.

Overall, I think this is pretty interesting stuff. I was honestly surprised that the clusters turned out to be as cohesive as they were. Additionally, besides being a descriptive tool, I have to wonder whether this information can be used for predictive purposes. For example, we often talk about regression to the mean when discussing a player’s performance, whether it be a pitcher of a batter. It is possible that the appropriate mean for many pitchers is the cluster mean that they happen to fall into.

For the type of baseball fan I’ve become — one who follows the sport as a whole rather than focuses on a particular team — 2016 was the season of Statcast. Even for those who watch the hometown team’s broadcast on a nightly basis, exit velocity and launch angle have probably become familiar terms. While Statcast was around last season, it seems fans and commentators alike have really embraced it in 2016.

Personally, I commend MLB for democratizing Statcast data, at least partially, especially when they are under no apparent obligation to do so. I’ve enjoyed the Statcast Podcast this season, but most of all, I’ve benefited from the tools available at Baseball Savant. For it is that tool which has allowed me to explore xISO. I first introduced an attempt to incorporate exit velocity into a player’s expected isolated slugging (xISO). I subsequently updated the model and discussed some notable first half players. Alex Chamberlain was kind enough to include my version of xISO in the RotoGraphs x-stats Omnibus, and I’ve been maintaining a daily updated xISO resource ever since.

Happily for science, all of my 2016 first half “Overperformers” saw ISO declines in the second half, while most of my first half “Underperformers” saw large drops in second half playing time. Rather than focus on individuals, though, let’s try to estimate the predictive value of xISO in 2016.

Yuck. This plot shows how well first-half ISO predicted second-half ISO, compared to how well first-half xISO predicted the same, for 2016 first AND second-half qualified hitters. Both of these are calculated using the model as it was at the All-Star break. There are two takeaways: First-half ISO was a pretty bad predictor of second-half ISO, and first-half xISO was also a pretty bad predictor of second-half ISO. Mercifully though, first-half xISO was a bit better than ISO at predicting future ISO. This is consistent with the findings in my first article, and a basic requirement I set out to satisfy.

Now, an interesting thing happened recently. After weeks of hinting, Mike Petriello unveiled “Barrels”. Put simply, Barrels are meant to be a classification of the best kind of batted balls. Shortly thereafter, Baseball Savant began tabulating total Barrels, Barrels per batted ball (Brls/BBE), and Barrels per plate appearance (Brls/PA). In a way, this is similar to Andrew Perpetua’s approach to using granular batted-ball data to track expected outcomes for each batted ball, except that the Statcast folks have taken only a slice of launch angles and exit velocities to report as Barrels.

By definition, these angles and velocities are those for which the expected slugging percentage is over 1.500, so it would appear that this stat could be a direct replacement for my xISO. Not so fast! First of all, because ISO is on a per at-bat (AB) basis, we definitely need to calculate Brls/AB from Brls/PA. This is not so hard if we export a quick FanGraphs leaderboard. Let’s check how well Brls/AB works in a single-predictor linear model for ISO:

Not too bad. The plot reports both R-squared and adjusted R-squared, for comparison with multiple regression models. I won’t show it, but this is almost exactly the coefficient of determination that my original xISO achieves with the same training data. I still notice a hint of nonlinearity, and I bet we can do better.

Hey now, that’s nice. In terms of adjusted R-squared, we’ve picked up about 0.06, which is not insignificant. The correlation plot also looks better to my eye. So what did I do? As is my way, I added a second-order term, and sprinkled in FB% and GB% as predictors. The latter two are perhaps controversial inclusions. FB% and/or GB% might be suspected to be strongly correlated with Brls/AB, introducing some undesired multicollinearity. While I won’t show the plots, it doesn’t actually turn out to be a big problem in this case. Both FB% and GB% have Pearson correlation coefficients close to 0.5 with Brls/AB (negative correlation in the case of GB%). Here’s the functional form of the multiple regression model plotted above, which was trained on all 2016 qualified hitters:

To be honest, there is something about my first model that I liked better. This version, using Barrels, feels like a bit of a half-measure between Andrew Perpetua’s bucketed approach and my previous philosophy of using only average exit-velocity values and batted-ball mix. My original intent was to create a metric that could be easily calculated from readily available resources, so in that sense, I’m still succeeding. Going forward, I will be calculating both versions on my spreadsheet. I’m excited to see which version serves the community better heading into 2017!

As always, I’m happy to entertain comments, questions, or criticisms.

With a wild comeback in Game 4 on Tuesday night, the Cubs secured their spot in the NLCS for the second straight season. Considering where the team was just five years ago, this is obviously an impressive achievement. But maybe more impressive is how they reached that second consecutive NLCS. The Cubs scored 17 runs against the Giants in their NLDS showdown, and six of those were driven in by their pitchers! That’s an absurd 35% of the Cubs’ run output coming from the guys who usually do the run prevention.

When Travis Wood hit his incredible home run as a relief pitcher in Game 2, it was the first postseason home run from a pitcher since Joe Blanton took Edwin Jackson deep in Game 4 of the 2008 World Series, and the first postseason home run from a reliever since 1924.

When Jake Arrieta left the yard in the first inning of the very next game, it became the first postseason series with multiple home runs off the bats of pitchers since the 1968 World Series, when Mickey Lolich and Bob Gibson each went deep in a seven-game series. Of course, Lolich and Gibson were rivals, not teammates, making the Wood-Arrieta accomplishment even more impressive — and rare. In fact, it was only the second time in the history of baseball (per Baseball-Reference Play Index) that two pitchers, on the same team, hit home runs in the same series. The only other time with in the 1924 World Series, when New York Giant teammates, and pitchers, Jack Bentley and Rosy Ryan homered in Games 3 and 5 of the epic seven-game series. Wood and Arrieta were the only ones to do so in back-to-back games.

* * *

Now, it wasn’t just the Cubs pitchers getting in on the fun. For a while Tuesday night, it looked as though Giants starter, Matt Moore, was going to be a two-fold hero. Shutting down the Cubs offense from the mound, and knocking in the first run of the game for the Giants in the bottom of the fourth. While that was the only hit from Giants pitchers in the series, it was still enough to set the combined hitting totals for the two teams to: .250 batting average, with a .625 slugging percentage, while knocking in 23 percent of the total runs scored.

Those are some pretty crazy totals, but are they the best ever?

Using the aforementioned Play Index search of all-time postseason home runs from pitchers, there are 18 different series (including the 2016 NLDS) in which a pitcher homered. In those series, on three occasions, the pitcher who hit the home run was the only pitcher to get a hit in the entire series (1984 Rick Sutcliffe, 1978 Steve Carlton, 1975 Don Gullet). Only twice did pitchers combine for more than the 10 total bases from the Giants and Cubs, and only once did they drive in more than the seven runs (and they never topped the percent of runs driven in). Let’s go to the chart:

Top Team Pitcher Performances in the Playoffs

After a brief peruse, it’s clear that there are only a few cases in which the pitchers in a series can even come close to what we just saw. Let’s take a look at the five best, in ascending order:

1968 World Series

This was one of the three series before the 2016 NLDS in which multiple pitchers hit home runs. In 1968, it was, as noted above, Bob Gibson and Mickey Lolich who homered in the series, one each for the Cardinals and Tigers. The reason this series is in fifth in the challengers to Cubs-Giants is because those two pitchers were really it. They drove in the only four runs from pitchers in the series (three of the four RBI coming on the two home-run swings), and there was only hit to hit come from a non-Gibson/Lolich pitcher.

1969 World Series

Just a year after our first entry into this challenge, the Mets and Orioles played in the first World Series to be led off with a League Championship Series. The extra-long season didn’t stop the Mets and Orioles pitchers from contributing all over the diamond, however, as they crammed five hits, 10 total bases, and five RBI into just a five-game series. Because of the abbreviated length of the series, this is one of the few series that can challenge the 2016 NLDS in terms of percentages. That being said, the Cubs-Giants pitchers take all three percentage categories, leaving there no real room for debate on this one.

1958 World Series

The 1958 series stands out in that it was the highest RBI total for pitchers in any postseason series to date. That was thanks in large part to top two pitchers for the Braves, Warren Spahn and Lew Burdette, tallying three RBI apiece. Burdette did it with the long ball, while Spahn preferred the death-by-a-thousand-cuts method, tallying his three RBI on four hits in the series. The Yankees got two RBI of their own from Bob Turley, but I’m not quite willing to give these guys the edge over the Cubs-Giants pitchers. The easiest argument for this year’s NLDS is that the Cubs-Giants pitchers tallied as many total bases and only one less RBI in three fewer games, as the 1958 World Series went to seven games, while this year’s NLDS went just four games.

1924 World Series

Here’s where the challenge gets real stiff. The 1924 World Series is the other series in which we have two home runs from pitchers, the aforementioned Bentley and Ryan teammates for the Giants. This series tops our charts in hits (8) and total bases (14), and is a reasonable choice for best-hitting series from a group of pitchers. I’m still giving the edge to Cubs-Giants in this showdown, though, and for a couple of reasons. Actually, really one reason with a couple different explanations: opportunity. Similar to the 1958 World Series, the 1924 World Series went to seven games, meaning that pitchers had far more games to rack up those hits and total bases. Pitchers were also left in games far longer in the 1920s, and as such, tallied almost three times as many at bats as the 2016 NLDS pitchers. When comparing batting average (.250 to .190) and, even more so, slugging percentage (.625 to .333) it becomes clear that this year’s Cubs-Giants pitchers still reign supreme.

1970 ALCS

Here’s our winner. The only series that I believe tops the recently concluded Cubs-Giants NLDS in terms of output from pitchers at the plate. This was an even shorter series than Cubs-Giants, as the Orioles only needed three games to dispatch the Twins. And their pitchers were a good chunk of the reason why. The Orioles used just four pitchers in the series, but all four got hits, combining for all of the offense you see above. (Twins pitchers were 0-for-5 in the series.) Not only did all four get hits, but all three starters got extra-base hits, as Dave McNally, Jim Palmer, and Mike Cuellar (Dick Hall was the reliever) all showed what they were capable of on the other side of the ball. Of course, the very next season, these three starters, along with Pat Dobson, would form just the second-ever set of four 20-game winners on the same team, proving just how awesome the late `60s and early `70s Orioles really were. They reign supreme for now, but let’s see how those Cubs starting pitchers do for the rest of the 2016 playoffs.

In “Hardball Retrospective: Evaluating Scouting and Development Outcomes for the Modern-Era Franchises”, I placed every ballplayer in the modern era (from 1901-present) on their original team. I calculated revised standings for every season based entirely on the performance of each team’s “original” players. I discuss every team’s “original” players and seasons at length along with organizational performance with respect to the Amateur Draft (or First-Year Player Draft), amateur free agent signings and other methods of player acquisition.  Season standings, WAR and Win Shares totals for the “original” teams are compared against the “actual” team results to assess each franchise’s scouting, development and general management skills.

Expanding on my research for the book, the following series of articles will reveal the teams with the biggest single-season difference in the WAR and Win Shares for the “Original” vs. “Actual” rosters for every Major League organization. “Hardball Retrospective” is available in digital format on Amazon, Barnes and Noble, GooglePlay, iTunes and KoboBooks. The paperback edition is available on Amazon, Barnes and Noble and CreateSpace. Supplemental Statistics, Charts and Graphs along with a discussion forum are offered at TuataraSoftware.com.

Don Daglow (Intellivision World Series Major League Baseball, Earl Weaver Baseball, Tony LaRussa Baseball) contributed the foreword for Hardball Retrospective. The foreword and preview of my book are accessible here.

Terminology

OWAR – Wins Above Replacement for players on “original” teams

OWS – Win Shares for players on “original” teams

OPW% – Pythagorean Won-Loss record for the “original” teams

AWAR – Wins Above Replacement for players on “actual” teams

AWS – Win Shares for players on “actual” teams

APW% – Pythagorean Won-Loss record for the “actual” teams

Assessment

The 2002 Toronto Blue Jays 

OWAR: 51.4     OWS: 312     OPW%: .572     (93-69)

AWAR: 34.2      AWS: 234     APW%: .481     (78-84)

WARdiff: 17.2                        WSdiff: 78  

The 2002 “Original” Blue Jays breezed to the American League East title, vanquishing the Yankees by a nine-game margin. Toronto topped the American League in OWAR and OWS. Shawn Green (.285/42/114) registered 110 tallies, achieved his second All-Star appearance and finished fifth in the MVP balloting. Jeff Kent (.313/37/108) drilled 42 doubles and attained a career-high in home runs. Carlos Delgado belted 33 round-trippers and coaxed 102 bases on balls. John Olerud (.300/22/102) laced 39 two-base hits and collected the Gold Glove Award. In the midst of five straight seasons with a batting average above .300, Shannon Stewart sliced 38 doubles and scored 103 runs. Vernon Wells reached the century mark in RBI and added 34 two-base knocks in his first full season. The “Actual” squad featured 2002 AL Rookie of the Year Eric Hinske (.279/24/84) at the hot corner.

Jeff Kent placed forty-eighth among second-sackers in the “The New Bill James Historical Baseball Abstract” top 100 player rankings while John Olerud secured the 53^rd slot at first base.

Original 2002 Blue Jays                            Actual 2002 Blue Jays

Roy “Doc” Halladay (19-7, 2.93) warranted his first All-Star invitation and led the American League with 239.1 innings pitched. David “Boomer” Wells compiled 19 victories with a 3.75 ERA. Toronto’s superb bullpen staff was anchored by Billy Koch (3.27, 44 SV) and Jose Mesa (2.97, 45 SV). The setup corps consisted of Steve Karsay (3.26, 12 SV), Ben Weber (7-2, 2.54) and Kelvim Escobar (4.27, 38 SV).

Original 2002 Blue Jays                          Actual 2002 Blue Jays

Notable Transactions

Shawn Green 

November 8, 1999: Traded by the Toronto Blue Jays with Jorge Nunez (minors) to the Los Angeles Dodgers for Pedro Borbon and Raul Mondesi. 

Jeff Kent 

August 27, 1992: Traded by the Toronto Blue Jays with a player to be named later to the New York Mets for David Cone. The Toronto Blue Jays sent Ryan Thompson (September 1, 1992) to the New York Mets to complete the trade.

July 29, 1996: Traded by the New York Mets with Jose Vizcaino to the Cleveland Indians for Carlos Baerga and Alvaro Espinoza.

November 13, 1996: Traded by the Cleveland Indians with a player to be named later, Julian Tavarez and Jose Vizcaino to the San Francisco Giants for a player to be named later and Matt Williams. The Cleveland Indians sent Joe Roa (December 16, 1996) to the San Francisco Giants to complete the trade. The San Francisco Giants sent Trent Hubbard (December 16, 1996) to the Cleveland Indians to complete the trade. 

John Olerud 

December 20, 1996: Traded by the Toronto Blue Jays with cash to the New York Mets for Robert Person.

October 27, 1997: Granted Free Agency.

November 24, 1997: Signed as a Free Agent with the New York Mets.

October 29, 1999: Granted Free Agency.

December 15, 1999: Signed as a Free Agent with the Seattle Mariners. 

Billy Koch

December 7, 2001: Traded by the Toronto Blue Jays to the Oakland Athletics for Eric Hinske and Justin Miller.

Honorable Mention

The 1995 Toronto Blue Jays 

OWAR: 27.1     OWS: 208     OPW%: .469     (76-86)

AWAR: 25.4       AWS: 168      APW%: .389    (56-88)

WARdiff: 1.7                        WSdiff: 40

The “Original” ’95 Jays plodded to a fourth-place finish in the AL East, eleven games behind the Orioles while the horrific “Actuals” placed 30 games behind the Red Sox. David Wells delivered a 16-8 record with a 3.24 ERA and made his first appearance at the Mid-Summer Classic. Jose Mesa (1.13, 46 SV) blossomed in the closer’s role, meriting second place in the Cy Young Award balloting along with a fourth-place finish in the MVP race. Derek Bell pilfered 27 bases and established personal-bests in BA (.334) and OBP (.385). Fellow outfielder Glenallen Hill clubbed 24 long balls and set career-highs with 86 RBI and 25 stolen bases. Geronimo Berroa clubbed 22 taters and knocked in 88 runs. Jeff Kent contributed 20 dingers and John Olerud socked 32 doubles.

On Deck

What Might Have Been – The “Original” 1902 Cubs

References and Resources

Baseball America – Executive Database

Baseball-Reference

James, Bill. The New Bill James Historical Baseball Abstract. New York, NY.: The Free Press, 2001. Print.

James, Bill, with Jim Henzler. Win Shares. Morton Grove, Ill.: STATS, 2002. Print.

Retrosheet – Transactions Database

The information used here was obtained free of charge from and is copyrighted by Retrosheet. Interested parties may contact Retrosheet at “www.retrosheet.org”.

Seamheads – Baseball Gauge

Sean Lahman Baseball Archive

One of the most common phrases in all of sports is “defense wins championships.” Defense isn’t flashy; it doesn’t put people in the seats (unless you’re a desperate Twins fan wanting to see Byron Buxton do more of this — or this). People like to see the home runs, the strikeouts. People also like to see the diving plays, but diving plays are a poor indicator of a team’s total defensive quality. So even the plays on defense that do put people in the seats aren’t indicative of a team’s overall level of defense. Other sports are the same way. People don’t realize the ins and outs of NBA defenses; they only see the steals and the lockdown plays — or lack thereof. NFL fans love to see big hits, but sometimes these big hits could be avoided if a team had defended the play better and stopped the ball carrier earlier.

Yes, it is true the nuances of defense can be monotonous, and this is true through all sports. Another factor about defense is the lack of a way to quantify defensive skill. Some metrics, like RPM (shameless plug to my boy Ricky Rubio, clearly a top-5 PG), try to do this for basketball. But in baseball, defense really is quantifiable, using different metrics that track can track how effective a defensive player or team is against league average. For example, read up on UZR, just one of the metrics that can put a number on a defense.

I came to this thinking on the undervaluation of defense through a different path. I had always wondered if an incredible defense could bail out an average pitching staff. I had always been interested in this facet; to reminisce, I once created an outfield of Torii Hunter, Rocco Baldelli, and Carl Crawford on MVP Baseball 2004. These were the best and fastest fielders in the game, and it seemed like they could get any fly ball. As much as I want to credit EA Sports for making an accurate game, I obviously cannot deduce the real-world effectiveness from a video game. Instead, I turned to the numbers.

To quantify how much a defense could “bail out” their pitching staff, I looked at the team’s average ERA compared to its average FIP. The difference between these numbers can somewhat quantify how much a team’s defense (and other factors) influence pitching from what we would expect it to be. For example, if a team had a FIP of 4.00, and an ERA of 3.50, this would indicate that a good defense was able to reach more balls than an average defense, meaning the team’s ERA should be lower, as there were more recorded outs than what we expect. The opposite, a team’s ERA being greater than its FIP, would indicate that a poor defense hurt their pitching staff’s performance, as they should have been able to get more balls that they did. To sum up, my hypothesis was that the teams with the largest FIP-ERA differences had great defenses, while teams that had the lowest FIP-ERA differences (negative values), had poor defenses. Now, I understand that many factors outside of defense can influence ERA, and that FIP does not perfectly match what a pitcher’s ERA would be with an average defense, but these anomalies will be canceled out in a large enough data set.

For the data, I measured playoff-contending teams (at least 85 wins) since 2002 (the furthest back I could get a value for a defensive rating) through 2015. From these teams, I parsed values for ERA, FIP, and defense, as well as the team’s payroll, runs scored, runs allowed, and run differential.

While taking my initial walks through the data, I saw two types of teams on this list. There were teams that scored few runs, but allowed even fewer, and there were teams that scored a host of runs, although they conceded a large, but lesser amount. The teams that scored little and allowed less had a common trend: they had great defenses and ERAs generally lower than FIPs. On the other hand, the teams that blasted the seams off the ball and had no problems putting runs on the scoreboard tended to have poor defenses, and their FIP-ERA difference was negative.

Using this data, I decided to run a regression analysis between a team’s defense and this FIP-ERA difference. There was a solid relationship between these two variables, with an r-squared of 0.48. This indicates that the difference between a team’s FIP-ERA difference tends to increase as the skill level of their defense increases.

Now we know correlation does not imply causation, but this relationship indicates the strength within this relationship. The better a team’s defense is, the more likely their defense will be able to positively influence their pitching staff’s performance. These were teams like the 2002 Atlanta Braves, the 2011 Tampa Bay Rays, or the 2004 and 2005 St. Louis Cardinals. These teams didn’t have great offenses, but they had great defenses, they had good team ERAs, and they prevented teams from scoring runs.

On the other hand, there were teams like the 2003 and 2004 Red Sox as well as the Mid-2000s Yankees. These teams were those with massive payrolls that paid a premium for a punishing lineup. These lineups, however, lacked defensive talent, causing their pitching staffs to underperform their expected performances, as their teams’ ERAs were higher than FIPs.

So how related is this FIP-ERA difference to the amount of runs allowed? Well, pretty strong, with an r-squared of 0.46. Again, a strong relationship, this time negative, indicating that as a team’s FIP-ERA increases, the runs that team allows decrease.

To reinforce this relationship, I looked at defense and runs allowed. Again, this relationship showed a good, not great relationship, with an r-squared at 0.28.

From these relationships, we can deduce that as a team’s defense rises in skill, the runs they allow tend to decrease and their team FIP-ERA difference tends to increase. Similarly, as a team’s FIP-ERA increases, the amount of runs a team allows decreases. From these relationships, we can conclude that these three variables are related.

As a team’s defense increases, they can positively influence the effectiveness of their pitching staff and will decrease their runs allowed. This may seem like common sense, and it probably is.

Now when we look at Bill James’ Pythagorean Win Expectation and other similar formulae, we notice that a team’s expected winning percentage is not dependent on the runs they score, but rather, their run differential. So yes, if you want to, you can construct a team like the Bronx Bombers and spend millions to assemble the some of the best lineups of recent history. If you’ll do that, you’ll hit score a host of runs, and with decent pitching and decent fielding (or below-average defense and good pitching — like those mid-2000s Yankees teams), you’ll be able to outscore your opponents and have a high run differential.

Or, you can assemble a team that will limit the amount of runs you’ll give up, by investing in defense. You will be able to compensate for average hitting and pitching, as you will boost your pitching staff’s effectiveness, and you will reduce the need for your offense to put up great numbers. Again, we have seen teams like this. The 2002 Braves were a combination of good defense, great pitching (aided by that defense), and average or perhaps even below-average offense; yet, this team won 101 games by scoring a mediocre 702 runs on the season (the average for the NL was 720 that season, 747 for all of baseball). Similarly, the 2011 Tampa Bay Rays put up 707 runs, against an American League average of 723, and still put up 91 wins and made the playoffs with good pitching and better defense. In fact, FIP would indicate their pitching was expected to perform right at American League average, a 4.08 ERA, yet they posted a 3.58 ERA.

Moreover, in that same season, the Los Angeles Angels won 86 games on just 667 runs, as they had even better pitching than the Rays. FIP would indicate the Angels’ pitching would be around a 3.94 ERA with league-average defense, but it was at a 3.57 ERA. The impact of good pitching paired with defense clearly is high, and I can’t think of one better, final example than the 2010 World Series-winning San Francisco Giants, who couldn’t have reiterated this structure any better: great pitching, great defense, and below-average offense.

So when one is trying to construct a team, and, unlike with the Yankees or Red Sox, money is a constraint, one might want to consider investing in defense. I say this because I looked directly at the relationship of a team’s payroll and their defensive ability, and it actually produced a negative relationship.

I know this data may be influenced by the fact that salaries have increased essentially every year in the span between 2002-2015, but if this truly did influence the graph, it would show either two things. Teams recently may have lessened their focus on defense and spent on hitting and pitching (explaining why defense-oriented teams had smaller payrolls); or, even with the rising caps, teams have still been able to assemble winning rosters by focusing on defense. Whether it is the first condition or the second, or perhaps a combination of both, perhaps defense is undervalued in today’s MLB. I doubt I’m the first to figure this one out, but the Cubs have far and away the best defense in baseball. Also, the Red Sox and Indians have stellar gloves as well, forming a solid second-tier level of defense that has put them in playoff position. So maybe Jason Heyward’s contract shouldn’t look so bad after all.

You don’t have to score a ton of runs to be a playoff baseball team. You just have to score more than the other team does, which can be done through limiting the amount of runs they score. It may seem like common sense, but common sense eludes us all at times.

There are many ways to construct a baseball team, and this might be just one more. And for stingy owners, it wouldn’t break the bank.

Last week, the Tampa Bay Times reported that the City of Dunedin and the Toronto Blue Jays put together a proposal that would keep the Blue Jays in Dunedin for another 25 years at a cost of $81 million dollars. The money invested in the project would be spent to upgrade the Blue Jays training facility, making it a year-round operating facility for the organization, and refurbish Florida Auto Exchange Stadium, expanding the stadium from 5,000 to 8,000 seats.

For nearly three years, my writing has taken a holistic view on baseball in Tampa Bay. I have taken to heart the premise of Major League Baseball and the mayors of our largest cities that Tampa Bay is a Major League region. In May of this year, I wrote an article for regional political website that asked whether local politicians believe this premise. I argued that unfortunately local politicians are acting in their own local self-interest and dividing Tampa Bay into four spring training/Minor League regions.

Last season, I wrote a post on another Rays blog that stated Tampa Bay is the fifth-most overextended sports market in America. The data for this post, from the American City Business Journals, stated Tampa Bay is currently $86 billion below where they need to be in personal income to support all the pro sports in the market. The study unfortunately did not include arena league football (Tampa Bay Storm), lower-level professional soccer (Tampa Bay Rowdies), and spring training, all of which locals in Tampa Bay spend money on.

This is why extending the Blue Jays in Tampa Bay is a bad idea. Allowing the Blue Jays to leave would allow other sports to receive fan dollars and aid their existence, removing one obstacle from an already overcrowded market. If the region values its major sports, it must allow the minor sports to walk away.

There are plenty of arguments used by the Blue Jays, the City of Dunedin, Bonn Marketing, and the team of hired economists that show why extending the Blue Jays is a good idea. This post will look at many of these points and provide alternate or opposing views.

Market Assumptions

In 2016, Blue Jays Spring Training attendance increased 5%. They were the only team in the Tampa Bay area that had a spring training attendance increase in 2016. Here is the Blue Jays spring training attendance since 2005.

First, the Blue Jays had their highest attendance the same year they had their most wins in 11 years. While this is not coincidence, there is little correlation between wins and attendance in previous seasons. This year, they again have a chance to win 90 games and make the playoffs. That should bode well for spring training attendance in 2017 and we can probably predict a similar turnout to 2016.

But what happens when the Jays stop winning? Will attendance fall below 5,000 again?

Second, the released economic studies detail how valuable spring training is to Pinellas County. The study states that of the over 70,000 fans that attended Blue Jays spring training, 79% resided outside of Pinellas County. These tourists brought in $70.6 million in income to Pinellas County.

If we subtract 5% from the $70.6 2016 income, we can estimate a $67 million impact in 2015. In 2015, the tourism total for Pinellas County was $4.65 billion.

Therefore in 2015, the Blue Jays accounted for 1.4% of Pinellas County’s tourism income.

The Dunedin-Blue Jays study fails to account for the other spring training venues. If 23,539 (32.4%) of the Jays spring training attendance stayed in Pinellas County, did they see the Phillies and Yankees who also train in the local region? If the Jays left, the region might only lose one night of visitors’ stay, not the entire 7.4 nights reported. Because of the other local teams, the Jays cannot assume they are the only cause of visitors.

Next, let’s breakdown the Blue Jays 2016 spring training attendance:

• 72,652 total
• Non-county attendance: 57,395 (78.9%)
• In county attendance: 19,257 (26.5%)
• Out of state: 23,539 (32.4%)
• In state/Out of county: 33,856 (58.9%)

While we can safely assume the out of state fans stay in local hotels, what about the “in state/out of county”?

Local Spring Training Market Conflicts

Of the Jays 16 games in Dunedin in 2016, 7 were against teams with local ties (Phillies, Yankees, and Rays). Fans for those games could have either been from Hillsborough County or stayed at a hotel to also see another team’s games.

As for the 19,257 Pinellas County residents that went to see the Blue Jays spring training in 2016, their money could be spent on any other leisure activity, to include supporting the Tampa Bay Rays regular season games a month later and 21.7 miles away.

Many spring training supporters do not understand regional money spent on spring training could be spent on the Rays. They argue that the Rays don’t train in Tampa Bay, so they are not potential gainers of local spring training spending. Proponents of this view need to understand that money in hand on March 30 does not disappear on April 1. Fans of 28 other teams (Arizona excluded) wait until April to spend leisure money on baseball. If they are fans of an out-of-town team, they wait until that team visits their local team. This spending behavior is done all over the nation.

Waiting until the Blue Jays visit Tropicana Field would help the Rays’ bottom line and support Major League Baseball in the region. When locals buy tickets to spring training, they are spending their annual leisure money on a replacement good available before the premium product is released.

In 2016, the Rays accounted for 60% of all baseball tickets sold in the Tampa Bay area. This was an increase from the 58% in 2015, but far from the 71% of tickets sold to Rays games in 2009 and 2010. As a small-market team, the Rays can’t afford to have that much revenue diverted from their pockets. The Dunedin-Blue Jays agreement might even decrease the Rays percentage and give them less market share.

According to the Tampa Bay Times, 40% of the $81 million cost will go to stadium renovations. The goal is to expand capacity at Florida Auto Exchange Stadium by over 30%. If the Jays sell-out every spring training game (highly unlikely, but possible), their total spring training attendance will be 112,000. This would place the Blue Jays on level with the Pirates in Bradenton, who play in 8,500-seat McKechnie Field. Florida Auto Exchange Stadium would still be smaller than Bright House Field in Clearwater and Steinbrenner Field in Tampa.

A key missing piece in the presentations provided by the Blue Jays and the City of Dunedin is expected attendance. Where is an indicator of increased demand? Just because they’ll build it, doesn’t mean fans will come.

If fans do fill the new 8,000 facility, does the city and the team expect an increased amount of out-of-state fans to visit the new stadium or do they expect the same ratio of demand?

Using the same ratio of people from Pinellas County (26.4%) and assuming 100% sell-outs, 29,568 local residents will be spending money on a substitute baseball product in March 2019 onward. That is 10,000 more tickets purchased by money that could be going to the local Major League team.

Florida State League Market Impact

Following spring training, the facility will still be in use for the Florida State League season. Attendance for Florida State League baseball in Dunedin has been less than stellar. From 2010 to 2015, the Dunedin Blue Jays ranked last in the Florida State League in total and per game attendance. They did not rank last in 2016 due to the relocation of the Lakeland Flying Tigers to a smaller facility while their home stadium was being refurbished.

The current population of Dunedin is less than 40,000. Dunedin is one of the smallest towns in America to host a Minor League team. To fill an expanded Florida Auto Exchange Stadium would mean 20% of the entire population would have to attend. That is a huge demand for a small town.

Only 5.4 miles from the home of the Dunedin Blue Jays is Bright House Field, home of the Clearwater Threshers. Although they rarely play on the same day (only seven times in 2016), these two teams are in direct competition for hyperlocal dollars. They are the same product at the same level for the same cost. The Clearwater Threshers, however, play in a stadium off a major thoroughfare and have excelled in promotions, enabling them to close in on Florida State League attendance records.

The Dunedin Blue Jays would have to increase attendance by at least 300% to match the Clearwater Threshers. Unless new fans are created, expanding Florida Auto Exchange Stadium would likely cannibalize the attendance of the Clearwater Threshers, especially when the Dunedin park is in its “honeymoon phase”.

Emotional Factors

The City of Dunedin promotes that Dunedin is the only location the Blue Jays have called their spring home in their 40-year existence. While this has emotional value, the Dodgers were in Vero Beach from 1949 to 2008 before moving to Arizona and Dodgertown was among the most revered spring training locations in Florida. Teams move; it is the nature of finding the best place for business.

While there may be a bond between the Blue Jays and the City of Dunedin, according to polling, that bond has not translated into support for the Blue Jays. According the New York Times/Facebook survey in 2014, the top three most “liked” teams in Zip Code 34698 are the Rays (49%), the Yankees (16%), and the Red Sox (6%).

Understandably, Dunedin Mayor Julie Bujalski does not want the Blue Jays to leave. She is an elected official and maintaining the status quo is preferred to a loss that could cost her in the next election. She also doesn’t want to be the mayor who lost local revenue provided by spring training, although there is dispute whether or not revenue actually is what team-sponsored studies say it is.

On the other hand, there are many reports of areas such as Winter Haven, Florida, that have lost spring training and not suffered at all economically. University of South Florida Economics Professor Phillip Porter has been often quoted saying that “nothing changes” when a team skips town. Doubtful the City of Dunedin contacted Porter. They did however, contact Bonn Marketing, a Tallahassee, FL marketing firm that has written positive reports about spring training in Florida since 2009.

Other Blue Jays Options

Instead of reinvesting in Dunedin, the Toronto Blue Jays had several other options. They could have done any of the following:

• Move to Clearwater and split the Phillies facility
• Move to Viera, Florida where the Nationals recently vacated
• Move to Kissimmee, Florida where the Astros recently vacated
• Move to Port Charlotte and split the Rays facility

Of these options, only moving to Clearwater would keep the Blue Jays in a Major League market.

Due to the closed nature of the Dunedin and Toronto Blue Jays negotiations, we will never know what other options the Blue Jays considered. All we know is what they want in Dunedin and that Dunedin seemingly bid against itself.

Conclusion

Contrary to what the City of Dunedin, the Toronto Blue Jays, Bonn Marketing, and their hired economists have promoted, extending the Blue Jays in Dunedin is a bad idea. Until the Tampa Bay Rays are a successful franchise and have the same potential revenue as other small-market teams, local officials should decline renewal of spring training facilities in Tampa Bay. They should stop hedging their bets against the Rays and providing local residents inferior baseball goods in which to spend their money.

Even with tourism, Tampa Bay is not a big enough market to support Major League Baseball, four spring training facilities, and four Minor League teams. Declining to renew the Blue Jays and allowing them to find a new home in Florida is in the best interest of the region.

I was looking into a separate but overlapping issue when I ran into the puzzling home run question. As has already been pointed out in prior research, exit velocities (EV) are up about a half a mile per hour over the last year; however, for most, this is not really a satisfying conclusion given the relatively small expected distance change from that amount of an EV increase. There has to be more to the story.

My other overlapping project was initially looking into loft. There seems to be an organizational push for more loft and players have made comments along these lines. Although the benefits of loft in terms of incremental runs are well-known, there has been very little discussion of the cost side of the equation – what is a player sacrificing in terms of optimal bat path / ball path matching? Of the three ways to generate loft, what is the cost for each and how do they rank? More to follow on all that in another article.

Organizations and players have touted backspin even longer than the more recent focus on loft. In terms of additional distance from backspin, it is significant. Research by Alan Nathan indicates spin could add 30-50 ft starting from a low spin rate. What if backspin was a key piece in the missing home run puzzle?

Since spin rates on hits are not yet available, I created a Distance Model based on EV and LA data from Baseball Savant where combinations of both EV and LA could be held constant (to a tenth) in order to separate out Unexpected Distance where spin is likely the largest component. I excluded all balls hit at Coors Field and focused on balls hit 90 MPH or more between the launch angles of 15 and 45 degrees. The Unexpected Difference was calculated for each hit in the range above for 2015 and 2016. Since the data showed a clear bias depending on the location of the hit, I made the following adjustments to take out directional bias based on the 2015 data:

Hit Location          Directional Bias (Ft)

Pull-Side Gap                   +17

Oppo-Side Gap                 + 7

Center                                + 7

Pull                                    –  6

Oppo                                  -12

Clearly, balls hit predominantly with backspin have more lift than those hit flat or with side-spin. Considering that Coors Filed alone was a +17.5 average difference, the average ball hit to the pull-side gap is about the same magnitude as hitting at 5,200 feet. Just for fun, I ran the Unexpected Distance for a pull-side gap hit at Coors Field — a whopping 39.8 feet!

Analysis of Launch Angle Buckets

On the whole, exit velocity, launch angle and distance on well-hit balls (>=90 MPH and >=15 degree LA) are all little changed from last year. However, the launch-angle buckets indicate that backspin is likely a factor, particularly in the 30-35 and 35-40 degree segments which account for a combined 58% of the increase in HRs over 2015 while only representing a combined 32% of the categories. Additionally, the majority of the 6ft and 7ft increase in these categories, respectively, are coming from the Mean Unexpected Distance (MUD) — or most likely spin.

Note: Home runs in both years only include those with EV and LA data.

Looking at the distribution of balls in the launch-angle groups over the past two years, there has been very little movement between the groups other than a slight move from the lowest to the highest group (below).

Distribution of Balls Hit >=90 MPH and >=15 Degrees

As reflected in the data, it is not that there are significantly more lofted balls being hit but the ones in the 30-40 degree range are being hit with significantly more backspin relative to last year.

In diving into the home runs in the 30-40 degree category for both years, I was expecting to see players with either high or increasing MUD values. While there were some of those players…

HRs in the 30-40 Degree Group (Backspin Gainers)

There were also some in the “flat” hitting group that were simply just hitting the ball “less flat than last year” that are showing up in the positive MUD change group…

HRs in the 30-40 Degree Group (Flat Hitters – Hitting Less Flat)

At this point, I was about to conclude that spin is definitely a factor but it could just be noise rather than an organizational push for more loft and/or backspin…and then I read Jeff Sullivan’s post the other day and now it all fits! Look at the table below of the players with the highest and lowest MUD values for 2016 and see if you can find it.

Yes, of course! The answer is that it is not just because chicks dig the long ball, it’s that the market that values the players digs the long ball. Notice the significant difference in the exit velocities of the two groups. The players who are relying on spin are doing so because they have to get more distance and HRs out of their existing tool kit and are willing to pay (in terms of consistency) in order to get it. The players with higher exit velocities and hence more “natural power” can continue in their square hitting ways since they have no need to pay a high price for something they already possess. I didn’t average the height and weight of the two groups but I think it is clear that the backspin group is significantly smaller in stature than the flat-hitting group. Note the 2 ft average distance advantage of the backspin group with a whopping 3.4 lower average MPH difference!

Another interesting tidbit from the above data is the average launch angle is significantly lower for the higher backspin group. While this may seem counter-intuitive, it actually makes complete sense – in order to get backspin, you have to have less loft in the swing and rely on the ball contact point for loft. Since this is no easy feat, balls will tend to come off the bat with more variability with many hits matching the amount of loft in the swing and hence a lower trajectory.

What is happening with the home run issue is not randomness that is going to revert to the mean. It is a secular trend that is the result of the incentives in the system. Hitting for average with no power is out of style and players, particularly those with lower EVs, are likely responding by getting the ball out of the park any way they can – whether it is swinging harder, utilizing more backspin, or hitting to the shorter (pull) side of the field. (Could the latter be the next big trend?) While there will likely be additional findings regarding the home run question, the way I see it, at least part of it is as clear as MUD.

After reading through Projecting X by Mike Podhorzer I decided to try and predict some rate statistics between minor league levels. Mike states in his book “Projecting rates makes it dramatically easier to adjust a forecast if necessary.”; therefore if a player is injured or will only have a certain number of plate appearances that year I can still attempt to project performance. The first rate statistic I’m going to attempt project is walk rate between minor league levels. This article will cover the following:

Raw Data

Data Cleaning

Correlation and Graphs

Model and Results

Examples

Raw Data

For my model I used data from Baseball Reference and am using the last seven years of minor league data(2009-2015). Accounting for the Short-Season A (SS-A) to AAA affiliates I ended up with over 28,316 data points for my analysis.

Data Cleaning

I’m using R and the original dataframe I had put all the data from each year in different rows. In order to do the calculations I wanted to do I needed to move each player’s career minor league data to the same row. Also I noticed I needed to filter on plate appearances during a season to make sure I’m getting rid of noise. For example, a player on a rehab assignment in the minor leagues or a player who ended up getting injured for most of the year so they only had 50-100 plate appearances. The minimum plate appearances I ended up settling on was 200 for a player to be factored into the model. Another thing I’m doing to remove noise is only attempting to model player performance between full-season leagues (A, A+, AA, AAA). Once the cleaning of the data was done I had the following data points for each level:

• A to A+ : 1129
• A+ to A: 1023
• AA to AAA: 705

Correlation and Graphs

I was able to get strong correlation numbers for walk rate between minor league levels. You can see the results below:

• A to A+ : .6301594
• A+ to AA: .6141332
• AA to AAA: .620662

Here’s the graphs for each level:

Model and Results

The linear models for each level are:

• A to A+: A+ BB% = .63184*(A BB%) + .02882
• A+ to AA: AA BB% = .6182*(A+ BB%) + .0343
• AA to AAA: AAA BB% = .5682(AA BB%) + .0342

In order to interpret the success or failure of my results I compared how close I was to getting the actual walk rate. FanGraphs has a great rating scale for walk rate at the major league level:

The image above gives a classification for multiple levels of walk rates. While based on major league data it’s a good starting point for me to decide a margin of error for my model. The mean difference between each level in the FanGraphs table is .0183. I ended up rounding and made my margin for error .02. So if my predicted value for a player’s walk rate was within .02 of being correct I counted the model as correct for the player and if my error was greater than that it was wrong. Here are the models results for each level:

• A to A+
  • Incorrect: 450
  • Correct: 679
  • Percentage Correct: ~.6014
• A+ to A
  • Incorrect: 445
  • Correct: 578
  • Percentage Correct: ~.565
• AA to AAA
  • Incorrect: 278
  • Correct: 427
  • Percentage Correct: ~.6056

When I moved the cutoff up a percentage to .03 the model’s results drastically improve:

• A to A+
  • Incorrect: 228
  • Correct: 901
  • Percentage Correct: ~.798
• A+ to AA
  • Incorrect: 246
  • Correct: 777
  • Percentage Correct: ~.7595
• AA to AAA
  • Incorrect: 144
  • Correct: 561
  • Percentage Correct: ~.7957

Examples

Numbers are cool but where are the actual examples? OK, let’s start off with my worst prediction. The largest error I had between levels was A to A+ and the error was >10% (~.1105). The player in this case was Joey Gallo. A quick glance at the player page will show his A walk rate was only .1076 and his A+ walk rate was .2073 which is a 10% improvement between levels. So why did this happen and why didn’t my model do a better job of predicting this? Currently the model is only accounting for the previous season’s walk rate, but what if the player is getting a lot of hits at one level and stops swinging as much at the next? In Gallo’s case he only had a .245 BA his year at A-ball so that wasn’t the case. More investigation is required to see how the model can get closer on edge cases like this.

The lowest I was able to set the error to and still come back with results was ~.00004417. That very close prediction belongs to Erik Gonzalez. I don’t know Erik Gonzalez, so I continued to look for results. Setting the min error to .0002 brought back Stephen Lombardozzi as one of my six results. Lombo’s interesting to hardcore Nats fans (like myself) but I wanted to continue to look for a more notable name. Finally after upping the number to .003 for A to A+ data I was able to see that the model successfully predicted Houston Astros multi-time All-Star 2B Jose Altuve’s walk rate within a .003 margin of error.

What’s Next:

• Improve algorithm for generating combined season dataframe
• Improve model to get a lower error rate
• Predict strikeout rate between levels
• Eventually would like to predict more advanced statistics like wOBA/OPS/wRC+

When we were growing up, my dad would sometimes refer to my sister and me as ingrates. I always had a sneaking suspicion that statement was ruthless. I was young and under the assumption that he provided us everything we needed and wanted because that was what he was designed to do. In a sense, that perception of him probably does reflect the “ungratefulness” that young children tend to posses, innocent as it may be, what with a child’s inherently feeble comprehension of interpersonal relationships. I am now the parent of a two-year-old boy and just the other night he saw a commercial for a Power Wheels Jeep Wrangler that elicited the following outburst:

“I want to go in there!”

“I want one!”

Finally he turned to peer into my eyes and, in order to accentuate the severity of his next mandate, he raised his index finger and spoke;

“Daddy, better buy me one.”

His tone became dramatically more somber than it had been for the first two exclamations, and it made me laugh the hardest. I am certain I was the narrator of many statements similar to this as a kid, but the reality is, when kids are given everything they want, it’s up to the parent to understand that if there is a perceived lack of gratitude, it is a direct byproduct of the parent’s efforts to make them happy or even to keep them alive.

Lately I’ve been thinking of how I can be really ungrateful for even truly fine baseball seasons. Even some All-Star seasons disappoint me, and I know I’m not alone. If Mike Trout was in the middle of putting up a 5-win season, we’d all be talking about what could be wrong with Mike Trout. When players set the bar so ridiculously high we tend to hold them to that standard for better or worse. As an actual example, it’s completely understandable to be disappointed by Bryce Harper’s 2016 season after last year’s masterpiece. The reality is, however, that he’s 23 and has currently produced 3.4 WAR. His baserunning and defense have been positives and he’s compiled over 20 home runs and 20 stolen bases while hitting 14 percent better than league average; that’s damn fine and yet it’s still a damn shame.

Paul Goldschmidt, meanwhile, is hitting .301/.414/.494 and has accrued 4.7 WAR and might surpass 30 SB this year. His 136 wRC+ is still great even if it’s not quite the 158 he’s put up over the last three seasons. So why do I feel the loathsome inklings of disappointment bubbling inside of me? Firstly, and admittedly shallow of me, I like my Goldschmidt with more extra-base hits. For the first time in his professional career, at any level, Goldschmidt’s ISO starts with a number under 2. It’s possible he has a nice final week and brings that number up into the .200 range, but there are still some potentially concerning blips in his batted-ball profile that could portend of further decline in production. What I’m referring to most specifically, as the title suggests, is that Paul Goldschmidt has developed a pop-up problem.

From 2011 through 2015, Goldschmidt’s cumulative IFFB% was 4.8%. This year it sits at 14%. He has 17 IFFB this year, which is the same amount he had in the three previous seasons combined. Pop-ups aren’t good as they’re essentially as productive as a strikeout. Here are the 10 players with the biggest increases in IFFB% in 2016 compared to 2015 among qualified hitters in both years.

I’m not suggesting there’s a positive correlation between popping up and performance, but it’s easy to make sense of some of the names that appear on this list. If you watched Josh Donaldson break down his swing on the MLB Network, you know that a lot of players are thinking about not hitting the ball on the ground because damage is done in the air. Did you know that DJ LeMahieu, at the time of this writing, has a higher slugging percentage than Goldschmidt? That’s bonkers. The league’s slugging percentage last year was .405, and this year it’s .418, but this group of players, minus Goldschmidt, have added, on average, 21 points to their slugging percentage, and part of that, for this group, has to be chalked up to putting more balls in the air.

What I’m hoping to highlight is that what is even more troublesome for Goldschmidt is that he is the only player in this top 10 who had an increase in their IFFB% while also seeing his fly-ball rate and hard-hit rate drop.

So I have what could be an insultingly obvious hypothesis: since Goldschmidt has long been a quality opposite-field hitter, I am theorizing that pitchers are exploiting him with more fastballs up and in where he can’t quite get his hands extended. A cursory glance at his heat map vs. fastballs in 2015 and 2016 reveals a minor shift in approach by the league.

 

Besides the obvious, which is that pitchers are avoiding the zone even more than they had before, we can see just a bit more red in the specific zone I was referring to. It’s not so glaring or even enough information to make any conclusions, so let’s see if that area is where pitchers are getting Goldy to pop up. On the year, per Brooks Baseball, he has 22 pop-ups, 19 from fastballs and three from offspeed pitches. The 17 that are classified as IFFB by FanGraphs are plotted in the graph below.

*the two pitches towards the outside corner (for Goldschmidt) are sliders.

However, it’s not as if pitchers have previously avoided throwing Goldschmidt up and in; it just appears, despite his overall swing rate being at a career-low 39%, he’s upped his swing rate against fastballs by over five percentage points in that specific area just above 3.5 ft. And that area has the largest concentration of his pop-ups.  Looking at the entire area middle/up/and in to Goldschmidt, he has increased his swing rate from 57.2% in 2015 to 60.7% in 2016 while staying away from lower pitches in general. It’s a philosophy that is being echoed throughout baseball right now, and it is not at all a bad plan, but it has caused him, either deliberately or due the effect of swinging at these pitches more often, to go to the opposite field this season less than he ever has. This also is not necessarily a negative shift in regards to a batted-ball profile, but from 2013 – 2015 Goldschmidt was the fifth-most productive hitter in baseball going the other way, and in 2016 he’s 33rd. That represents a drop in wRC+ from 204 to 158, and from a .729 SLG (.329 ISO) to a .647 SLG (.255 ISO). I’ve long since regarded Goldschmidt to be in the same tier of hitters as Trout, Votto, Cabrera, and pre-2016 McCutchen, and it would be a shame for him to move away from a facet of his game that enables him to produce at that elite level.

At the end of this season I don’t think I’ll actually be all that worried about Goldschmidt; I can reconcile a 136 wRC+, even if it would feel a little disappointing. I wrote about Paul Goldschmidt last year and I wasn’t worried then, either. But I do think if I’m going to take a 136 wRC+ for granted I should place that appreciation toward the catalyst for this change in Goldschmidt’s performance, and a lot of that credit has to go to the pitchers who have induced 17 IFFB from a player who only averaged 5.7 over the last three seasons.

Now I know that setting up a pitch has so much more to do with an entire at-bat, game, or even season than the pitch that was thrown immediately before it, but for this exercise I want to look at the pitch that caused Goldschmidt to pop up and how it relates to the pitch thrown immediately before it. It’s crude and does not tell the whole story, but it still shows a definite approach — and, for all intents and purposes, it’s probably a decent representation of a general tactic used across the league for inducing pop-ups. I found all the data I needed using PITCHf/x at Brooks Baseball and I recorded the velocity, horizontal movement, vertical movement, horizontal location, and vertical location of each pitch Goldschmidt popped out on as well as the same data set for each set-up pitch if there was one (which would be in any situation where Goldschmidt did not pop up on the first pitch of an-bat). Below you’ll find a plot that shows the average location and characteristics of each pitch.

And here is that data in a table represented as the average difference between the two plot points.

Doesn’t it make you feel warm when something fits into the shape you had pegged it to be? That’s just really simple and makes a hell of a lot of sense. Or maybe I feel warm for taking something that was disappointing and turning it into something I can really appreciate.  Now if you’ll excuse me, I have a Power Wheels Jeep Wrangler to buy.

(Author’s note: This analysis was originally published on the Baseball-Fever forum a year ago. I thought it might be of interest to the FG community.)

As I have perused the all-time list of career WAR, one feature has always struck me as odd and in need of some explanation: catchers are much lower than other position players. The highest career WAR (I’m using FG WAR or fWAR here, but BBRef’s rWAR makes the same point) of any catcher is Johnny Bench, who comes in at 42d among all position players, at about 75 WAR. That is not just lower than the highest career WAR at any other position. It’s less than two-thirds the next lowest WAR; moreover, every other position has multiple players with higher career WAR, the fewest being SS with four (and that doesn’t include Alex Rodriguez, who I count here as a third baseman).

The following table, which compares the top ten players in career WAR at each position, provides further perspective (If a player is listed at more than one position, I included him only in the position in which he played more. Since the corner outfielders comprise two positions, I took the average of the top two as highest, and the average of the top 20 as equivalent to the average of the top 10.):

Table 1. Top 10 Players in Career WAR by Position

Pos       Ave. PA     Highest WAR     Ave. top 10    Ave./700 PA

C               8677              74.8                     63.4               5.11

1B           10,137             116.3                     85.9              5.93

2B          10,458             130.3                    88.1              5.90

SS           10,440             138.1                    81.1               5.44

3B           10,534             114.0                    86.9               5.77

CF            10,210            149.9                    97.5               6.68

L/RF        11,267            166.4                    98.5               6.09

Except for catcher, the highest career WAR at every position is well over 100. Moreover, if we take the average WAR of the top 10 at each position, catcher again is well below the others. In fact, on that basis, there seem to be three general groups. The highest values are clearly associated with the OF. The highest WAR values of all time were achieved by outfielders, and the average WAR of the top ten center fielders as well as of the corner fielders is nearly 100.

A second group is comprised of all the infield positions. The highest WAR values of players in any position in this group are somewhat lower than the highest values of outfielders, but are roughly equal to the highest values at any other position in this group. Thus the highest WAR values range from about 115-140, and the average WAR of the top ten at each position ranges from 81-88, with an overall average of 85.5. This is 87.3% as high as the average value of the OF.

Finally, catchers are clearly in a class by themselves — and not in a good sense. As noted earlier, the highest career WAR attained by any catcher is only about 75, and the average of the top ten is about 63. This is less than two-thirds as high as the average value of the outfielders (64.8%), and about three-quarters as high as the average value of the infielders (74.2%).

At first glance, this ranking might not seem surprising. For most players, hitting is by far the most important component of WAR, and outfielders are on average better hitters than most infielders, who in turn are on average better hitters than catchers. But these differences are supposed to be compensated for by positional adjustments. For example, catchers are given more positional runs than players at other positions, and corner outfielders are given fewer positional runs than players at all other positions except first base. Specifically, the positional run benefit has the following general ranking: C > SS > 2B/3B/CF > LF/RF > 1B.

This raises the question, if these positional adjustments are approximately correct, why don’t the best catchers have about as much career WAR as the best outfielders? In fact, why are there significant differences also between outfielders and infielders? I will explore these discrepancies here.

This is not just an academic question. The relatively low WAR values for catchers have implications for their HOF chances. Assuming that WAR has some meaning for HOF voters — and even if some of them aren’t fans of this approach, they may still evaluate players using stats that are ultimately reflected in or correlated with WAR — they must either select fewer catchers than players at other positions, or set the bar somewhat lower for catchers. Based on the current HOF composition, one could argue that a little of both are occurring. Thirteen catchers are in the HOF, which is the lowest of any position except third base, which has 11. On the other hand, the mean WAR value for these catchers is about 50, well below the overall mean for the HOF of about 60. Moreover, 70% of the catchers in the HOF have a WAR of less than 60. No other position has more than 50% of its members below this value.

So it may be that, consciously or not, HOF voters think the best catchers are not quite as good as the best players at other positions, yet at the same time, go a little easier on them than they do on other players. I hope the following discussion will shed some light on how we are to understand the value of players at this position, which everyone recognizes as the most important one on the diamond for everyday players.

Positional Adjustments
I posed the issue earlier by pointing out that if one takes the positional adjustments seriously, one would think that the best players at every position would have about the same WAR. Though players at some positions don’t hit as well as players at other positions, they get extra value for playing what is considered a more difficult position. The positional adjustments are supposed to correct for the differences in hitting.

One might therefore first wonder if the positional adjustments are simply wrong, that catchers need to be given more runs. While this is a possibility — there has been some interesting work recently re-evaluating these adjustments — the amount of correction necessary appears far too large. For example, the difference between the average WAR of the top ten catchers and the average WAR of the top ten shortstops is about 18. The average length of the catchers’ careers is about 2200 games, or 13-14 full seasons, so to bring the catchers’ WAR up to that of the shortstops, one would have to give them an additional positional adjustment of about 1.3 WAR, or 13 runs, per year. That is two and a half times the current difference in positional runs between the two positions of 5 runs. An even larger adjustment in absolute though not relative terms would be necessary to bring the catchers’ WAR up to that of the outfielders.

Now the recent appreciation of pitch-framing — the ability of some catchers to receive the ball in such a way that a borderline call is more likely to be called a strike than it would if it were not for the catcher’s manipulations — could in fact add that much WAR, if not more, to the totals of some catchers. But that is not really relevant here, because when the positional adjustments were first developed, they did not (and still don’t) take into account pitch-framing. That is, it was assumed that even without pitch-framing, the positional runs actually given the catchers were adequate, and if pitch-framing does become adopted by the major sabermetric sites, it won’t be to compensate for some perceived shortage in positional runs.

That said, even before efforts to quantify pitch-framing were developed, it was recognized as a valuable skill by many observers familiar with the game. And it’s conceivable that when HOF voters decide on their choices, one reason that they’re fine with selecting catchers who, by WAR or by more traditional stats, may be inferior to some position players who are not chosen is that they feel that there is some hidden value in catching that WAR or traditional stats are not capturing. And pitch-framing could be a large part of that value. I won’t discuss pitch-framing further, but I think this is an important point to keep in mind.

Do Catchers Decline Faster than Other Players?
A second reason why the best catchers have lower WAR values might be that because of the demands of their position, they decline with age sooner and/or faster than other players, and thus don’t accumulate enough counting stats to finish their careers with really high WAR levels. Table 1 provides some support for this. The average number of PA by the top ten catchers, 8677, is significantly less (15-20%) than the average number of PA by the top ten at any other position, which ranges from about 10,000 to 11,000. If we normalize the WAR values per 700 PA, the differences between catchers and other position players are therefore reduced. However, catchers are still lowest, and they are quite a bit lower than all the other position players except for SS.

Of course, if catchers do decline sooner and/or faster than players at other positions, this might affect not only their counting stats, but their rate stats as well. How would we assess this possibility? If that were the case, one might expect that the WAR differences that do exist between them and other position players would be reduced if not eliminated earlier in their careers. It’s widely accepted that age-related decline in production begins in the late 20s. Traditionally, it has been thought that players improve steadily in their early 20s up until that age; more recent evidence suggests that players may actually peak at a younger age, then stay more or less at a plateau until their late 20s. But in any case, there is no evidence of a decline much before the late 20s, barring, of course, injuries or other health problems.

Accordingly, I next examined career WAR values at each position through age 27. As before, all OF comprise one group, and the highest WAR and average of top ten were modified for this group accordingly. I also remind the reader that the ten players in each group are not all the same players as the ten in the career cohorts shown in Table 1, though there is substantial overlap. That is, the leaders in WAR through age 27 are not necessarily the ultimate winners, as determined by career totals.

Table 2. Top 10 Players in WAR by Position Through Age 27

Pos   Average PA      Highest WAR     Ave. top 10     Ave./700 PA

C            4029                     50.4                   31.7                    5.51

1B           4115                      64.6                   39.8                   6.77

2B          3976                     64.6                    37.9                   6.67

SS          4937                     62.0                    38.0                   5.39

3B          4326                     53.5                    39.8                   6.44

CF          4921                     68.8                    51.3                    7.30

L/RF     4365                     68.3                    41.9                    6.72

Compared to the WAR values for full careers (Table 1), a number of differences are apparent in this table. First, the average PA for catchers is now about the same as that for several other positions, including 1B and 2B, and not much different (< 10%) from that for 3B or corner outfielders. This is consistent with the possibility that their lower average career PA results largely from earlier or faster decline, since if that were the case, we would expect to see less, if any, of this decline through age 27.

Interestingly however, the best SS and CF have a much larger number of average PA than players at all other positions. This might be because players at these two premier positions develop sooner, but I won’t pursue this further except to point out that this relationship is reversed later for CF. That is, if we compare Table 2 with Table 1, we see that while the top ten CF through age 27 had more PA than the corner outfielders, the latter had more at the end of their careers. When we normalize for PA, the CF are clearly higher than the corner outfielders, as well as any other position, but because their PA drops relative to corner outfielders as they age, their total career WAR values are comparable. One could speculate that CF decline a little faster because of the greater amount of outfield territory they’re expected to cover.

Second, the WAR differences observed over the full careers of these top position players are quite evident even at this earlier age. The average WAR of the top infielders through age 27, 38.8, is 86.2% the average WAR of OF, very similar to the 87.3% observed when comparing over a full career. Actually, the average WAR of IF is fairly close to the average WAR of the top corner outfielders, but as I noted above, the average WAR of the best CF at this age is much higher. Thus the ratio of the IF WAR to CF is only about 75%.

Similarly, the average WAR of catchers, 31.7, is 70.2% of the average WAR of OF, a little but not too much higher than the 64.8% observed over a full career, and much lower relative to CF, about 60%. The C WAR is also 81.7% of the average WAR of all the top IF taken together, compared to 74.2% for the career comparisons. While the highest WAR for a catcher through age 27 is much closer to the highest WAR at other positions at this age, indeed, is almost as high as the highest value for 3B, this value appears to be an outlier, as it is much higher than the next-highest value for a catcher at this age.

This finding of large WAR gaps between catchers and other players even at a young age is somewhat surprising, because it suggests, contrary to the evidence discussed earlier, that the lower WAR values for catchers are not in fact the result of an accelerated decline — not unless this decline begins much sooner than age 27. In fact, based on this evidence, it appears that most catchers produce lower WAR from the get-go.

A third conclusion we can draw from Table 2 is that the general order of OF > IF > C is for the most part preserved when WAR values are normalized for PA, though some of the differences are reduced. However, the normalized WAR value for SS at this age is much reduced, in fact, is a little lower than that for C. So the general order is now OF > 1B/2B/3B >> C/SS.

Offensive and Defensive Components of WAR Differences
To summarize the discussion so far, career WAR values generally trend as OF > IF > C. If the values are normalized for playing time, the differences are reduced somewhat in some cases, but the general order remains the same. If we consider WAR just through age 27, the order is still the same, OF > IF > C. If we normalize these values for playing time, the order is still generally preserved, except that now SS join catchers as the lowest group.

The fact that the order is generally preserved at age 27 suggests that while decline might be an issue for catchers — because of the lower average PA for their careers — some other factors must play a major role in accounting for the WAR gap. At this point, we need to look more closely at how WAR is determined. WAR at FG has four main components: offensive runs, defensive runs, league runs and replacement runs. Replacement runs are proportional to PA, and thus won’t account for any differences between players and groups when WAR is normalized for the same amount of PA, though they will add to differences when total PA are different. The same is true for league runs, which are a very minor component, anyway.

So let’s look at offensive and defensive runs. Offensive runs include batting runs and baserunning runs, and defensive runs include fielding runs and the positional adjustment. In the table below, I have listed the top 10 in career WAR at each position, the same groups that appeared in Table 1. For each group is shown offensive runs, defensive runs, fielding runs and positional runs. I have also listed the average wRC+ for each group of ten. This is a rate stat that measures hitting, so is useful to compare among the best players at each position.

Table 3. Offensive and Defensive Performance of Top 10 Position Players

Pos      wRC+    Off Runs     Fielding Runs     Pos Runs     Def Runs  Pos Runs/700PA

C           122          200.6               32.7                     79.2              111.9             6.39

1B          147          579.4               46.8                 -106.1               -59.3           -7.32

2B         132          427.6                40.5                   40.8                 81.3            2.73

SS          121          264.7                78.6                   112.1               190.7            7.52

3B         128          388.5               93.8                    22.8               116.6             1.52

CF         143           591.9                65.4                  -39.3                26.1            -2.69

L/RF     147           653.1                51.9                  -111.9             -60.0            -6.95

Consider wRC+ first. Notice that as expected, the best hitters are first basemen and corner outfielders, who have the highest positional adjustment. The center fielders are close behind, followed by the second and third basemen, while shortstops and catchers are the lowest, and also very close to each other. So the ranking is 1B/L-RF > CF > 2B > 3B > SS/C, which compares fairly well with the positional adjustments of 1B > L-RF > 2B/3B/CF > SS > C. The most significant discrepancies are that CF are somewhat better hitters than indicated by their positional adjustment, while SS are somewhat worse.

Now let’s turn to offensive runs. This includes baserunning as well as hitting, and since it’s a counting stat, it also reflects PA. The order is similar to that with wRC+, except corner fielders now are ahead of first basemen, who even trail center fielders slightly, and shortstops are ahead of catchers: L-R/F > CF/1B > 2B/3B > SS > C. This makes sense if we assume that outfielders, particularly center fielders, tend to be better baserunners than first basemen, and shortstops tend to be better baserunners than catchers; this can be confirmed by comparing the baserunning values of these groups (not shown). In addition, the top ten SS, as we have seen earlier, have a significantly larger average PA than catchers, so even if they are no better as hitters, they will accumulate more total value through hitting.

So some of the WAR difference between catchers and infielders, particularly SS, results from greater offensive runs, a reflection mainly of more playing time and, to a lesser extent, of better baserunning. In fact, the difference of about 60 runs corresponds to about 6 WAR. Recall that I showed earlier that the top ten catchers average about 18 WAR less than the top ten SS. So about one-third of this difference comes from offense, and mostly simply because of more playing time (because most offense is hitting, and by wRC+, the two groups are the same).

Now consider defense, where things get interesting. Defensive runs at FG are the sum of fielding runs, which evaluate a player’s actual defense, and positional runs, which vary according to the position. Catchers have a large total here (average about 112), which is to be expected, given that they have a large number of positional runs, about 80 on average. Note, though, that the top ten 3B have a slightly larger average number of defensive runs than catchers (about 116), and the SS have a much larger number (about 190). Why is this?

From the positional runs total, we can see that catchers have a much larger total than 3B, as would be expected, since their positional adjustment is much greater. The third basemen, though, have a much higher total of fielding runs, nearly 100 on average, vs. a little over 30 on average for the catchers. In other words, the top ten 3B were on average much better defensively at their position than the top ten catchers were at theirs, and this more than compensates for their lower positional adjustment. I will return to this point later.

SS, on the other hand, have a higher total of positional runs than catchers (about 112 on average), as well as of fielding runs (nearly 80). So on average they, like the third basemen, are also better defensively than the catchers. But how can shortstops have a higher total of positional runs than catchers, given that the latter have a higher positional adjustment? Clearly, because catchers don’t play every game at that position. They are sometimes rested by moving them to another defensive position, and that position is usually the one with the worst positional adjustment: first base. Thus it doesn’t take a lot of time at that position to have a significant impact on a catcher’s net positional adjustment.

How much impact? From the last column in the table, we can see that the top ten catchers averaged about 6.4 positional runs per full season over their career. This compares to the current positional adjustment of 12.5 runs that would be given them if they played exclusively at catcher. Since first base has a positional adjustment of -12.5 runs, we can estimate that the top ten catchers played an average of about 25% of their time at first base. The SS, in contrast, had a career positional adjustment of 7.5 runs, which is just about what they should have playing full time at that position.

The net result is that SS average about 80 defensive runs more than catchers (from the table, 190.7 – 111.9). This accounts for another 8 WAR or so in their differences, bringing the total up to 14 (6 for offense plus 8 for defense). We saw earlier that the top SS on average accumulate about 18 WAR more than the best catchers. Where do the other 4 WAR come from? Replacement. As was shown in Table 1, the top ten SS on average had about 1800 more PA than the top ten catchers. This corresponds to roughly 50 more replacement runs, or about 5 WAR, close enough for this rough estimate. Since all of the difference in replacement runs (50), and most of the difference in offensive runs (60, from Table 3) is due to the greater playing time of the SS, we can say that roughly 60% of the WAR difference is due to this greater longevity, and the other 40% (80 runs, from Table 3) to better defensive value. Of the latter, a little more than half results from better defense (45 more fielding runs, from Table 3), and the remainder from a net positional advantage (33 more runs, Table 3).

The other positional run averages shown in the table are fairly easy to account for. For second basemen, it’s about 2.7 runs, slightly higher than the 2.5 value for this position. This could reflect some time playing SS for some of these players, or higher positional adjustments in the past. I haven’t looked into the historical trends in positional runs, and am just going on what are generally considered the current values. For third base, it’s 1.5 runs, slightly lower than the 2.5-run adjustment, and may reflect a little action at 1B or in the OF. The negative value for CF, which have a positive positional adjustment of 2.5 runs, is not unexpected, because most CF play part of their careers, particularly as they get older, at the corners, where the adjustment is negative. The higher negative positional runs of the corner outfielders is of course expected. It’s actually slightly higher (less negative) than the positional adjustment of -7.5 runs, which probably reflects that most corner fielders have played a little at CF. Since the difference in adjustment between these two positions is 10 runs, the corner outfielders would only have to play CF about 5% of the time to bring their positional run average up to -7.0.

Summary
We’re now in a position to understand why the greatest catchers finished their careers with lower WAR than the best players at any other position, despite having the advantage of a greater positional adjustment. One factor, which I discussed earlier, is that on average they had fewer PA than other players, by about 15-20%. When we normalize WAR to PA, catchers are still the lowest, but the differences are reduced somewhat. We came to the same conclusion by showing that about 60% of the WAR difference between catchers and shortstops is due to offensive runs and replacement runs, which are mostly a reflection of more PA for the SS.

In addition, though, catchers rarely get full advantage of their positional benefit, because they play some of the time at another position, generally first base. Many catchers may move permanently to this position later in their career, but even when they are younger, they are likely to put in some time at 1B. This, I suggest, is a major reason why we find that even at age 27, when they should be at their peak and when they have played a comparable amount of time to players at several other positions, catchers still lag behind all other position players in WAR. Statistically speaking, they aren’t “pure” catchers; they’re in effect competing with other players who are supposed to be better hitters.

In fact, Johnny Bench, whose 50 WAR through age 27 I earlier described as an outlier among catchers, averaged 8.2 positional runs/700 PA at this point in his career. This relatively high net positional adjustment, together with a high amount of PA, account for his unusually high WAR.

There is a third factor evident from the analysis, though. As I noted above, the top ten catchers have a lower average total of fielding runs — meaning they are poorer defensively at their position — than players at other positions. This difference is especially great in comparing them to shortstops and third basemen, but in fact, catchers have the lowest average total of fielding runs of any group analyzed.

It’s not hard to understand why this might be the case. Since catchers as a group are relatively poor hitters, and since the largest component of WAR is usually hitting, a catcher who hits well but doesn’t play the position well is likely to rack up more WAR than a poor-hitting catcher who plays excellent defense. In fact, three of the top ten catchers — Joe Torre, Ted Simmons and Mike Piazza — finished their careers with negative fielding runs. Only one top-ten SS — Derek Jeter — and one top-ten 3B — Chipper Jones — finished their career with negative fielding runs.

That’s not to say that good-hitting, poor defensive players can’t make it at other positions, but there the difference in hitting between best and worst is not so great. The hitting standard is higher at these positions, which means that even an excellent hitter can’t exceed it as much as he might catching. That being the case, the bar for defense is in effect set a little higher.

What implications does this have for evaluating catchers? I think it justifies lowering the WAR bar a little for them. From Table 3, we can estimate that if catchers played full-time at that position throughout their career, they would add about 6 runs per season to their defensive total. Over an average career of 13-14 full seasons, that amounts to about 8 WAR. As we also saw, catchers lose 4-5 WAR in replacement value relative to other position players because of shorter careers. So if they played a career of normal length, and exclusively at catcher, they could add about a dozen WAR to their total, even assuming that they were little better than replacement at the end. That would raise the 50 WAR average for current members of the HOF to a little over 60, right in keeping with the average for other position players.

I think the nub of the problem is that when positional runs are adjusted, they assume that a player can and will play the entire season at a particular position, and that doing so will have no adverse effect on his career, above and beyond the normal aging process that all players undergo. In other words, positional runs do not look at the long-term picture. They consider the demands of the position in the present. It’s rather like comparing two cars, one that is expected to drive in snow, mud, extremes of heat and other challenging weather conditions on bad roads, while the other is used in mostly temperate weather on good roads. Just because the two cars have a certain relative performance at the outset does not mean that we should expect this relative performance to be maintained over their lifetime.

I’ll close by pointing out that other questions remain, in particular the WAR differences between OF and IF. Returning to Table 1, the top OF have an average WAR about 15% higher than the average IF. If WAR is normalized for PA, the difference between corner outfielders and infielders drops somewhat, but the difference between center fielders and infielders remains. Center fielders clearly have the highest WAR/PA of any of the positions.

The other factors that underlie the differences between C and the other players do not appear to contribute to the difference between OF and IF. The fielding-run average of OF, both CF and corner outfielders, is about in the middle, higher than that for C, 1B and 2B, but lower than for SS and 3B. While CF have a positive positional run adjustment, like catchers, their net adjustment is reduced by significant playing time at another position with a negative adjustment. Corner OF get a slight boost in their net positional runs when they play at CF, or in some cases perhaps at 3B, but this is a minor effect. So on the face of it, it seems that OF, and particularly CF, hit better than their positional adjustment would imply. This is also reflected in their average wRC+ values (Table 3), which are about on par with those of first basemen, which of course have a much larger positional adjustment.