Sunday, February 17, 2013

Putting Ballpark Effects into WAR

One of the most misunderstood elements of the Wins Above Replacement (WAR) framework is ballpark factors.  Most fans realize that extreme parks like hitter-happy Coors Field in Colorado and pitcher-friendly PETCO Park in San Diego tend to have significant effect on the production of hitters that play there.  However, some are not grasping how ballpark effects are used in WAR.  It's not important that people comprehend the complex formulas used in measuring ballpark effects.  It's more crucial that they see the purpose of ballpark factors, but some seem to be a little confused.  So, I'll try to clarify that here.

Rockies outfielder Carlos Gonzalez and Cardinals catcher Yadier Molina and had very similar batting lines in 2012.  Gonzalez hit .303//.371/.510 with 27.2 Runs Above Average (wRAA) in 579 plate appearances (PA), while Molina batted .315/.373/.501 with 27.3 wRAA in 563 PA.  However, Gonzalez played half his games in Colorado's Coors Field which was the best hitters park in the majors.  On the other hand, Molina played his home games in  Busch Stadium which was more of a pitcher's park.  These different environments need to be accounted for in our evaluation.

Some fans say they do not like ballpark factors because we don't really know what either Gonzalez or Molina would do in a different park.  In fact, Gonzalez's radical home/road split in 2012 (1.046 OPS versus .706 OPS) suggests that he might have benefited more from Coors than the average player.  In Molina's case, he actually did slightly better at home the last two years, so there is no guarantee that playing in a better hitter's park would have helped him.

It is true that a park can influence players in different ways.  A player's skill-set might be more tailored for his home park than another player.  For example, some parks are designed for left-handed batters over right-handed batters or power hitters over contact hitters.  In other cases, a player just might be more comfortable in one park over another.  These factors would all be important if we are interested in a player's ability to perform in a given park in the future.

WAR, however, is not designed to determine a player's ability or potential to play in a different park.  In calculating WAR, it doesn't matter what Gonzalez would do if he were traded to the Cardinals or if the dimensions at Coors were changed.  WAR is not concerned in a player's ability or innate talent.  The purpose of WAR is to estimate a player's value to his team.

The question of interest is how much is a run worth in Coors versus Busch?  Because it is easier to score runs in Coors than Busch, a run scored in Colorado is less valuable than a run scored in St. Louis.  In other words, the average player will contribute more runs playing in Coors than in Busch, so a Rockies hitter needs to produce more runs in order to have the same value as a Cardinals hitter.

Again,it does not matter if a player like Juan Pierre is not benefiting from hitting in Colorado.  If he is playing for the Rockies, he needs to have his value adjusted downward (as any other player would) because the Coors high-run scoring environment reduces the value of his runs contributed. 

Calculation of ballpark factors is complex.  A detailed description can be found here at Toirtap's sabermetrics site.  This is also the method used by FanGraphs.  In short, five years of home and road runs scored data are used to calculate park effects.  If a park is new or has been renovated within five years, then a shorter time period is used.

It has been determined that it is 26% easier to score runs in Coors Field than a neutral park.  A Rockies hitter plays half of his games in Coors and half in a combination of parks that averages to near neutral (Since schedules are unbalanced, that's not quite right in every case, but we'll keep it simple here).  So, the value of the average run produced by a Rockie is 13% less than if his home park was neutral like Turner Field in Atlanta.

Given the above, We say that that the Rockies Ballpark factor (BPF) is 113.  The BPF for a neutral park is 100.  The most pitcher-friendly park is PETCO with a BPF of 92.  See the FanGraphs Guts section for a list of all ballpark factors by year.

Getting back to the opening example, remember that Gonzalez had 27.2 wRAA in 579 PA and Molina 27.3 wRAA in 563 PA.  Let's now calculate their ballpark-adujusted run values: 

The average player created .114 runs per PA in 2012, so he would  have an estimated .114 x 579 = 66.0 Runs Created in 579 PA in a neutral park. The same player would have 66.0 x 113/100 = 74.6 Batting Runs if his home park was Coors.  So, Gonzalez's value is reduced by 74.6 - 66.0 = 8.6 runs. Gonzalez had 27.2 wRAA in 2012, so his ballpark adjusted batting value becomes 27.2 - 8.6 = 18.6.  

An average player would create .114 x 563 = 64.2 runs in a neutral park.  Using the Busch Stadium BPF of 97, that player player would create 64.2 x 97/100 = 62.3 runs playing for St. Louis.  So, Molina's value is increased by 64.2 - 2.3 = 1.9 runs.  Thus, his ballpark adjusted batting value is 27.3 + 1.9 = 29.2.  After correcting for ballpark, Gonzalez and Molina no longer look like the same hitter.  Instead, Molina comes out ahead 29.2 to 18.6.


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