THE BOOK--Playing The Percentages In Baseball

Tuesday, April 14, 2009

Is wOBA all it’s cracked up to be?

A reader wrote, in full:

I recently came across this article at The Harbdall Times: http://www.thehardballtimes.com/main/article/the-great-run-estimator-shootout-part-1/ , and it got me thinking a bit about wOBA.  I was initially sold on wOBA because of its really solid conceptual background (especially when compared to EqA, which I can’t make any sense of) and the way it helps correct for the shortcomings of OPS and distinguishes between players who may have the same OPS but different OBPs and SLGs.

The above article, however, confused me because it seems to indicate that wOBA correlates worse (albeit very, very slighty) with run scoring than does OPS, OPS+ and RC.  The mean average error and RMSE were also slightly larger for wOBA than for OPS and OPS+.

This got me thinking about how to measure how “good” of a stat wOBA is.  Since it definitely seems to be a stat geared towards individuals, I’m not sure it makes sense to correlate it to runs scored on the team level (as I think was done in the article, though it was done per inning).  Also, I’m not even sure it is intended to correlate with runs at all, considering that it doesn’t claim to generate the actual runs a player was worth, but rather how many runs he would be worth if all of his offensive contributions took place in an average setting.  If this is the case, and it isn’t actually meant to correlate with runs scored, how do we test the quality of the stat, or really, the quality of any stat which focuses on individual performance?

Does the strength of wOBA lie entirely in its intuitive derivation and the way it modifies and complements OPS, or is there some other way to measure its quality?  Or, is it the case that even if wOBA makes perfect intuitive sense, at the end of the day it isn’t as important a stat as some of its seemingly inferior counterparts, such as OPS, if it does not correlate as well with run scoring as they do?

Sorry, this e-mail was pretty long and I know you’re very, very busy.  Hopefully you get a chance to read it and respond.  Thanks in advance for your response and for all the great content you post up on the web.

My response:

If you start with Linear Weights, you will get to exactly 100% wOBA.  They are identical stats.  At the same time, if you start with wOBA, you can get to Linear Weights exactly 100% of the time.  They are identical.  Whereas wOBA presents data in two dimensions (the rate portion of wOBA, and the number of PA), Linear Weights presents it as one-dimension.

The conversion of Linear Weights (denominated in runs, but based on runs above/below “average") to total Runs Created (denominated in runs, but based on absolute number of runs) requires two separate processes, depending on whether you care about total team runs scored, or whether you care about total “player” runs scored.  The second-dimension of Linear Weights requires either the use of PA or outs, depending on what translation you are making. The allocation of how many runs an “average” hitter creates requires great care to ensure that the value of the outs (the inning killer) is handled properly.

I do not know what Colin did in order to convert wOBA to total runs created.  Seeing that wOBA is Linear Weights, then I expect an r = .999 of any results coming out of wOBA or Linear Weights.  If you don’t see that, then there’s a gap somewhere in the translation.

A related thread can be found here.