The Deal With Derby Participants

In 2005, Bobby Abreu of the Phillies put on a showcase at the Home Run Derby, breaking the single-round record en route to a derby victory.  All told, Abreu swatted 41 home runs into the Detroit stands that night.  Since that fateful day, three and a half years ago, Abreu has hit just 47 home runs total.  From 1999-2004, he averaged 24.3 HR/yr; combining the second half of 2005 with the first half of 2008, and adding it to 2006-07, Abreu has averaged just 16 HR/yr since.  While several factors could account for this drop, such as age, a decline in bat speed, more grounders, to name a few, many fans and analysts alike attributed his second half dropoff to a “tired swing” due to the derby.
This story is not alone, either.  Juan Rodriguez, in this Florida Sun-Sentinel article, discusses the highly popular idea that home run derby participants will experience a second-half dropoff.  According to his research, half of those studied experienced drops in their home run rates while the other half stayed stagnant or increased their rate.  Still, whether in jest or born out of complete concern, the idea of a derby-driven dropoff is a very popular one.
There have not been many studies on the subject either, meaning nothing has necessarily debunked the myth or proven it to be true.  I have seen a couple of studies but they, just as I did in an initial look at this very subject, fell into the same trap.  By straight up comparing first half to second half, our results are not truly expressing what we intend.  The problem stems from a selection bias in that those named to the all-star team or home run derby are likely having big first-halves.  Overachieving first-halves, that is, meaning they are naturally due for a second half regression whether they participate in the derby or not.
To properly conduct this study, by using the true talent level, we need to compare the actual second half production to the projected production based on the previous three years and the big first half of the year in question.  This way, the real test will be whether or not players fall short of their projection in the second half.  If so, then yes, the idea of a decline following the derby does carry some weight.  If not, and/or the results are ambiguous, then it is nothing more than a theory as their would be nothing to suggest a decline. 
Those supporting the idea could play the “tired swing” or “uppercut mentality” cards but I say it’s largely poppycock.  I am, however, willing to be openly swayed by the numbers should they come to suggest such a result.  My first step was compiling a list of all derby participants from 2000-2007, then entering their actual second half performance into a spreadsheet.  Using the in-season Marcel projector, I then manually entered the pertinent numbers into the required fields, which took forever (Hardball Times, you need to go prior to 2004!) but eventually offered the projections for the second halves in each of those years for each of those players. 
Next, I tested the strength of the numbers by running a simple correlation.  As you will see below, everything other than batting average correlated quite strongly to each other between the halves:

• AB/HR: .49
• BA: .28
• OBP: .65
• SLG: .58
• OPS: .61

Testing the correlations or running a linear regression could help in this study but I decided to go with a paired samples t-test instead.  A t-test compares the means between two sets of data and lets us know if the differences between the means are statistically significant or not.  Keep in mind the sample size here is 64 players so these results may not be anything definitive, but I’m really just testing to see if the idea of a decline should be given any credence, whether or not it shows up in any way in the numbers. 
Anyways, back to t-tests: In them, a p-value of .05 or less suggests that the means are, in fact, statistically different.  Higher than that and the means are not really that different regardless of whether or not one appears higher or lower than another.  Since we are testing for a decline here, the expectation is that the mean of the projected statistics will exceed the mean of actual statistics.  After running the t-test I was surprised to find that all five measured stats (AB/HR, BA, OBP, SLG, and OPS) had a p-value below .05; in fact they were all below .03, with batting average being the least significant.  Since the means are all significantly different from a statistics standpoint, here are the comparisons:

• Projected AB/HR: 17.8
• Actual AB/HR: 19.9

• Projected BA: .293
• Actual BA: .299

• Projected OBP: .382
• Actual OBP: .397

• Projected SLG: .546
• Actual SLG: .563

• Projected OPS: .928
• Actual OPS: .961

According to these results, the derby participants from 2000-2007 have actually outdone their projections in the slash line department as well as in OPS.  This offers, at least amongst these numbers, that these players are not declining in overall production in the second half relative to what they were expected to do.  In fact, it might even point in the opposite direction, that the derby was merely a stepping stone towards a great year for the players in question.  By outdoing the second half projections and beating the expected regression, the slash line and OPS do not suggest decline in the least.  We may be picking nits over whether it suggests improvement, but definitely not decline.
However, and it’s a big however, the AB/HR did get worse in the actual data.  On average, the projected player would hit a home run once every 17.8 at-bats, while the actual players did so once every twenty or so at-bats.  Essentially, the overall production of these players did not decline but their rate of home runs did.  From a psychological standpoint, Pizza Cutter noted that perhaps pitchers will bear down more in the second half against these all stars and derby participants to avoid surrendering home runs from them, even though pitchers tend to give up more flyballs in the second half.
Overall, I would like to extend this into a larger study unless someone beats me to the punch, to see if the results hold up when we add say 12-15 years of derby data to the fold.  Based on this study, however, it does appear that players will experience a drop in their home run rates while simultaneously beating their projections in BA, OBP, SLG, and OPS.  The key to remember is that we are comparing projected second halves to actual, not a straight up comparison between both halves for each players; that would produce different results, and wouldn’t be a fair test for decline.
Taking this to the next level would involve using a larger sample of derby participants and conducting another t-test to compare the means in several areas.  Additionally, we would want an equal sample of non-derby participants with similar numbers in perhaps the AB/HR area.  We would conduct the same t-test for them and see if the derby actually has an effect; if it does, then we would see the same lower AB/HR rates for derby guys but different results for the non-derby guys.  They would be our control group.  For now though, it’s interesting to see that the derby participants only decline in that area.  Essentially, we cannot automatically assume that the derby caused the ab/hr decline until we see them stacked alongside similar players not in the derby as a control.