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Wednesday, June 15, 2005

Walks Followed by Homeruns

A week or so ago someone on the SABR-L list asked the question as to whether the theory that homeruns are more frequent following walks was true. The reasoning behind this theory, which the questioner had heard an announcer posit, is that the pitcher often tries to re-establish the strike zone after a walk and hitters end up taking advantage.

To see if this is true I calculated the frequency of homeruns following a variety of events in 2004. Here are the results sorted by frequency.

Event HR Events/HR
Homerun 197 27.7
Walk 430 34.5
K 920 34.6
Double 240 37.2
Single 751 39.0
Triple 22 40.8
I-Walk 30 46.0
HBP 39 47.4
Out 2584 47.5

From this it doesn't seem like the theory probably holds as any kind of general rule. Homeruns occur more frequently after other homeruns and are not signficantly more frequent following walks than strikeouts or doubles.

Note: This analysis doens't include homeruns that followed errors, fielder's choice, leadoff homeruns, and 118 homeruns that followed other plays that were not batter events out of the 5,451 homeruns in 2005.


Jim Mohl said...

Your statistics are interesting. However, by not clearly stating the question you are trying to answer, you arrived at the wrong conclusion. Comparing home run rates after various events doesn't tell you anything by itself. For example, the HR rate following a double should be significantly lower than the rate following a walk or single, simply because first base is open. If the batter represents a serious HR threat, the option to put him on (either intentionally or by "pitching around") is always there. You need to compare the HR rate following a walk to comparable situations, namely the rates following a single or HBP. (Intentional walks aren't really comparable either.) Thus, the null hypothesis is: given the last batter reached first safely via either (unintentional) walk, single or HBP, it makes no difference which route he took to get there in evaluating the likelihood of a subsequent homerun. That hypothesis can be rejected given the data you present, using just about any reasonable test of significance. If HR's were equally likely in all 3 cases, you would expect to get around 394 HR's following 14,835 bases on balls, with a standard deviation of 17. Instead you have 430, which is more than 2 standard deviations away from the mean. There is only about a 1-in-40 chance that the null hypothesis is true.

Dan Agonistes said...

That is a good point. With first base not occupied pitchers would tend to pitch more carefully to sluggers. Same argument could be made for why homeruns follow homeruns more often in general. With the bases empty a pitcher is not as careful.