Home Run Rate by Pitch Location
So far I have looked at the run value of a pitch based on its location as it passes the batter's plane. Today I am going to take a slightly prosaic break from that and look at everyone's favorite contributor to run value: the home run. Below are maps of HR rate per pitch by pitch location. Again I average over pitch type, count and speed, so there are some obvious limitations to the analysis. The number presented at the top of each figure is the average HR rate per pitch.
Since the batter's handedness is more important than the pitcher's I averaged across the rows above to create just two maps, one for RHBs and one for LHBs. Over the composite map I plotted all the home runs for an individual hitter to see how he compares to his peers. Here are the HRs of everyone's favorite HR hitter, Jack Cust, plotted over the composite LHB map. Cust's home runs are, for the most part, where you expect for a left-handed batter: the highest density slightly in from the center of the zone, none in the down and away corner of the zone and more above the zone than below.
Here are two other batters I thought were particularly interesting. Alfonso Soriano is almost a caricature of a right-handed batter with his highest HR rate region even more down and in than expected. Carlos Pena, on the other hand, mashes outside pitching and the inside half of the zone has surprisingly few HRs. A possible explanation for this pattern could be that Pena just gets very few inside pitches because pitchers know he is a dangerous HR hitter. This shows one problem with my analysis. I am comparing the composite HR rate to a player's raw HRs not adjusted for the number of pitches a player sees in that region. I should be comparing that player's HR rate to the composite rate. For two reasons I did not do this: (1) I am having a hard time creating rate maps for individual players based on so few HRs and (2) even if I had such a map I cannot think of an effective way to overlay the two rate maps (individual player and composite) as nicely as I can overlay the actual HRs on the composite rate map. But it is something I am going to think about and work on in the future.