Optimal Fastball-Changeup Speed Separation
A large part of the success of a changeup is assumed to be based on its deceptive nature. Hitters expect a fastball based on the changeup's delivery and movement, but the pitch is about 10% slower. This throws off the hitter's timing, hopefully causing him to whiff or make poor contact. If this is the case we should expect the success of the changeup to be at least partially based on the difference in velocity between it and the fastballs that precede it. In this post I am going to examine this assumption. Is the success of a changeup tied to this difference? What is the optimal difference is speed?
Josh Kalk examined this question in a slightly different manner, looking at the relationship between the success of a pitcher's changeup over the course of a season and the difference in speed between his average changeup and average fastball. He found a linear relationship with increasing success based on increasing difference. I wanted to take a more granular approach and look at the success of a changeup based on the difference in its speed from the last fastball thrown to the batter, all the fastballs thrown to the batter in that at-bat and all the fastballs thrown to the batter in that game.
Here is the run value of a changeup based on how much slower (release speed) it was than the most recent fastball thrown to the batter in the at-bat the changeup was thrown. Changeups thrown before any fastballs were thrown in an at-bat were excluded from this analysis.
This suggests that the optimal changeup is between 5% and 12% slower than the previous fastball. The gray lines show the standard error. The results are similar if you compare the changeup to all previous fastballs thrown in the at-bat and all previous fastballs the hitter has seen in the game. The results are highly non-linear. There is little difference between throwing a changeup between 5% and 12% slower, but if it is less than 5% or greater than 12% slower the effectiveness rapidly drops off. This rapid drop off it not surprising; changeups that are too fast are effectively slow fastballs and changeups that are too slow don't look enough like fastballs. But, I am very surprised by how flat the graph is between 5% and 12%.
These results are seemingly at odds with Kalk's. He found that pitchers who average only 5 mph difference between their fastball and changeup over the course of a season have less successful changeups than those who average 10 or more mph difference. My results suggest that an individual changeup has about the same success if it is preceded by a fastball that is 5 mph or 10 mph faster. I am not sure how to reconcile these two different conclusions, but I am going to think about it more in the future and welcome any comments.