F/X Visualizations May 22, 2009
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.

If you average only 5 mph separation, there is variance around that. Say a standard deviation is 2 mph, you're going to be at 3 mph or below quite often, and getting hit hard. If you average 8 mph separation, then even w/ variation you're almost always going to be in your sweet spot with your changeup.

Good point Joel, but continue this out. Hamels and Santana who have very good changeups are at about 11% slower. With variation they should at times throw ones 13 to 15% slower which will get hit hard too.

At the low end, perhaps the absolute speed of the change matters as well as the differential (or instead of the differential). If the pitch is slow enough, hitters can adjust and whack it. So, a guy with a 95-mph fastball can do well at -12% (84 mph), but an 89-mph FB pitcher might get killed with a -12% change (78 mph).

Guy,

That is a great point. It would be interesting to do the analysis looking at how absolute changeup speed and the speed difference from the preceding fastball jointly explain changeup success. I bet you something like what you suggest is going on.

these are interesting results, but of course there's also a question of how well a pitcher hides his changeup in his delivery. while some of that is connected to the speed of the pitch, a lot of it is separate.

Error bars! Woohoo!

Besides the methodology, I assume there are at least two differences between your data and Josh's - please correct me if I'm wrong.
1) Josh adjusted data for park/climate factors
2) Josh applied his own pitch classifications

Good point Harry, I have done neither.

I swear, like two days ago I was just thinking about whether somebody had researched this. Excellent work!

I'd love to see the stats for former closer and changeup master Doug Jones, since his fastball wasn't much better than 80.

There are a few cases that may violate the rule of optimal separation. A lot of it depends on how you measure changeup success -- do changeups 'succeed' only based on the results from the changeup itself, or also by how the hitter reacts to later fastballs. A really good changeup should make it more difficult for the batter to time the next pitch as well.

I took a look at some pitchers with great changeups in 2008, and Clay Buchholz's 75-80 changeup (which obtains excellent results by itself) doesn't necessarily make his 91-95 fastball better:

http://sonsofsamhorn.net/index.php?s=&showtopic=34118&view=findpost&p=1724531

Al,

Good question. I used the pitch f/x data to do the analysis which only goes back to 2007. You need pitch-by-pitch data to do it. I think BIS has pitch-by-pitch data going back further, but I am not sure how far.

Alex,

Good point, there are definitely exceptions. These are averages and I am sure there are pitchers who can succeed with less than 5% and greater than 12% separation. It would be interesting, as you imply, to see the impact that changeups have on fastballs later in the at-bat.