Touching BasesJune 15, 2010
Bimodal Distributions
By Jeremy Greenhouse

Dave Allen has written at length about Mariano Rivera's pitch locations. PITCHf/x has recorded over 2,500 Mo-thrown pitches, and from the following graph, you can see that Rivera spots his fastball on either side of the plate, but is able to avoid the middle.


Dave described this horizontal scattering as a bimodal distribution, which Rob Neyer in turn called his "new favorite baseball term." Chris Moore, too, was intrigued, and he found that Rivera is indeed the best at hitting the corners. "On average, Rivera places his pitches 4.4 inches away from the very edge of the plate."

I'm interested in who can throw to both sides of the plate, but avoid the middle. So I broke the plate into thirds and counted the number of each pitcher's separate pitch types in each zone. Overall, I came up with a list of about 60 pitchers who threw fewer pitches in the middle zone than they did in either of the outer thirds. Andy Pettitte, Carl Pavano, Jake Peavy, and Livan Hernandez command multiple pitches on both sides of the plate. Rivera, of course, stood out, as he throws only 20% of pitches over the plate in the middle third, while other pitchers are 25% and up. But using the invaluable Texas Leaguers' PITCHf/x tool, which provided the above graph for Rivera, I'd like to take a look at some other pitchers who manage visible bimodal distributions.

Here's Shaun Marcum, who throws the third-softest fastball in the American League, but commands it better than nearly anyone.


Livan Hernandez's fastball shows a bimodal distribution, but unlike Rivera and Marcum, he doesn't keep the batters guessing. He only throws his fastball outside.

Livan vs. RHB:


Livan vs. LHB:


Since Livan demonstrates the ability to throw his fastball to both sides of the plate, shouldn't he keep hitters honest by coming in on them once in a while?

Hiroki Kuroda follows a similar approach to Livan, but more impressively, he avoids the heart of the plate with his slider.

Kuroda vs. RHB:


Kuroda vs. LHB:


But I prefer pitchers who can throw the same pitch to both sides of the plate against the same batter, like Jamie Moyer's cutter to righties.



Great article Jeremy, nice work tracking these guys down.

I second that emotion. Good stuff.

Perhaps you could do a bimodal distribution on high and low strikes or "changing the eye level" as they say.

Thanks for the comments, gentlemen. The numbers say that Ted Lilly is the best at locating his pitches high and low in the zone while avoiding the middle, but I can't find any visual that represents it. There just aren't many pitchers who would want to elevate a pitch in the strikezone, I think.

Think Livan's current stretch of good pitching is because he started keeping the hitters honest by throwing some pitches inside?

Just because Livan Hernandez CAN throw his fastball to both sides of the plate doesn't mean he SHOULD. Remember that Livan's "heater" clocks in at 84-85 mph and it's historically been his worst pitch in terms of run values at -0.44 runs/100.

I think part of his success this year may be due to avoiding the inside half of the plate, where hitters often pull it out of the park.