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“Hitting is timing. Pitching is upsetting timing.” – Warren Spahn.

It’s all about changing speeds. Baseball is a game of fractions of a second. A batter has less than half a second to make a decision of whether he will swing at a pitch, and when he does, he has to generate a motion that will meet the ball within a very small window of time. If he’s off, his bat will likely miss or he’ll make weak, glancing contact. Pitchers, of course, love swings and misses and weak, glancing contact and will try every trick in the rulebook in order to get it to happen.

Previously, I’ve been on a quest to learn more about pitch sequencing, starting from the assumption that what a pitcher is really doing is looking for a neuropsychological weakness in the batter. He may not know that he’s an amateur neuropsychologist, but he is. Previously, I’ve looked at the effects of velocity on hitters and found (no surprise) that faster fastballs are harder to hit. The more interesting finding is that, statistically, the size of the effect is highly variable from batter to batter. Some guys can be beaten with speed. Some don’t really notice. I’d suggest that the difference is that some people have better reaction times than others.

But there’s another way that a pitcher can use speed to his advantage. It’s one thing for a batter to be able to time a 95 mph fastball headed his way. It’s another to be able to not get stuck in the mindset expecting a 95 mph fastball and being fooled by an 80-something change. The power of the changeup is that, if done right, it looks like a fastball coming out of the hand, but travels a good bit slower. More slowly enough that if a hitter is looking for a fastball, he’ll be out in front.

In neuropsychological terms, the pitcher is trying to play on what’s called functional fixedness in the batter. It’s the idea that once a batter sees a pitch at 92 mph, he will calibrate himself to the next pitch being a 92 mph as well, and gets so fixed on that idea that he forgets that it’s perfectly legal to throw a ball more slowly and can’t adjust quickly enough. Or perhaps he’s just really bad at judging speeds out of the hand. Are there players who can’t be fooled by raw velocity, but can be fooled by changing speeds?

Warning! Gory Mathematical Details Ahead!

Once again, I acknowledge the fact that a pitch is a combination of velocity, movement, location, the pitches that came before it, and a few other factors. We will account for this rich complexity by completely ignoring it. One variable at a time.

One of the problems with looking at changes in velocity is that you can get confounded really quickly. For example, suppose that one pitcher throws a 95 mph heater with an 87 mph changeup. Another has a 90 mph fastball with an 82 mph off-speed offering. Both pitchers try a sequence where they set up their fastball with an off-speed pitch. The difference between both sets of pitches is 8 mph, but of course, the fastball that the first pitcher throws is going to be harder to hit because it’s coming in at 95. While we can easily create a variable that takes the difference in velocity from one pitch to the next, we also need to control for the raw velocity.

I found all hitters from 2014 who saw more than 1,000 pitches (There were 302 such hitters). I looked at all two-pitch sequences within the same at-bat in which the first pitch was not a fastball. (Later on, I looked at two-pitch sequences where the first pitch was a fastball.) For right now, I looked only at whether the batter made contact if he swung at that second pitch.

I created 302 separate (one for each hitter) binary logistic regressions. This allows us to look at each hitter as his own data set. Since teams are normally not kind enough to send an aggregate of everyone in the league to the plate, this is a pretty good idea. Into each regression I entered the speed of the second pitch in the sequence (to be clear, the first and second pitch in an at-bat were their own sequence, as were the second and third, the third and fourth, etc.), and the absolute difference (expressed as a positive number) between two pitches. Because there could be some interaction effect (it’s easier to deal with a 90 mph fastball after an 83 mph slider vs. a 95 mph fastball after an 88 mph curve) I used a multiplicative interaction term of the raw velocity and the difference from the (for the initiated, this is a bread-and-butter moderator analysis set-up). I also controlled for the league-wide contact rate on the relevant count. The batter’s own average contact rate is implicitly controlled because he’s the only one in the regression.

Once I had regression coefficients for all 302 hitters in the sample, I was able to estimate what a hitter’s contact rate would be on a 90 mph fastball, following an 80 mph off-speed pitch, vs. a 90 mph fastball, following a 90 mph fastball. This holds the velocity of the second pitch (and yes, the 10 mph separation between the fastball and the off-speed is a bit much, but I picked the numbers because they are round) and we can isolate how much of an effect the change in speeds had, rather than just trouble with velocity in general.

The hitters who had the biggest splits in making contact with a fastball after an off-speed pitch were…

Name

Est. Contact rate on 90 mph pitch after 80 mph

Est. Contact rate on 90 mph pitch after 90 mph

Delta

Brandon Barnes

.60

.80

.20

Mike Zunino

.56

.75

.19

A.J. Ellis

.75

.94

.19

Corey Dickerson

.69

.88

.18

Juan Uribe

.71

.85

.14

Devin Mesoraco

.68

.82

.14

Ike Davis

.81

.95

.14

Caleb Joseph

.76

.89

.13

Raul Ibanez

.72

.85

.13

Cody Asche

.82

.95

.13

The hitters who didn’t seem to notice that the pitcher was throwing a little faster…

Name

Est. Contact rate on 90 mph pitch after 80 mph

Est. Contact rate on 90 mph pitch after 90 mph

Delta

Michael Bourn

.86

.86

.000

Jason Kipnis

.87

.87

.001

Freddie Freeman

.82

.82

-.001

Victor Martinez

.94

.95

.002

Everth Cabrera

.86

.85

-.003

Shin-Soo Choo

.84

.84

.003

Stephen Vogt

.95

.95

-.003

Angel Pagan

.93

.93

.003

Logan Morrison

.93

.93

.004

Andrelton Simmons

.89

.89

.004

There were also a number of hitters who seemed to hit better on the fastball that followed the off-speed pitch than a fastball following another fastball.

Name

Est. Contact rate on 90 mph pitch after 80 mph

Est. Contact rate on 90 mph pitch after 90 mph

Delta

Brandon Guyer

.88

.60

-.28

Adam Dunn

.83

.57

-.26

Drew Stubbs

.81

.57

-.24

Ryan Flaherty

.90

.69

-.20

Josh Willingham

.91

.72

-.19

Yasiel Puig

.89

.70

-.18

Xander Bogaerts

.90

.73

-.17

Chris Heisey

.87

.70

-.17

Troy Tulowitzki

.94

.79

-.16

Justin Turner

.92

.77

-.15

That’s a fastball after an off-speed pitch. What about throwing an off-speed pitch after a fastball?

Those who had the biggest splits in the fast-then-slow (vs. fast-then-fast) combo?

Name

Est. Contact rate on 80 mph pitch after 90 mph

Est. Contact rate on 90 mph pitch after 90 mph

Delta

Dustin Pedroia

.46

.76

.30

Sam Fuld

.55

.83

.29

Asdrubal Cabrera

.41

.68

.28

Josh Reddick

.47

.73

.25

Garrett Jones

.31

.56

.25

Eric Hosmer

.47

.71

.24

Ryan Flaherty*

.32

.57

.24

Carlos Beltran

.53

.76

.22

Nate Schierholz

.49

.71

.22

Cameron Maybin

.50

.70

.20

* – Careful readers will notice that I estimated Flaherty’s contact rate on a fastball-fastball combo at 69 percent above and at 57 percent here. This is due to the fact that the fastball first and off-speed first data sets were done separately. It’s possible that Flaherty was systematically thrown different sequences in different counts (which will affect contact rates), so we might have an artifact that the training data set can’t yet cope with. We’ll chat more about this later.

The group that didn’t notice that the pitcher had just slowed it down…

Name

Est. Contact rate on 80 mph pitch after 90 mph

Est. Contact rate on 90 mph pitch after 90 mph

Delta

Brian Roberts

.79

.79

.000

Derek Norris

.40

.40

.001

Yadier Molina

.82

.82

.001

Justin Turner

.93

.93

-.001

Alcides Escobar

.77

.77

.001

Miguel Cabrera

.74

.74

.002

J.D. Martinez

.58

.58

-.002

Logan Morrison

.63

.63

.003

Lucas Duda

.69

.68

-.003

Torii Hunter

.83

.83

-.004

And then there are the guys who enter beast mode if you try to play the fast-then-slow game

Name

Est. Contact rate on 80 mph pitch after 90 mph

Est. Contact rate on 90 mph pitch after 90 mph

Delta

Joey Votto

.93

.75

-.18

Kelly Johnson

.74

.58

-.17

Rougned Odor

.92

.76

-.16

Wilson Ramos

.83

.67

-.16

Todd Frazier

.81

.67

-.15

Nick Castellano

.85

.70

-.14

Pedro Alvarez

.77

.63

-.14

Shin-Soo Choo

.64

.51

-.14

Lyle Overbay

.90

.76

-.14

Stephen Drew

.80

.66

-.14

Warning! This Is All Very Preliminary!

OK, before we go any further, please read this sentence. Do not take the actual numbers above to heart. These numbers are the product of some regressions that give us some idea of who is fooled by changes in speed and who isn’t—and that’s valuable—but as I mentioned above, a pitch is a symphony of movement, spin, release point, velocity, location, and sequencing, and we have conveniently ignored (for now) a good chunk of that.

One major issue is that the two data sets produced two different lists of players who were “unaffected” by changes in speed. It even gave us different estimates of what should have been the same thing (a player’s contact rate on a 90 mph fastball followed by a 90 mph fastball) depending on whether the estimate came from the fast-then-slow data set or the slow-then-fast data set. The correlation between the fast-slow and the slow-fast data sets on the projected 90-90 contact rate for each player is .35, which isn’t bad, but it suggests we might need to tweak the model.

I made that split very consciously, as the neurological system that takes care of response inhibition (wait to swing a little longer) is actually different than the one that initiates a motor response (the visual motor cortex), but because off-speed pitches are thrown more often in a different set of counts than are fastballs, we might be modeling a batter’s contact rate on different sets of counts. It’s not surprising that he might take a different approach to contact with two strikes, for example, than before two strikes. But still, when I ran a correlation of the two sets of deltas reported above, the result was practically zero (r = -.02), suggesting that knowing how well a hitter responds to a slow pitch after a fastball tells us practically nothing about his ability to catch up to a fastball after an off-speed pitch. It’s not clear to me right now whether that’s a methodological issue or a real finding. Part of the fun of these articles is that I’m not entirely sure where they’ll end up.

We also need to allow that we only have contact rate presented here. Pitchers are often trying to do different things when they throw a pitch. Some pitches are meant to freeze a batter. Some are meant to try to induce (weak) contact. We need to think about the swing rate that a batter uses and the quality of the contact that he makes when we get around to figuring out the expected value of a pitch.

But what we do have is a nice little starting place. Changing speeds is one trick that a pitcher can use, and we see that there are some players who are good at handling that, some who are bad, and some who just don’t care. It’s not the only trick that pitchers can use, and the fact that off-speed stuff is slower is not the only thing that makes it hard to hit. (And yet, it moves!) But slowly, we can start to see that there are real differences between players and that they have real consequences for strategies to get them out.