Alright, let’s figure this pitch sequencing thing out.

I’ll start by looking into pitch velocity. Velocity is the easiest part of a pitch to measure, mostly because all you need is a decent radar gun to measure it. It’s also the easiest to explain. The ball is either going fast or it is going obscenely fast. And we haven’t even gotten to Aroldis Chapman yet. And because velocity is so easy to measure, it’s the piece that gets talked about the most. We have a language to describe it. Even people who know little about the game of baseball know what a fastball is. Even if they don’t, it’s not that hard to figure out.

Some pitchers basically live on world class gas. They can throw that speedball by you and make you look like a fool. But let’s talk about what’s really going on. The fundamental unit of a baseball game is the batter trying to hit the ball that the pitcher throws. The pitcher starts with the ball, so he controls what sort of ball will be headed homeward, but once he lets the ball go, there’s nothing he can do. He’s counting on the ball to somehow fool the batter into doing something silly, like swing and miss or to stare at a perfectly good ball in the strike zone.

Now the pitcher can try to prey on a couple of very human weaknesses. The guy in the batter’s box is human, after all. Humans need time to react to things. It takes your average human being around 250 milliseconds (a quarter of a second) to respond to something. It varies some from person to person, and a lot from time to time within the same person. But the quicker the ball gets to the plate, the less time that a hitter has to execute his response after he reacts. And in a game in which where the bat strikes the ball is rather important (swinging late is likely to produce weak contact, when it produces any contact), that can make a huge difference.

A ball traveling 90 mph can travel 55 feet in 417 ms. A ball traveling at 95 mph covers the same distance in 394 ms. Now, that might not seem like much (the difference is 23 ms, slightly more than the blink of an eye), but if the average human takes 250 ms to even react, then a hitter has 167 ms to actually execute his reaction to the 90 mph fastball and 144 ms to actually react to the 95 mph fastball, or roughly 13 percent less time. Rocket that ball in at 100 mph, and the hitter has 125 ms to produce his response. The batter has lost a quarter of the time allotted to him to respond. This is why teams love guys who can light up the radar gun. It takes away valuable time that a hitter might have used to respond. It’s also why some pitchers fear losing even a bit of velocity. Baseball is a game where milliseconds matter.

A note before we continue: there’s much more to a pitch (and to pitching) than velocity. There’s movement. There’s location. There’s sequencing. Sometimes, there’s just luck. I’m aware of this and my plan to solve for that complexity for the time being is to ignore it. Right now, I’m on a quest, and I’m not entirely sure where it’s headed. My initial models will be far too simple, and I’m OK with that. There’s a strange and unspoken expectation of sabermetrically focused articles that they represent fully-formed thoughts. Sorry to disappoint.

Warning! Gory Mathematical Details Ahead!

To look at velocity, we’re going to look at some simple metrics. On a given pitch, we get several pieces of information. Whether or not the batter swung. If he didn’t, whether the pitch was a called ball or strike. If he did swing, whether he hit it (and hit it fair). And thanks to the magic of Pitch F/X, we have all sorts of data on each pitch, including velocity. Again, I’m ignoring everything other than velocity on this one. Yes, that’s silly, but right now, I’m more interested in finding the broad contours of the subject, and if an effect is that big, it will show itself through.

But we do want to control for some things. We’ll be looking at rates of swinging, and if there’s one thing we do know, it’s that different batters have different tendencies when it comes to swinging. Some will swing at anything. Others like to watch. Some are good at making contact. Others, not so much. So, the first thing that we control for is the batter’s average swing (or contact) rate, expressed as a natural log of the odds ratio. Also, we know that batters are given to swinging on some counts more than others. So, I took the league-wide swing (or contact) rate for each count as a control. Certain counts are also more given to fastballs than others as well. So, once we control for that, we can get a better look at how much velocity affects the batter.

I ran a binary logistic regression, looking at all pitches from 2012-2014 (thanks to Harry Pavlidis for hooking me up with a sweet data set) and looked at whether velocity affects a player’s behavior. For all pitches, more mph brought about more swings and more contact, but that includes off-speed pitches. Limiting the sample to just fastballs, we see that faster fastballs predict fewer swings in general, more called strikes, and more swings and misses. Again, this is over and above the batter’s general swing/contact/called strike rates and controlling for count. This is also not a surprise.

That’s interesting (if old) information on fastballs in general, but a pitcher isn’t pitching to a hitter in general. There’s a name on that guy’s back. In the 2014 Baseball Prospectus Annual (which is about to be eclipsed by the new edition!), I wrote an essay arguing that we need to go beyond just “hitters in general.” We need to get personal. The reason is that humans vary in their neurological abilities (and reaction time is the quintessential neurological task). Some guys are just really quick to react. Consider that the difference in flight time between a 90-mph and a 95-mph fastball is 23 milliseconds. Now, let’s go to this graph, which plots scores from an online reaction time task. We can see that the standard deviation on this task looks to be about 25-30 ms. Baseball players are probably not your average humans when it comes to reaction time, but some are bound to be better than others. If a player is perhaps one standard deviation better than the league average, suddenly, you might be throwing 95, but he’s able to react quickly enough that it’s effectively a 90-mph pitch to him.

We can test for that. I built another logistic regression that added in a variable that was the interaction of the batter and the pitch velocity. This essentially allows the program to create a personalized term for each hitter (minimum 500 pitches seen) on how much velocity affects him. I only looked at 2014 for this one. For the super-initiated, that variable had an overall Wald value that was significant for swing rate, contact rate, and called strike rate. In fact, looking at the relative contributions to the model (using -2 log likelihood as my benchmark), the interaction term containing the identity of the batter generally was several times more powerful than the raw velocity reading. (Translation: To really understand how velocity affects the outcome of a pitch, you need to take it down to the individual level.)

To give some idea of how this works out, all hitters got worse at making contact as velocity went up, but some weren’t as affected. (Again, remember that this controls for a hitter’s general contact rate, as well as the count that the pitch happened on.) The hitters who seemed least affected were Ben Revere, A.J. Pollock, and Martin Prado. The hitters who ran into the most trouble making contact on fast fastballs were Jonathan Singleton, Tyler Flowers, and Javier Baez. Probably not a lot of surprises there. The separation between best and worst was only a couple of percentage points, but that can be big over the course of a season.

The Power of N = 1

So we’ve learned a few things. We’ve learned that the basic idea that faster fastballs are better fastballs is true, but that the effect is not the same for everyone. In fact, the individual level effects are more important. That’s why you hear pitchers talk so much about their game plan against individual hitters. They have individual weaknesses and it’s important to strategize to those rather than try a one-size-fits-all approach. But those weaknesses have never really fully been analyzed numerically (at least publicly… who knows what goes on behind closed doors…)

This is just fastball velocity. We can apply these same principles to learn about other vulnerabilities that a hitter has, both on individual pitches and then on sequences of pitches. For example, in a future article, I plan on looking into whether changing speeds has an effect on a hitter. Are (some?) hitters thinking about the last pitch and can they be fooled easily by simply throwing something that moves a little slower? Or is there no sequencing effect there. What happens when a pitcher changes location? What about when he comes inside? I’m hoping that this the first in an arc of articles on the topic. It’s something of a New Year’s resolution for me. And in all honesty, I have no idea what’s going to come from them. That’s the fun of it. I hope you’ll stick with me through all of them.

Thank you for reading

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This was excellent, and the promise of what is to come is even more exciting.
I find it funny that we can like comments, but not articles.
"...there’s much more to a pitch (and to pitching) than velocity. There’s movement. There’s location. There’s sequencing. Sometimes, there’s just luck."

And spin! Don't forget spin.
Really good stuff! on to nitpicking.

I'm a little bit skeptical about the effect size. Was the batter*velocity cross term a random slope/random intercept thing or a fixed effect? I think that if it was a fixed effect it would overestimate the effect size, perhaps considerably. Or, if you'd used BIC criteria (with a penalty for the number of parameters in addition to the log likelihood) maybe the batter variable wouldn't have made so large of a contribution?
Great take. I am guessing higher spin rates will be meaningful in following analysis. Are you familiar with Perry Husband & his work on effective velocity? If not,worth checking out.
I think it would be interesting to include a term representing total career pitches seen (though I'm not sure how early in the career this should start - do college PAs count? HS? Should it only be pitches - or fastballs? - with >90 mph speed?).

The reason that term could be helpful is that one of the big factors making ML hitters so good is their ability to "chunk" visual images of the type they usually see. I read an article that was discussing why Jenny Finch was able to regularly strike out major league hitters ( that argued it had a lot to do with disrupting the typical patterns they look for when at the plate. Using those patterns essentially gives hitters more time to react because they grasp the important information faster.

So I'm suggesting that hitters with more exposure to fastballs (and actually, now that I'm thinking about it, more exposure to an individual pitcher) will essentially react faster, even though their baseline reaction speed isn't any different.
Could be a lot of survivor bias there: hitters who don't learn how to pick up a fastball don't stick around long enough to see a whole bunch of them.