Last Friday, I had the pleasure of devouring Dan Brooks’ and Daniel Mack’s introduction of Brooks Baseball’s newest toy, pitch sequence visualization. To me, this is a major step forward in deciphering how every aspect of one pitch—be it type, velocity, or location—affects the strategy of the next. I’m not even so concerned with the results of the sequences—ultimately, well-executed pitches get results irrespective of other factors—but the massive insight we now have into a pitcher’s plan of attack is exciting whether you’re an amateur sabermetrician or a young player looking for a strategic edge.

Pitch sequencing is one of the great white sabermetric whales; we’ve been trying to get into pitchers’ heads for years, but in a game where all hurlers aspire on some level to complete randomness, that’s a very difficult thing to do. One sentence from the piece struck me as particularly insightful, however, and I think it bears repeating. It’s exactly how we’re going to refine this holy grail of baseball into as useful, practical, and applicable a tool as it could ever be. Write Brooks and Mack,

Pitching is not the sum of individual statistics about individual pitches any more than a piece of music is the sum of an individual set of notes.

The sentence doesn’t simply tell us that each pitch affects the pitches that follow; it also helpfully frames the challenge at hand not as science, but as art. (And pitching is an art, as any pitcher will happily boast.) To some extent, we can take a prospect’s production in the minors and, filling in certain variables and using historical comparisons, scientifically estimate his chances of big-league success. Sequencing, however, is a different matter: with so many variables in play, many of which will be relevant only on one day—I didn’t have my splitter in the pen; or, he ripped my fastball last time up!—progress necessitates a working relationship between Brooks’ and Mack’s research and sheer knowledge of the game that seems to come only from exposure. We have to bridge the gap between art and science, and a sturdy bridge can’t be built from just one end of the river.

The sequence visualizations give us a rhythm section of sorts, some scientific foundation on which to build our magnum opus. But we’re still (and perhaps always will be) a few violins short of a concerto. The next step, then, is getting those violins to play. If our goal is to predict with greater accuracy what the next pitch may be, we must take care to examine the short-term variables that affect the pitcher’s mentality. That’s where analysis of real-life examples comes into play. What follows is one example, out of countless occurring each day, in which a smart hitter would balance what he learned from Brooks and Mack with what he’d just seen.


I flipped on Sunday’s Reds-Marlins game at just the right time. Reds closer pro tempore Jonathan Broxton needed just one more out to lock down an 11-inning victory in Miami and strengthen Cincinnati’s grip on the NL Central. With a 5-4 lead, Donovan Solano at first, and a 2-2 count on John Buck, Broxton threw a slider outside that Buck lined into the right-field stands. The Marlins’ announcers agreed the pitch was too close to take. “We’ve seen that pitch called a strike today,” said analyst Preston Wilson. (Wait a second: analyst Preston Wilson? How old am I?) Discussion then turned to the on-deck hitter, back-up catcher Rob Brantly, who was the Marlins’ last position player available off the bench.

After fouling off a 92-mph fastball from Broxton, Buck took a slider just off the outside edge to run a full count. On 3-2, Broxton came with a third slider, and Buck mashed it out to deep center, but Drew Stubbs made a fantastic leaping catch at the wall to end the game.

Strange, though, about those sliders. Here we have John Buck, currently slugging all of .335, seeing sliders on 2-2 and 3-2 from a guy whose fastball averages 95.5 mph this season, when a walk would put the tying run in scoring position. Broxton hasn’t thrown 68 percent fastballs (four-seamers plus sinkers) this season for no reason: in 2012, his slider has been nearly three times as likely as his sinker to be hit for a line drive, and over eight times likelier to be hit for a fly ball. In a potential walk-off situation, he’d want to avoid those two scenarios. So why the sliders? And how was Buck able to think along with him?

Before we dive into Broxton’s actual performance, let’s briefly go over some other variables previously mentioned in passing. First, Buck isn’t a great hitter, but he probably demands more respect than Brantly (who has been hot lately after a brutal start to the year in Triple-A), and the Reds certainly wouldn’t be worried about Bryan Petersen, who was in the hole. Also, while home plate umpire Alfonso Marquez has a smaller-than-average strike zone, Wilson’s perception was that he’d been rather generous in this particular game. Broxton may have been thinking that since he’d already gotten Buck to offer at a slider outside the zone, it was worth a shot to push his luck, expand the zone, and risk the walk with two relatively weak hitters coming up.

There’s often much more to it than that, though. Buck likely saw that in addition to the other variables, Broxton wasn’t quite himself out there. It had been five days since Broxton had last taken the mound, and in that previous outing, he’d twice touched 96 mph and had thrown a fairly typical four sliders against nine fastballs. Sunday was a different story, so let’s place ourselves in Buck’s shoes and figure out how that 4:9 ratio suddenly skewed to a bizarre 13:9.

You could almost excuse Broxton for starting Carlos Lee with three sliders. It was a one-run game, he didn’t want to get burned, etc. Fine. Lee lined out to right on the third slider, and then things started to get interesting. Facing Greg Dobbs, Broxton poured in a fastball strike at 92 mph. Hmm. He’s supposed to be throwing 95 to 96, but he just threw three sliders in a row, and now he’s coming in at only 92.  The difference between 96 and 92 is the difference between “a heater I have to gear up for” and “stuff I see every day.”

Ahead 0-1 to Dobbs, Broxton threw a pair of curveballs (rather than sliders, because Dobbs is a left-handed hitter) that missed by a mile to make it 2-1. Then Broxton brought another fastball, but it was 92 mph again and over the plate, and Dobbs was disappointed to foul it straight back. At this point, the TV cameras showed Todd Redmond warming up in the Cincinnati bullpen—an odd move, to warm up a same-sided reliever in a walk-off situation.

Perhaps unwilling to throw the slider to a lefty, and having failed twice with the curve, Broxton finally brought a four-seamer that broke 93 mph to get Dobbs to ground out to third. That brought up Solano, a hitter from whom Buck could glean quite a bit because, like Buck, Solano is right-handed and not a big power threat. With Buck on deck, Broxton started Solano, who was 0-for-3 with three strikeouts on the day and had gone homerless in 368 at-bats between Triple-A and the majors on the season… with a slider down the middle for strike one.

Alarm bells. It’s one thing to be careful with Lee; it’s another to mix in the rarely used curveballs to Dobbs (five percent frequency to lefties this season); it’s still another when the fastball isn’t quite what it usually is; but to Buck, treating Donovan Solano with respect had to have been the final straw. Something was going on here. The Marlins weren’t facing the Broxton they expected, and the next four pitches bore that out. On 0-1, Broxton’s fastball (92.9 mph) was about a foot outside and high, and the big righty bent another slider outside the zone on 1-1. And then, in the most telling pitch of the inning, Jonathan Broxton decided that Donovan Solano deserved a 2-1 slider.

At this point, there may be some readers following this logic and others less so—some of you may be thinking that this was just one pitch from one at-bat, and that it wasn’t that predictive of what pitches would follow. So I want to stress that 2-1 sliders to Donovan Solano with two outs in the last inning of a one-run game don’t just happen; for that pitch to be thrown to that hitter in that situation, there has to be something wrong. It’s not that it’s particularly rare for a player not to be in peak form—pitchers take the hill all the time only to find they aren’t operating at maximum efficiency due to one problem or another. But when these situations do arise, the pitcher gives the opposing dugout information about himself with each pitch, either by throwing subpar pitches or by avoiding his usual bread and butter. A smart hitter picks up on that change in pattern. In this case, Buck would have realized that Broxton didn’t trust his fastball, because he was willing to risk a 3-1 count to a weak hitter on the chance (apparently larger than we would’ve thought) that Solano would hit the fastball for extra bases.

That risk became a reality, as Broxton’s slider bounced in to run the count to 3-1. His subsequent fastball (again, 92.9 mph), with Reds catcher Dioner Navarro set up away, was off the plate inside, and Solano took first base.

That brought Buck to the plate. He took (what else?) a first-pitch slider low for ball one, and a 1-0 fastball way outside for ball two. Needing to come in with a fastball on 2-0, Broxton brought a heater middle-middle, and Buck, like Dobbs before him, was unhappy to have fouled it away. I don’t want to grasp at straws to explain the next pitch, an inside fastball that Buck swung through—perhaps Broxton wanted to protect against the possibility of Solano stealing second, or maybe Buck was thinking slider after Solano had seen one on the same count—but it was a missed spot, as Navarro had set up away. With the count even at 2-2, Broxton dialed up a fourth straight fastball, his hardest of the day and only the second pitch that would break 93 mph (it was 94.7). Buck fouled it back to the screen. He fouled off the next two as well—a slider and then a fastball—before taking a slider outside to make the count full. On 3-2, Broxton shook Navarro off (empirically, this is a dead giveaway in baseball circles), and Buck crushed the slidepiece to deep center. In most parks, he would’ve had a walk-off home run.


So what have we learned? I mean, other than Donovan Solano: Modern-Day Mantle? Well, there’s one thing we didn’t learn, because we already knew it: pitchers, especially relievers, can be pretty volatile commodities. It’s almost axiomatic that they can be All-Stars one day and scrubs the next. But maybe an algorithm can learn that, and maybe it can learn it in a way that could help a team in a tight game like the one we just examined. We’ve presented a number of variables relevant to a game in progress that could help us predict a pitcher’s patterns more accurately than his overall tendencies would without them. Among them:

  1. An umpire with a bigger strike zone: It’s not that Marquez necessarily had one, it’s that the perception was there. Does a larger strike zone make pitchers more or less likely to try to expand the zone with breaking pitches? Could the data be stratified that way in real time?
  2. A pitcher throwing a fastball at sub-optimal velocity: If we think of a pitcher warming up to enter a game as a binary equation—either “I have my good fastball today” or “I don’t have my good fastball today”—does the latter scenario make the pitcher more likely on average to throw breaking pitches? Could the data be stratified in real time to reflect which fastball has shown up that day? To some degree, Broxton’s velocity was predictive of his pitch selection. One day, maybe the data will tell us just how much so.
  3. Poor hitters on deck: Okay, so John Buck isn’t Babe Ruth. In fact, he’s a pretty poor hitter himself. But having Brantly and Petersen waiting in the wings wasn’t scaring Broxton, either. Does a weaker hitter on deck make a pitcher more likely on average to throw breaking balls, if he’s willing to risk a walk and deal with the man on deck?
  4. More sliders beget… more sliders: Okay, say none of those first three conditions applies. What if a guy is out there throwing a lot of sliders just for the heck of it, while all the grizzled baseball men in the opposing dugout are furiously packing an extra lip of Skoal trying to figure out why he’s doing it? Can we stratify the data to reflect a guy who just wants to bend them in there today?

I don’t know what the future holds here.  Regardless, Brooks’ and Mack’s research is a much-needed step toward the marriage of sabermetrics and good ol’ fashioned baseball knowledge. Science has extended its hand; now it’s time for the artists to respond in kind.

Thank you for reading

This is a free article. If you enjoyed it, consider subscribing to Baseball Prospectus. Subscriptions support ongoing public baseball research and analysis in an increasingly proprietary environment.

Subscribe now
You need to be logged in to comment. Login or Subscribe
This is great. Very interesting.
After reading, "pitch sequence visualization" earlier this week, I totally envisioned myself sitting down with a massive database to predict pitch types throughout this falls games. I haven't compiled anything yet, but this article got me all excited again :)
Once again, great analysis. Even better are the potentially, predictive variables that you've presented that could add something to a hypothetical "Next Pitch Prediction Algorythm".

You mention a goal of pitch sequence being randomness. This makes sense, as even if you could determine what the "perfect" pitch would be for a scenario, if the batter knew that as well, throwing almost anything else that he is not expecting would be better. So would the output of a pitch prediction tool be percentage weights for each potential pitch type? Would we be disappointed in our pitchers/catchers if the tool could become somewhat accurate? I find this line of thinking interesting (although I am still terrible at guessing pitch sequence).
First, thank you! On those questions:

1) Percentage weights seem like the tidiest output, right? I always think of practicality for a team, though, and you don't want to overwhelm guys with too much information like the percentage chance they might see a certain pitch. What would be cool, though, is to be able to tell your team, for instance, "I know this guy doesn't have his best heat, but the data show that *won't* affect his pitch selection, so don't expect anything different."

2) I'd say we wouldn't be disappointed per se. Sure, pitchers aspire to total randomness, but no one ever gets there because no one throws all their pitches with 100% efficiency. So the priority when choosing a pitch is most often not simply to trick the batter. Good pitches get outs no matter what, and if a catcher has a pitcher who just feels comfortable throwing a certain pitch, no matter the situation, he'd be silly to call for anything else.
It's also interesting that Broxton was missing location with his fastball - variable #2 notes velocity, but not location. That may have concerned Broxton (and Navarro) more than the speed.
You can't really look at the pitchers without taking the catchers into account. Some more than others...