Trevor Bauer and the Math of Pitching Backwards

When I was a kid, my dad taught me about baseball whenever he got a chance. A lot of these lessons were just meaningless baseball truisms: always hit to the right side of second base when there’s a runner on, the best count to steal on is 2-0, catchers are never lefties. Most of these sayings stuck in my brain without ever registering on a conscious level, but one of them fascinated me the moment I heard it. “Throw fastballs when the batter is ahead in the count and breaking balls when he’s behind.” It is known. I’ve pondered the reasoning and factuality of that rule of thumb ever since.

At the most basic level, I totally understand the thinking going on. Fastballs are easier to locate for a strike, and when you’re behind in the count you can ill afford to throw a pitch for a ball. It’s not just that, either. When a batter is down in the count, they need to be much more proactive about swinging at any pitch in the strike zone. If you throw a 1-2 breaking ball that starts out looking like a strike, the batter needs to swing. Throw the same pitch on 2-0, however, and even if it looks like a strike at the start, the batter might not swing — they could be looking for a specific location rather than defending the entire plate.

Go one level higher, however, and things get a lot more confusing. Pitchers throw fastballs when behind in the count, and batters know that pitchers throw fastballs in hitters’ counts. If a hitter knows you’re going to throw a certain type of pitch, that makes their job a lot easier. One of the hardest parts of being a major league batter is that you have to determine how a pitch is going to break after leaving a pitcher’s hand almost instantaneously. Curveballs and fastballs might start at the same place, but they end up in different areas entirely. Take this deception out of the equation, and hitting gets quite a bit easier.

That’s only one level up, though. We can go further. Pitchers know that hitters know that pitchers throw fastballs when behind in the count. If you’re getting a Princess Bride vibe here, you’re not alone. This is a complex issue. What batters expect pitchers to do plays a role in what pitchers should do, and vice versa. There’s an entire field of economics, game theory, devoted to solving this problem. Maybe you saw the movie about it, where Russell Crowe inexplicably writes on every glass surface he can find.

Let’s leave that all aside for now, though. Whatever the theoretical equilibrium is, pitchers do indeed lean away from breaking balls when behind in the count. In 2018, for example, pitchers threw sliders and curveballs 18.8% of the time when behind in the count, versus 27.5% of the time when they were ahead. That’s major league baseball as a whole, though. Collin McHugh has gone to a breaking ball 58% of the time when down in the count. Gerrit Cole is above 40%, and Robbie Ray isn’t far behind him.

Trevor Bauer, on the other hand, seems to have listened to my dad’s advice. Bauer has thrown 139 pitches while behind in the count this year. He’s gone to a breaking ball exactly twice. He’s on pace to set a career low for breaking balls while down in the count, and it’s not even particularly close. In 2016, Bauer fired only 43 breaking balls out of 878 pitches he threw while behind in the count. That was a preposterously low 4.9%, and still triple the rate he’s put up this year so far.

When something is this much of an outlier in April, it’s easy to throw a small sample size disclaimer on it and move on with life. After all, Tim Anderson is still batting .400 — it’s too early in the season to be sure of anything. That said, this feels consequential to me. Bauer has thrown 3,463 pitches while behind in the count since 2015, and only once in that time frame has he abandoned his breaking pitches to anywhere near the extent he has this year. Take a look at a 100-pitch rolling graph of how many breaking pitches Bauer has thrown in the last 100 pitches he’s thrown while behind in the count:

What’s amazing about this change is that as recently as last year, Bauer hit 30 breaking balls out of 100 pitches. He used to be extreme in the opposite direction. What gives?

Well, for one thing, Bauer isn’t the same kind of pitcher he was four years ago. Take a look at how his pitch mix has changed over time:

Bauer is throwing fewer breaking balls this year all over the place, not just when he’s behind in the count. When he was even or ahead in the count last year, he threw a breaking ball 50.7% of the time. This year, that number is down to 30.7%. He’s replaced most of the decrease in breaking pitches by throwing his cutter and changeup more. The cutter in particular has come in handy this year — he’s already thrown 19 while down in the count.

Still though, that doesn’t come close to replacing the missing breaking balls. Bauer threw cutters in hitters’ counts last year, too. This change can’t be explained away by saying that he’s throwing a harder slider and calling it a cutter. For the most part, Bauer looks like he’s shelved breaking pitches when behind in the count and replaced them with fastballs, staying true to the old adage.

What’s driving it? Well, with a lot of players, I’d call it accidental and move on with life. With Bauer, however, you can safely assume nothing is an accident. Let’s take a look at the outcomes he got on these pitches in 2018:

Plug in Bauer’s career whiff and foul rates on breaking balls in and out of the zone, and you get a grid that looks like this:

Now that we have the outcomes, we can do a little math to see the impact of throwing a breaking ball in these situations. To do this, we’re going to need to use a Markov chain, so heads up, brief math details follow. To figure out the wOBA impact of a ball, we calculate the difference in wOBA between a given hitters’ count and the same count plus a ball (I used 2018 stats). Then, we weight by how often each hitters’ count comes up. We can do the exact same for a strike.

The balls in play were trickier to handle — I decided to calculate Bauer’s career wOBA on contact on both in and out of the zone breaking balls and compare that to his wOBA allowed in hitters’ counts. I’m willing to believe this isn’t perfectly right, because I’m mixing league-wide rate stats with Bauer’s rate stats, but it’s a place to start. The result looks like this (including accounting for foul balls on 3-2):

Overall, throwing a breaking ball while down in the count was ever so slightly better than neutral for Bauer. Let’s repeat this process for cutters, changeups, and fastballs:

The situation is as clear as mud. Throwing more cutters looks to make sense — even if you believe batters are going to continue to tattoo out-of-zone cutters (career .435 wOBA on contact on cutters out of the zone), which seems unlikely, they lead to the best outcomes. Fastballs fail because they get put in play too often, which makes sense. A batter swinging at an in-zone fastball when he’s looking for it is not what you want. Changeups fail because Bauer couldn’t locate them for a strike in 2018. In a small sample this year, he hasn’t done much better, but you can at least see how a changeup might work.

Overall though, Bauer seems to be tinkering with his pitch mix without the numbers telling him he needs to change. Maybe he doesn’t have a good feel for his curve and slider so far this year. Maybe it’s situational. Maybe it truly is a small sample mirage. Still, as with most things Bauer, I’m fascinated by digging into the numbers, knowing that he and the Driveline team are probably doing the same. I’ll be watching the rest of the season to see if this was a blip or the start of a new trend.

Well, for all that investigation, it looks like Bauer’s pitch mix change can’t be easily explained. Still, we have this neat Markov chain toy. Let’s use it to see how league-wide breaking balls in hitters’ counts looked in 2018:

Now that right there is a result. When pitchers threw breaking balls in the “wrong” counts last year, they prospered. This isn’t necessarily a stable result. Batters could adjust to pitchers throwing more junk. It could be that most pitchers can’t spot their breaking balls for strikes, so that the league data is actually two populations, one that should throw way more breaking balls and one that should throw fewer. Still, it’s fascinating.

Conventional wisdom tells you to pitch to the count. So far in 2019, Trevor Bauer, not exactly a paragon of conventional wisdom, seems to agree. The league-wide numbers, however, tell you something else entirely. Nothing quite lines up, because there are too many possibilities, too many things that both pitchers and batters can change to try to get an edge. Baseball is neat like that.