Four-Man Outfields Gone Wild

Five years ago, gimmick defenses were bush league. I don’t just mean that in the pejorative baseball sense, though of course I mean that too. Rather, I mean that when Sam Miller and Ben Lindbergh were running the Sonoma Stompers, they toyed with adding gimmick defenses to their indy ball team, and the team rebelled. The players tolerated it — not without reservation — but the reason the wild defensive alignments merited mention in the book is because they were wild.

That was 2015, however, and sensibilities have changed since then. Strange defensive alignments are hardly unusual now. Joey Votto faced a four-man outfield in 2017, and it’s gotten weirder from there. Joey Gallo faces four-man outfields with some frequency. Five-ish man infields have sometimes been a thing in do-or-die late game situations, but the Dodgers rolled one out against Eric Hosmer in the middle innings last year.

I know what you’re thinking. Ben’s going to talk about the “seven-man outfield” the Royals used against Miguel Cabrera. I’m not exactly sure that’s a novel defensive alignment, though. Backing up when somebody slow is batting isn’t the same as forfeiting a right fielder or inventing a new position. It was funny, no doubt, the ultimate mark of disrespect for someone’s speed, but teams have been doing something similar to Albert Pujols for years.

Even though the shock of novel positioning has mostly worn off, I did do a double take on Monday night. With the Pirates attempting to lock down a 5-1 win against the Brewers (about that…), Justin Smoak came to bat. The Pirates checked their laminated positioning cards, shuffled around, and presto! Four in the outfield:

Offhand, it feels weird. What are four man outfields for? In a general sense, the point is to convert more batted balls into outs, but that’s hardly useful. That’s the point of all defense. Staying broad, the idea of a shift is that you move a fielder from a place where they were unlikely to field many batted balls and find a place where they can field more, or potentially more valuable, batted balls.

For infield shifts, the tradeoff is grounders in one place for grounders in another. Count up the expected batting balls, move people away from the places where there aren’t many to the places where there are tons, and profit. It’s not hard.

Exotic shifts like overloaded outfields, on the other hand, require more calculation. Uncaught fly balls and line drives don’t only become singles, though they do their fair share of that. They also become doubles and even triples, which means that a straight tradeoff doesn’t make sense. Consider the raw math: with a runner on second base and no one out, teams scored 1.142 runs per inning in 2019. With one out and no one on, they scored a mere 0.287. Turning a double into an out saves the defense 0.855 runs on average.

On the other hand, turning an out into a single (should the batter hit a grounder to a vacated spot) turns that 0.287 run expectancy into 0.926 runs of EV, a cost of 0.639 runs. Just divide the two; from a none on, none out situation, you can give up 1.33 doubles in exchange for one single.

Only, uh, that math is all wrong. That might be fine in the first inning or the fifth, but in the ninth inning, run expectancy is absolutely the wrong way to look at things. The Brewers were down four runs with one inning left. Either they’d score four-plus runs, or they’d go home. By the time that fourth run scored, Smoak would long be in the hotel, whether he reached on a single or double. The only added value of a double is avoiding double plays, a real but minor concern.

For the purposes of our math here, let’s ignore the double play possibility. It’s a tiny edge, and the Pirates would likely let Smoak take second on defensive indifference anyway. This has a huge calculation benefit: now that we’re counting singles and doubles equally, the math gets much easier. How many base hits does a fourth outfielder save, and how many base hits does playing without a third baseman surrender?

The first thing to do is work out how often Smoak even puts a ball in play. We’ll use his projections for this year to handle the percentage of his plate appearances that end in dingers, walks, strikeouts, hit by pitches, and finally, balls in play:

Russell Carleton’s research has shown that shifting has effects on non-contact outcomes. Notably, pitchers walk more batters with a shift on. I’m going to completely ignore that finding, however, for one simple reason. The uncertainty around the magnitude of that effect would likely swamp the actual numbers I’m looking for: the difference between a straight up defense, an over-shift, and a four-man outfield. If you’d like, you can sprinkle a little shift-walk-dust on my equations at the end of the calculations.

Great news! If we ignore the effect on non-contact outcomes, we can just ignore the non-contact outcomes altogether. All we care about, then, are the 56.3% of plate appearances that end with a ball in play. Let’s dive deeper into Smoak’s batted ball tendencies to see what gives:

The above table is something of a special blend of mine. It uses 50% 2019 data, 30% 2018 data, and 20% 2017 data, and only when he’s batting left-handed. That will already make the numbers look a little different than you’re used to with Smoak, but there’s another twist: this is batted ball data for balls in play only, not all batted balls. That’s why his fly ball rates are lower: short of employing Cirque du Soleil, no defensive alignment is going to help catch those home runs.

A few other quick notes on the data: I used Baseball Savant classifications to separate extremely high-angle balls, listed here as popups. Defensive alignment matters less for those — they’re just hanging there to be caught. Also, there’s probably some bleed-over between line drives and fly balls, and between grounders and low line drives. That’s just the nature of the beast here.

The Pirates got one thing right: Smoak hits an absolute boatload of fly balls. Only 40% of his batted balls are on the ground, which makes the idea of putting half of the available fielders where he hits the ball more often quite tempting. Let’s work out what to do with those grounders.

As I mentioned above, we’re considering three scenarios: no shift, over-shift, and four-man outfield. Working out the BABIP for the first two is easy enough; we can just look at Smoak’s career grounder BABIP in the two shift types. The numbers are grim on Smoak’s end; a .183 BABIP against a regular alignment and .116 against the shift.

Next, we need to come up with a BABIP against a three-man infield. Look at the picture again; it’s a normal infield alignment for a left-handed hitter, minus exactly one third baseman. If we want to guess what that looks like, we can treat pulled and up-the-middle grounders as occurring against a regular defense and opposite-field grounders as occurring against a shift. Here are Smoak’s spray angle on grounders, again blended over the last three years:

Yeah, that’s a lot of pulled grounders. Next, we need to know his career BABIP in the three requisite areas. We’re very light on data against standard alignments, because teams simply don’t play Smoak straight up, but we can at the very least plug in overall BABIPs for lefty batters and regress him towards those. Put it all together, and Smoak’s expected grounder BABIP comes out to .191 against this goofy defense.

You might notice that that’s basically the same as his BABIP against a regular alignment, which means there’s probably something wiggly in the numbers somewhere — likely due to regressing his standard-defense production to the mean. That’s okay, though — we don’t actually need to worry about the Pirates playing Smoak straight up, only about whether they should over-shift or hang someone out in the outfield.

Next, take a look at a tantalizingly incomplete chart:

All the Pirates have to do is work out those question marks, and they’ll know whether it makes sense to deploy this zany shift in a four-run game. The only problem is, it’s really difficult to work out those question marks!

You might think we should look at the league-wide data. I’d love to. There’s just one problem — there isn’t any league-wide data. Batters have hit exactly 40 line drives against alignments that Statcast classifies as “four outfielders.” They have a .718 BABIP on them. They’ve hit 40 fly balls, with a .129 BABIP. Popups? A whopping 17, with no hits to speak of. We can’t use those numbers, so we’ll have to make our own.

You want to look at some dots? Let’s look at some dots:

Too many dots! We aren’t doing a psych test here. Let’s look at fewer dots:

There’s probably something to be done with these, based on an analysis of hang time and outfielder speed. You could in theory come up with a maximization algorithm to place your four outfielders in the places that could cover the most balls given location and hang time.

That sounds like a real pain, though. What are we, data scientists? Let’s answer a different question: What would those BABIPs need to be for this to make sense? Then we can see if those numbers seem reasonable and go from there.

First things first: we’re setting popups to a zero BABIP. I know, I know, nothing’s zero, but deal with it. Next, we’re setting both line drives and fly balls to some fraction of their regular BABIP. This isn’t perfect, but we’re not going for perfect, we’re going for functional. Now the table looks like this:

Our next problem is to solve for x, and if you’re wondering when this article turned into seventh grade algebra, well, you did see my name in the byline, soooooo. In any case, the answer works out to roughly 85%. In other words, if the Pirates can turn 15% of the line drives and fly balls that would previously have been hits into outs, they’ll break even — Smoak’s BABIP against a four-man outfield will come out to .255. Bad news, friends. This means it’s time to look at more dots:

That’s the location of every line drive or fly ball that went for a hit since 2015. It will be hard to fix the ones in right field, as those are mainly roped line drives, but the doubles down the line and singles into the alleys are easy pickings. It’s not hard at all to believe that the Pirates could turn 15% of those dots into outs.

In fact, 15% might even be too high. That .116 BABIP that Smoak posted against the shift is wildly low. Bump it up to .150, still miles below the league average, and they’d only need to turn 8% of those hits into outs to break even.

Smoak is simply the perfect shift target: he hits almost everything in the air, and even when he hits it on the ground, he rarely hits the ball the other way. In fact, among left-handed batters who have hit at least 500 grounders since 2015, Smoak has the second-lowest opposite field rate, ahead of only Carlos Santana. He simply doesn’t hit the ball there.

That explains the no third baseman. The over-shift is because in that same cohort, Smoak has the fourth-lowest groundball rate. None of his balls are grounders, and none of the grounders are to third. Might as well deploy those infielders somewhere they can get some work.

There’s a wild conclusion to all of this. If you’re willing to shift against Smoak here, when doubles and singles are interchangeable, you should shift against him basically every time he bats left-handed. Maybe you can go to an over-shift enough to keep that in his mind, or maybe with a runner on base you can’t go without someone at the hot corner. Whenever possible, though, it’s a good idea to put cleats in the outfield.

It won’t matter much. It’ll hardly matter at all! Let’s say you can find a new alignment that saves 20 points of BABIP, a huge margin. That would require turning a quarter of those hits into outs, no small feat. That’d be 36 hits saved over Smoak’s entire 10-year career, and that’s if you shifted every single time he batted lefty. It’s a tiny edge, as edges in baseball so often are. But it’s still more than zero, and teams are in the business of adding non-zero amounts to their chances of success whenever possible.

Oh, by the way. Smoak smacked a groundball single through the infield, one that an over-shift might have had a chance at. The Brewers tied the game with two outs and won in extras. Percentage plays don’t always work, even if they’re the right call. Sometimes you work out all the angles, and then this happens: