I was not an art major. Kind of like my dreams of being a major-leaguer, my artistic abilities peaked in about third or fourth grade, when the art-class assignments went beyond pasting construction paper shapes on top of each other in some pre-specified order. But I was handy with the collage, which is the big-kid version of pasting vague shapes, this time cut out of magazines, in at least a bit of a formation. The important task is to get all of the important stuff onto the page. How it’s arranged is secondary.

I think the common assumption is that baseball teams are put together the same way. Just put 25 really good players onto the field and you’ll be fine. It doesn’t matter whether they fit together or not. Get their baseball cards glued onto the paper and add up the WARs. It’s one of those things that is intuitively both true and false at the same time. Of course, a team with 25 legitimate all-stars has a better shot than the team with 25 guys who all belong in Triple-A. Talent is a huge part of the game. But there has to be some accounting for the fact that baseball teams aren’t just the sum of their parts, right? Baseball might be a game in which the fundamental unit of existence is the batter-pitcher individual matchup, but it’s still a team game.

In child development, there is a concept known as the mesosystem. The idea is that there are several influences on a child’s life. Of course, the primary caregivers (usually the parents) are the most important, but then there are the teachers and the extended family members and the day care workers and the pediatricians and the parks and rec employees. All of them influence a child in some way, but how well are all of those people connected to each other, as least as it relates to the child? For example, I might be a good parent and my daughter might have a good teacher, but if I never communicate with the teacher, then the teacher doesn’t get the additional benefit of my knowledge of my daughter, nor do I get to know what needs to be reinforced at home. But if we have a good way of communicating (and use it), then we both become better at our respective jobs. I’ve not changed as a parent, nor has my daughter’s teacher changed, but the strength of that connection between the two of us will have a real effect on my daughter.

We pay lip service to the idea of a mesosystem in baseball. James Shields (or any pitcher) going to the San Diego Padres is a good idea because the park is so big. The Padres staffing their outfield without a true center fielder (sit down, Melvin Upton Jr.) is a bad idea because the park is so big. We talk about ground-ball pitchers in front of good infields and how the fly-ball defense of the Royals’ outfield is making their pitchers look amazing last year. But then we worship at the altar of WAR, which by its very nature tries to strip the context out of everything. There are plenty of times when that’s a feature rather than a bug, but this is a bit of a weakness. Is there a point where a player who is worth more by WAR is not actually the best player for a job? Should we instead go for the guy who’s a better fit? There’s bound to be a line somewhere in there, but where?

Warning! Gory Mathematical Details Ahead!
For this one, we’re not going to worry about the third decimal place. Here, I mostly want to get at the correct order of magnitude for a couple of ideas. For example, how much does a good infield mean to a ground-ball pitcher? To test that, we’re going to get a little bit abstract.

I looked up the best, 10th-place, 20th-place, and worst infield defenses when it came to ground balls in 2014. They were, respectively: Oakland (76.1 percent of all ground balls ended up as outs), Milwaukee (73.7 percent), the Yankees (72.2 percent), and the Rays (69.8 percent). It’s a big spread from end to end, but we can see that there’s also a lot of bunching in the middle.

Now I’m going to take the starting pitcher (ERA-title qualifier) with the highest ground-ball rate in 2014, the guy one-third of the way down the list, the guy two-thirds of the way down the list, and the guy at the bottom. They are: Dallas Keuchel (63.5 percent), Corey Kluber (48.0 percent), R.A. Dickey (42.0 percent), and Chris Young the Pitcher (22.3 percent). Same pattern. There are ground-ball machines, fly guys, and a bunch of guys in the middle. To make things a little more standardized, I’m going to assume that each of these starters gives up 600 balls in play (no strikeouts or walks) each year. That’s not true, but we’re just trying to establish some boundaries here.

So, let’s put each of these pitchers in front of each one of these defenses and see how many outs would be recorded in each case on ground balls. If you want to follow along at home, it’s simply 600 * pitcher’s ground-ball rate * team’s ground-ball conversion rate.

A’s (76.1%)

Brewers (73.7%)

Yankees (72.2%)

Rays (69.8%)

Keuchel (63.5%)





Kluber (48.0%)





Dickey (42.0%)





Young (22.3%)





Let’s look at this from the pitcher’s perspective. It’s easy to look at Keuchel on the A’s (290 outs on his ground balls) vs. Keuchel on the Rays (266) and say “Wow!” but of course, that’s the extreme case. Still, it’s worth noting that even guys who are middle-of-the-pack when it comes to inducing ground balls, like Kluber and Dickey, would see four extra outs if they played in front of an above-the-median team like the Brewers instead of a below-the-median one like the Yankees. That may not sound like much, but turning an out into even a single is worth something like .75 runs of value. Those four grounders are three runs of value, and that’s just kinda muddling around the middle of the table. For someone like Kluber, going from a bad situation like the Rays even to the Brewers at no. 10 would be worth 11 ground balls turned into outs, which would be on the order of eight runs. Given the old “10 runs equals one win” standby, if we assume that everything else is equal about the two teams (yes, that’s silly, but just go with it for a moment), we can start to make statements like “Corey Kluber or R.A. Dickey could actually be worth most of a win more just by moving from a bad situation to a good-but-not-amazing one, at least as far as infield defense goes.”

(Note: There are probably some secondary effects in there as well. A grounder guy might feel more comfortable pitching to contact in front of a good defense and alter his pitch-selection that way. There’s much more to explore here!)

If a team knows that it has a good infield defense, it would do well to look for pitchers who will feed that defense ground balls. For example, if the Rays decided to move from a pitcher like Young (bottom of the ground-ball rate scale) to a pitcher like Kluber (above the median), they would net an extra 108 outs on ground balls. If the Brewers did so, they would net 113 extra outs. An extra five outs. (And yes, it may be counter-balanced by good or bad outfield defense on the team for the fly balls that Young would give up, but that can be calculated too.)

That sort of interaction between ground-ball pitchers, even making moves that aren’t “worst-to-first,” can be worth a substantial fraction of a win, and that’s just the interaction of one pitcher with the defense. We crow about pitchers who are worth two wins a season and pay them eight-figure salaries. A team that betters its infield defense can expect an impact at least somewhere in that neighborhood. When that two-win pitcher signs in free agency, people dissect the move from every angle. But when the team signs a new starting shortstop, fewer comment on what his signing will mean for that two win pitcher. It’s starting to happen more often, but given that the value that starting shortstop could bring (or take away from!) the pitching staff, perhaps it should be a standard part of all transaction analyses. Maybe that shortstop should also get a mention for how much better he’s going to look fielding behind a staff that will feed him a lot of ground balls. The magnitudes of the effects are at least on the same scale.

Let’s turn to another area where people sometimes talk about interaction effects: lineup construction. Is it enough to just have 9 good hitters or are there issues of fit to consider there too? We intuitively know that there’s at least some effect of how hitters are arranged in a lineup, although in a study that is not quoted nearly enough, Tom Ruane found that the difference between the usual lineup that managers tend to use and the perfectly optimized lineup (at least according to a computer simulation) is about 2.5 runs over the course of a season. So, realistically, moving the pieces around in a lineup doesn’t actually have as much of an effect as we might think. You might as well just hit the better hitters closer to the top to get them more plate appearances. But what about a player who has a particular skill that might come in handy. For example, should a team invest in a lesser hitter if he is a good bunter?

We know that bunting isn’t the great sabermetric sin that we used to consider it. The way it is used in the present day, it is mostly a break-even strategy. We also have to factor in how often a good bunter would get to use his skills. In 2014, Brett Gardner, Jose Ramirez, and Shelby Miller led baseball in sacrifice bunts with 13 each. Miller is a special case because he’s a pitcher, but even assuming that Ramirez and Gardner had a bunt attempt or two that didn’t go so well, it means that the best bunters in the league were at the plate when the manager believed it made sense to bunt a grand total of 15 times over the course of a year.

Perhaps there’s something to be said instead for having a proper mix of guys in a lineup who make their living off of singles vs. guys who make their living off of home runs (vs. guys who make their living off of their defense). In the Ruane study, the “traditional” lineup composed of a composite of each of the nine positions in the lineup (i.e., the aggregate line of everybody batting in the one-spot, two-spot, etc.) in their traditional order outperformed a lineup in which the spots were ranked by OPS. The size of the effect would be about three runs over the course of a season for the whole lineup, so the balance must have some effect. But then again, if the decision is between a hitter who fits the “ideal profile” of a no. 2 or a no. 6 hitter vs. a guy who is a superior hitter, it doesn’t seem like it would take much for the superior hitter to win out. Most of the skills that would call for interactions effects involve a batter who can do a special something with a runner on base, and the majority of plate appearances take place with no runners on base anyway.

Inventing a Language
This is one of those areas where there’s a lot of unexplored territory. We know that the pieces on a team can fit together in ways that make them more than the sum of their parts, but we need to know how much more. And there seem to be areas that are more ripe for this sort of interaction effect than others. I think when people talk about the ways in which players fit together, they tend to lapse into describing some sort of mystical property of baseball. Maybe not all of the ways that a team can fit together can be measured (we still have no idea how to measure chemistry), but there are some ways where we can at least get an idea of how big the effect is and then we can decide whether we want to chase it or not. The mystical blurring has a way of making it sound like all interaction effects are of the same magnitude. They aren’t.

The reason that there’s a lot of unexplored territory here is that sabermetrics—and baseball in general—has tended to base all of its stats on assigning credit to one person, or crediting the pitcher while blaming the batter (or vice versa). There’s very little room in the sport for recognizing how two forces interact with one another. It’s not just that we don’t have the stats, we don’t even have the vocabulary for it. But the effects can be real and perhaps there is some effect that’s quite valuable. Want to win a sabermetric Nobel Prize?

Thank you for reading

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What? No comments in 24 hours? A day ago I read this and thought it was awesome, so much that I came back to read it again for the gory math.

I've been hoping/begging for this for years (I'm one of the Orioles fans who used to complain about how sabermetrics was dissing my Birds) and I hope you keep it up.

Hey, just for fun, were Mark Belanger and Brooks Robinson just good on their own, or were each better because of the person next to them? Was Don Baylor less bad in left field when Paul Blair was in center?

Youth wants to know.
There's actually evidence that two good defenders next to each other makes them both a little worse!
Putting two hitters with high ISO next to each other in a lineup may also have negative synergies. Back-to-back extra base hits are often wasteful.
I've always thought batting order would be good as motivational technique/reward. Using static analysis, it may not matter for runs/game - but it sure does matter for player contracts. If at the margin, players have control over improving some of those skills that really do matter at producing runs - esp at particular spots in the order - then why not directly use batting order as the positive feedback loop that rewards those players who best improve the skill.

Kind of like the good parking spot for the 'employee of the month'.
Or how about this: since the difference between an optimized and a typical lineup is so small, why not let player comfort dictate where players bat? If a player is more comfortable batting sixth than batting second for whatever reason, screw it, let him. You're costing yourself at most like two runs per season, and that seems like a fair price to pay to keep your employee happy. Maybe, because he's happy, he'll play better and get you those runs back somewhere else.