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In Thursday’s Boston Globe, Alex Speier had an interesting piece about new Red Sox first baseman Mitch Moreland. Speier began by noting that Moreland and Anthony Rizzo of the Cubs, who field and throw left-handed, won the two Gold Glove awards at first base in 2016, and that left-handed first basemen seem to have a substantial advantage in Gold Glove voting. His question: Why?

We all know several of the reasons and Speier deftly touches on them all. The throw to second base is easier for a left-handed first baseman. A left-hander wears the glove on his right hand, which might give him an infinitesimal but real advantage on ground balls in the hole between first base and second base. Some of the footwork around the bag can be more easily done in the optimal way by a lefty. There are myriad selection biases at work, too. Red Sox infield coach Brian Butterfield summed it all up by telling Speier: “The whole infield was made for right-handers, except for first base." That’s true.

My question: What if it’s also not true?

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The 2016 season was a breakthrough campaign for Cubs infielder Javier Baez. He didn’t answer every question about the viability of his hyper-kinetic swing or his hyper-aggressive approach, but he flashed all of his tools, made huge plays during the postseason, saw his jersey become one of the best sellers in baseball, and emerged as one of the game’s most exciting defenders.

The fun quirk that drove some of the nerdiest attention Baez’s way was the speed and panache with which he applied tags at second and third base. It’s a small thing, but the more we learn about catchers’ arm strength and pitchers’ role in controlling the running game—and the razor-thin margins between safe and out—the more it seems like a small thing that can make a big difference.

That made it worth asking how Baez came to be the quickest tagger in baseball, and the answer turned out to be a twist on Inigo Montoya: [Baez] is not [right-]handed. In fact, if you were just having dinner with him or asking him for his autographs in the parking lot, you’d call him a lefty. He briefly took up switch-hitting in high school. While he bats and throws right-handed (and throws hard that way), it’s probably more fair to call Baez ambidextrous than to say he’s either left- or right-handed. That helps explain his remarkable prowess with the glove hand on tags, and his body’s easy cooperation in that effort.

That’s a strange, seemingly isolated case, but we know very well that it’s not the only one. I read Roger Angell’s The Summer Game this winter. It’s a collection of his New Yorker essays from the 1960s and early 1970s, and during his description of the 1969 World Series between the Orioles and the Mets he includes this aside about Brooks Robinson:

Almost from the beginning, I became aware of the pressure he puts on a right-handed batter with his aggressive stance (the hands are cocked up almost under his chin), his closeness to the plate, his eager appetite for the ball. His almost supernaturally quick reactions are helped by the fact that he is ambidextrous; he bats and throws right-handed, but eats, writes, plays ping-pong, and fields blue darters with his left.

Don’t ask me to name a third infielder who shares Baez’s and Robinson’s anomalous commonality. I can’t. For all I know, Yuniesky Betancourt is out there brushing his teeth with his left hand right now, ruining whatever prospective value we might extrapolate from the data points of Baez and Robinson. It’s also important to say that neither Baez nor Robinson would be hapless defenders without their exceptionally deft work with the glove itself.

Baez excels, as Robinson excelled, at barehanded picks and throws across the diamond. Baez has, as Robinson had, a dancer’s blend of light feet and physical explosiveness, and he has, as Robinson had, a fearless way about him. None of that can be traced solely or directly to their handedness. Still, that strand of information pulled me down a rabbit hole, and if you look hard enough it’s not hard to find many examples of players’ handedness being more complicated than a pair of one-letter codes on the back of a baseball card.

Hank Aaron famously hit cross-handed until nearly the end of his Negro League career, with his left hand above his right from the right side of the plate. Ernie Lombardi hit with his fingers interlaced on the bat, radically changing the way his arms interacted relative to almost all other swingers in the history of the game, and he won a batting title. Billy Wagner broke his arm playing hat football when he was a kid, so the natural right-hander learned to throw baseballs left-handed rather than miss out on a season. According to The Bill James Historical Baseball Abstract, Tris Speaker was right-handed as a kid, then fell off a horse when he was 10, and “ever after threw left but was basically ambidextrous, like many of the great glove men.”

These are just stories. There’s no hard data here. That’s not because I’m just ramping up to the good stuff; it’s because we don’t have hard data on handedness. Sure, we know which hand everyone uses to throw, and we know who bats from which side of the plate (and about the guys who hit from either), but we don’t have detailed information on those players’ lateralization.

A recent study (handedness is a rich and well-farmed field of genetic research) suggests that sport-specific handedness correlates only loosely with handedness in everyday life and that that’s especially true at the highest levels of sporting competition, so the odds are that there are dozens more players like Baez and Robinson, but we don’t know who they are. Various efforts have been made to develop useful lateralization quotients for general populations, with varying (but generally limited) success.

We simply don’t know how left- or right-handed most players are, and it leaves us with an incomplete understanding of most of their movements and abilities. Ted Williams believed he would have been a better left-handed hitter if he had been a natural left-hander, but is that true? It’s hard to say. For a long time, fast right-handed hitters were brought into pro baseball and taught to switch-hit, to avail themselves of their speed. Because most hitters mostly pull the ball when they hit it on the ground, though, maybe those hitters only hurt themselves by doing so. Maybe, on the other hand, they would always have been better off switch-hitting or batting left-handed in the first place.

We understand handedness in humans better than we almost ever have. Three weeks ago, a new study identified left-right preference in gene expressions within the spinal cord areas that control the arms and legs. It found it in fetuses in utero, at eight weeks. At that point, the motor cortex in the brain has not even developed a working relationship with the spine. Before brain development even enters the equation, epigenetics make us left- or right-handed.

We understand handedness in baseball only a little better than we ever have. We know about certain platoon interactions in batter-pitcher matchups that go deeper than “righties see the ball better out of lefties’ hands.” We’ve dramatically improved our understanding of hitting and pitching mechanics in recent years, and everything we’ve learned has helped us understand the way the body must cooperate across hemispheres (but also, which elements of either process require the dominant side to lead).

We can intuit the reasons why freak incidents like Wagner’s and Speaker’s can create historic talents: those players taught themselves to perform difficult athletic tasks at an elite level with the wrong hand, which likely means not only that they were unbelievably talented to begin with, but that they had better use of the off hand than most players, in almost everything they did.

We don’t know, though, whether being naturally left-handed makes a catcher a better framer. We don’t know whether a natural righty or lefty has a particular advantage when it comes to tracking fly balls (it sounds like there would be no chance of that, but given what we know about brain hemispheres and the correlation between handedness and the activity of those hemispheres, it’s at least possible). We don’t know how much stronger a natural right-handed shortstop’s arm is, relative to a naturally left-handed one, if at all.

I would want my scouts to tell me whether a high-school pitcher throws with the same hand he uses to write. I would want them to know whether a promising shortstop swings a golf club or shoots a basketball or holds his phone the same way he hits and throws. I don’t know whether we’d find a large number of unusual cases in this regard, or whether the ones we did find would consistently matter, or what valence any correlation between handedness and infield or catching prowess might be. I do know that, if I were running a team, my database would have the player’s lateralization for as many activities as possible, because baseball is a game with a unique geometry, one that ensures that handedness will always matter.

We don’t know the handedness of most running backs or wide receivers, and while we know which hand quarterbacks and three-point marksmen use, there’s no major, inherent, irreducible advantage or disadvantage there. The other major team sports are much less shaped by lateralization. In baseball, this stuff matters, so we should have better data on it.