Everybody’s Thinking About How Short You Are

Back in August, the baseball savants at Baseball Savant bestowed upon us nerds yet another helping of Statcast data, this time in the form of a first base receiving leaderboard. Mike Petriello and Tom Tango wrote explainers describing how the new metric works and what exactly it means. Want to know who’s the best at scooping the ball, or corralling bouncers, or jumping up and snaring high throws and then landing on the bag before the runner? Now you can learn that information without having to watch all that bothersome baseball.

In the simplest terms, receiving works like other Statcast metrics. Each throw to the first baseman has a catch probability, which then maps onto out expectancy. Say a throw has a catch probability of 75%. A first baseman who makes the play earns 25% of an out, while the first baseman who muffs it loses 75%. With this data, I can tell you that this season, Alec Burleson has been the best at this skill by a wide margin, while Bryce Harper has been the worst by the same amount. That last part’s not necessarily a surprise, considering that six weeks before the new metric dropped, I wrote an entire article detailing ways in which Harper needed to improve at the cold corner, and that four weeks after that, the Phillies moved Harper off the position altogether (maybe they should’ve tried some of my fixes).

Within his explainer, Petriello noted that, as is so often the case in the game we love, the numbers tell us that receiving is not quite as important as we might want it to be. In our hearts, scooping the ball is the soul of the first base position. If you can’t pick it, you don’t belong there. But in reality, opportunities to scoop the ball come so infrequently that its value is in no way commensurate with the premium we place upon it. Spencer Torkelson and Jonathan Aranda sit atop the scooportunity leaderboard with 18 apiece, which means that they don’t even see one per week. The next time you attend your Saturday night Moneyball singalong and you shout along with Ron Washington that first base is incredibly hard, feel free to voice your own addendum: “But it doesn’t matter much anyway.”

Nevertheless, I haven’t been able to keep away from this leaderboard. Tango and Petriello explained a whole lot, but I still found myself overflowing with questions that this new data can finally help us answer. Scoops and bouncers and wide throws may not be as important as I want them to be, but that doesn’t make them any less interesting. I have a bunch of article ideas about this topic, but today, we’re starting small.

More specifically, we’re starting with small first basemen. The leaderboard helpfully lists the height of each first baseman, and as I sorted and perused and re-sorted and perused further, I found myself wondering how much the height of a first baseman affects the throws he receives.

Say you play for the Reds. Earlier in the season, you were throwing to the 6-foot-4 Nathaniel Lowe, but today your target is the 5-foot-9 Spencer Steer. That’s a difference of seven inches, and we should probably add a couple more, because wingspan and reach are what really matter here. Let’s do some very, very oversimplified math and say that Lowe has a catch radius of nine feet even, while Steer’s is eight feet and three inches. When you plot those two semicircles around first base, you find that Lowe’s target is nearly 3,000 square inches bigger than Steer’s.

Here’s my question: Does a major league infielder notice the difference? If you’re Elly De La Cruz and you’re throwing the ball to first at Mach 2, are you throwing the ball differently based on who’s over there wearing the big weird mitt? Take a moment to consider it. On the one hand, we’ve established that the difference in catch radius is awfully big. On the other hand, you’re a major league infielder, which means that you have an excellent, accurate arm, and which also means that you have tons of confidence in your ability to hit the first baseman in the chest. You’ve done it countless thousands of times. Moreover, I know I made a meal of the difference in catch radius, but the difference in the actual location of the target is so small as to border on negligible.

Obviously, you’re likely aiming your throw for the first baseman’s center of mass, or maybe his chest. But the difference in the height of the chest is much smaller than the difference in wingspan (and even less so for the center of mass). Above is the only picture I could find where Lowe and Steer are standing next to each other. It’s by no means perfect, but you can see that the difference in the height of their chests is much smaller than the difference in actual height. That’s just how bodies work; in the same vein, I’ve written before about how the bottom of the strike zone is much closer for tall and short batters than the top of the zone.

So you’re De La Cruz – who is, as one of the game’s foremost purveyors of the throwing error, either the absolute wrong player to use in this hypothetical or the perfect one – and you’re throwing the ball to first base. Your tall first baseman has a much larger catch radius, but your standard target isn’t all that much different even when your short first baseman is in the lineup, and you’re certainly not worried about making a bad throw, for you are the one and only Elly De La Cruz. So we’ve thought it all through. Are you actually throwing the ball any differently? Are you consciously lowering your target, or taking an extra second to aim, or even taking something off the throw? Let me show you in a graph and then I’ll break down how we got there.

That’s a resounding yes. For every inch of height, you’d expect a first baseman’s rate of high throws to rise by a bit over a quarter of a percent. Baseball Savant doesn’t give us the granular data about each throw, which would be nice for this question because it would allow us to calculate each player’s average throw height. It gives us a breakdown of each first baseman’s chances, which are split into six categories: On Target, Bounce, Scoops, Low, High, and Wide. (Quick note: These categories don’t take the height of the first baseman into account. A throw is high when it comes in seven feet off the ground, regardless of the first baseman.)

I pulled the total opportunities going back to 2021 for each first baseman who’s received at least 500 throws. I aggregated the Low, Scoop, and Bounce categories to give us one number for all low throws, then I broke down the frequency of high and low throws based on the height of the first baseman. I figured that if shorter first basemen were getting significantly more low throws or fewer high throws, then that would be proof that infielders are indeed taking their height into account, and that’s exactly what we saw.

Here are the correlation coefficients between the rate of each kind of throw and the height of the first baseman. The first row shows the percentage of all throws, and the second row shows just the percentage of bad throws. As always, a correlation coefficient of 1.0 or -1.0 would be a perfect correlation, while a zero would be no correlation whatsoever. Frankly, the numbers are a lot higher than I expected.

The correlations here are strong enough to be indisputable. You’ve seen that tall first basemen are much more likely to receive high throws. Those who stand 5-foot-11 or shorter receive high throws 4.4% of the time, while those who stand 6-foot-2 or taller get them 5.9% of the time. We’re talking about small numbers here, but that means the likelihood is nearly 30% higher for a tall first baseman.

As you’d expect knowing all this, short first basemen are more likely to receive low throws. But that’s not true all the time. The correlation is half as strong as it is on high throws. However, that second row tells us the correlation is almost exactly as strong as long as we’re using off-target throws, rather than all throws, as our denominator. When infielders are missing, they’re much more likely to miss low for a short first baseman. In other words, when they know they can’t make a perfect throw, when they’re rushed or off balance – the exact times when you wouldn’t expect them to have the bandwidth to stop and think about how tall the first baseman is! – that’s when they’re definitely aiming lower.

Maybe the most convincing correlation of all is the one between height and on-target throws. It’s not quite as strong as the others, but it’s strong enough and it’s unambiguous. The taller you are, the fewer perfect throws you get. Infielders aren’t as likely to miss low, but they’re a bit more likely to miss wide and they’re much more likely to miss high. Basically, when they see a big, tall first baseman over there, they just let the ball fly. The 5-foot-10 Luis Arraez isn’t the shortest man in our dataset, but he certainly gets treated like it. His 3% high throw rate and 11% low throw rate are both the most extreme in the game. Compare his throw chart to the 6-foot-5 C.J. Cron, whose 7.8% high throw rate is the greatest in our sample. The difference is obvious even at a glance.

Cron gets way more high throws. Arraez gets more throws that are right in scoop territory, whereas Cron’s low throws are all over the place. He gets tons of long bounces, balls where the infielder just heaves it in the general vicinity of the bag and trusts his lanky first sacker to reel it in.

The really interesting part is that the makeup of the throws makes this whole thing just about a wash. Taller players get fewer perfect throws, but their larger catch radius allows them to complete a higher percentage of their extra tough chances. If we go back to our buckets of short players and tall players – 5-foot-11 or shorter and 6-foot-2 or taller – we find that both cohorts make the play on 94.5% of the throws they receive. In fact, we can even go one decimal place further. Both cohorts are catching 94.46% of those balls.

Now, maybe none of this surprises you very much. Of course taller players present taller targets and get higher throws. However, the numbers are way more extreme than I expected. Moreover, I have to guess that if you asked them, most major league infielders would tell you that they’re not thinking about the height of their first baseman at all, and they might even truly believe that to be the case. Instead, not only are they tailoring their throws to the size of the first baseman, but their calculus is basically perfect. All infielders have a clock in their head that tells them how much time they have, whether they can wait back for an extra hop, whether they can stop and set their feet, how fast their transfer has to be, whether they can take a peek at first base. Clearly, the height of the first baseman is part of the calculation too, or else the numbers wouldn’t break even so perfectly. No matter how tall you are, you’re likely to see chances that will allow you to make the play 94.46% of the time.