Aaron Judge and Jose Altuve shouldn’t co-existant in baseball, but their mutual success reveals an amazing fact about different paths to pitcher dominance.

Here’s a line of reasoning using the transitive property about short hitters and small strike zones:

- If a player is shorter, then his shoulders are closer to his knees.
- If his shoulders are closer to his knees, his strike zone should be smaller.
- If his strike zone is smaller, then it should be harder for the pitcher to throw strikes.
- If it is harder to throw strikes, he should get on-base more.
- So, shorter players should have higher on-base percentages.

But this isn’t how it actually works. Why not

Aaron Judge is tall and Jose Altuve is short. That’s analysis. They both are very productive at the plate. That’s deeper analysis. However, Aaron Judge gives pitchers a 25% larger strike zone to target due to his 6′ 7″ height, so he must be doing something different *and better *than Altuve to offset the larger area he gifts to pitchers with every pitch.

Have you ever asked yourself how weird the Judge/Altuve co-existence is? To me, it’s like quantum mechanics and general relativity – we don’t understand how these two things can be true at the same time, but they do. Aaron Judge is general relativity and the tallest every-day player in MLB and Jose Altuve is quantum mechanics and the shortest. They are opposites in stature, yet both are legitimate MVP candidates (or past winners in Altuve’s case). This is not common.

It’s not comparable to the NBA, where you can have a 6′ 11″ Giannis Antetokounmpo and 6’0″ Allen Iverson both as HOF players – they affect the games in different ways that accommodate their heights. Giannis uses his size like Thor’s hammer to dominate opponents, while Iverson played like a torpedo fired down the exhaust port of a Death Star. It *is* comparable to identifying the best Left Tackle in the NFL. Question – who am I describing when I `At 6' 5" and 330 lbs., he has the balance of a ballerina, reactions of a mongoose, and power of a silverback gorilla`

I looked at the distribution of strike zone heights and mid-points across all hitters who saw at least 400 pitches in 2018, and compared that to their season wOBA. The results below show a huge distribution in heights, but no strong correlation with wOBA. This is counter-intuitive and also shows how astonishing it is that Judge and Altuve are on extremes in both dimensions.

How uncommon are Judge and Altuve? They are both members of what we call `2 & 1 Club`

`Strike Zone Height`

(though obviously, they deviate in opposite directions), and 1 standard deviation above league average wOBA. In fact – This is so rare, they are the *only* members.

The odds of a player being >= 2 standard deviations away from the strike zone size is about 5%, and being 1 standard deviation above the wOBA average is about 17%. If we assume these are independent variables, then the probability of a single player being both of these groups is less than 1%. I suspect that is even over-stating the probability because tall players can fake-short and create small strike zones, but short players can’t do the opposite. This would be Judge an even rarer bird due to his tall zone.

Altuve is unique in this respect, but Judge is the true marvel to behold. First, he’s not only the only player in `2 & 1 Club`

`2 & 1 Large`

– he’s the only player in the `1 & 1 Large Club`

(1 standard deviation above the mean in both strike zone height and wOBA)! And it’s not even close. Amongst players who are at least 1 standard deviation over the average, Judge is still over .050 wOBA points ahead of the next-best hitters (Cody Bellinger and Jose Ramirez). Altuve has players who are at least almost-peers (Adam Eaton and the surprisingly-squatty Bryce Harper), while Judge stands tall and alone.

This begs the question – how does Judge do it? How does he offset the enormous liability of a strike zone 25% bigger than average well enough to be one of the best hitters in the league? I believe it has something to do with how he capitalizes on pitches in the zone while smaller hitters gain an advantage by avoiding pitches outside of the zone. That is Judge smashes hittable pitches while Altuve is *judicious* about what he swings at.

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