OK, so the NBA analogy I invoked the other day has prompted some confusion. I’m in Australia and have two ASA papers to finish and several more room-escape-puzzles to try, so I don’t have time for a longish post about this, but:
Everybody agrees and understands that height is important for success in basketball. Why does height matter? Is it because players heads are higher? A little, for purposes of vision, but mostly height matters because of what it implies about how far people can reach, both vertically and horizontally. Taller people have longer arms, and plus their shoulders are higher so they can reach farther up with those arms.
You know what else is unusual about NBA players? The length of their arms, relative to their height. The NBA scouting combine explicitly measures arm length, because it’s something NBA teams are very interested in when evaluating the potential of players.
Can you name a basketball whose ratio of arm-length to height was actually lower than what that ratio is for the general population? I can: Yao Ming. There are NBA players more than half a foot shorter than Yao Ming who have longer arms. But, Yao Ming was 7’6″, and that kind of height made up for not having longer arms.
Larger point: if height is really important for NBA success, then you’d expect that, among NBA players, height is going to be inversely correlated with a lot of other things that matter for basketball success, even if these things are uncorrelated in the general population. You’d be expect shorter people who make it to the NBA to be better pure shooters, for instance. You might expect them to be quicker on average, and better ball-handlers. Or, another way to put the matter would be to say: how could a slower and less-coordinated athlete possibly make it into the NBA? You’d think the most likely scenario would be someone who is crazy tall.
Any dots that can be connected from this example to GRE in graduate admissions is left as an exercise for the reader.