Tennis commentators will typically say about a tall player like John Isner or Marin Cilic that their height is a disadvantage because it makes them slow around the court.  Tall players don’t move as well and they are not as speedy.

On the other hand, every year in my daughter’s soccer league the fastest and most skilled player is also among the tallest.  And most NBA players of Isner’s height have no trouble keeping up with the rest of the league. Indeed many are faster and more agile than Isner.  LeBron James is 6’8″.

It is not true that being tall makes you slow. Agility scales just fine with height and it’s a reasonable assumption that agility and height are independently distributed in the population. Nevertheless it is true in practice that all of the tallest tennis players on the tour are slower around the court.

But all of these facts are easily reconcilable.  In the tennis production function, speed and height are substitutes.  If you are tall you have an advantage in serving and this can compensate for lower than average speed if you are unlucky enough to have gotten a bad draw on that dimension.  So if we rank players in terms of some overall measure of effectiveness and plot the (height, speed) combinations that produce a fixed level of effectiveness, those indifference curves slope downward.

When you are selecting the best players from a large population, the top players will be clustered around the indifference curve corresponding to “ridiculously good.” And so when you plot the (height, speed) bundles they represent, you will have something resembling a downward sloping curve.  The taller ones will be slower than the average ridiculously good tennis player.

On the other hand, when you are drawing from the pool of Greater Winnetka Second Graders with the only screening being “do their parent cherish the hour per week of peace and quiet at home while some other parent chases them around?” you will plot an amorphous cloud.  The best player will be the one farthest to the northeast, i.e. tallest and fastest.

Finally, when the sport in question is one in which you are utterly ineffective unless you are within 6 inches of the statistical upper bound in height, then  a) within that range height differences matter much less in terms of effectiveness so that height is less a substitute for speed at the margin and b) the height distribution is so compressed that tradeoffs (which surely are there) are less stark.  Mugsy Bogues notwithstanding.

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