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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January 25, 2011 at 9:35 am
rif
If speed and height were actually independently distributed, and they’re both valuable and can be substituted, then wouldn’t a player who was both extremely tall and extremely fast be on a higher indifference curve? In this case, I’d expect the very best tennis players to all be both tall and fast.
January 25, 2011 at 9:45 am
jeff
indeed they are both tall and fast. but height and speed are still substitutes. so among the tall and fast professional tennis players there are some who are taller. they are going to be slower.
January 25, 2011 at 10:50 am
Sean
But Jeff, height and agility are bounded. So if the distribution of these traits is indeed independent, with a large enough population we should get an observation of an individual who is both as tall and agile as possible. Provided tennis ability is strictly monotonic in height and agility, this individual should be on a higher indifference curve than anyone else; the curve is a singleton so it doesn’t have a slope.
So I think rif’s point stands, and the question is: Why do we not observe the “Lebron James” of tennis who simply dominates on both height and agility? Either height and agility are not independent (that is, at least in the tails they are negatively correlated; perhaps James is not nearly so quick as Agassi, and Bolt is merely fast but not agile), or individuals blessed to be both tall and agile do not play tennis.
Interestingly, my (limited) understanding is that there was always considered to be a similar trade-off between height and leg churn in sprinting, until Usain Bolt came along and shocked the world with a counter-example. Maybe his counterpart in tennis just hasn’t come along yet (or more likely is playing basketball).
January 25, 2011 at 10:55 am
jeff
I don’t think these traits are bounded. statistically it is rare to be 9 feet tall but it will happen from time to time.
To have someone exceptionally tall and exceptionally agile requires two simultaneous large deviations from the norm. That is rare squared. So more typically the exceptionally tall, like Isner, is average on other dimensions.
January 25, 2011 at 11:24 am
Sean
Fair enough. I didn’t realize these tall tennis players were 6’6″ and 6’9″. If “tall” in tennis was only 6’4″ as I expected, that’s not so far into the tail of height distribution that we should not expect to see a high agility draw (conditional on being 6’4″) every once in a while.
January 25, 2011 at 11:45 am
jeff
heights of some tennis players:
federer and nadal are both 6’1″
roddick 6’2″
ivanisevic was 6’4″
del potro and cilic are both 6’6″
isner is 6’9″
karlovic is 6’10”
January 25, 2011 at 9:46 am
Matt
This is a valuable observation in many settings. There are many more examples in sports; for instance, looking at the NBA you’d think that height was negatively correlated with the ability to make unguarded three-pointers, even when the population-wide correlation is surely positive. But the most interesting applications to me are in intellectual ability.
Say that you need to read a collection of essays produced by a cross-section of the American population. You’ll quickly realize that grammar and style are excellent proxies for the content of an essay — you quickly can weed out most of the weak contributions and select a few pieces for closer examination. Indeed, at the population level virtually *all* intellectual strengths are correlated. Good writers are also good mathematicians. If you know who fought in World War I, you’re more likely to know the difference between an atom and a molecule.
These tendencies give rise to some common screening mechanisms: you’re more likely to be taken seriously if you display strong general intelligence and clever writing, regardless of the strength of your specific ideas. And if we’re evaluating people drawn randomly from the population, this is completely rational.
But all these heuristics break down when they’re applied to the elite. The wittiest columnist is usually the worst on matters of substance. And this is easily understandable. Wit and substance are substitutes in the column production function; selecting from the top of the distribution induces a negative correlation between the two attributes that overwhelms their comovement in the broader population. Hardly anyone can write like Christopher Hitchens, but he’s one of the last people I’d ask to offer any practical advice.
January 25, 2011 at 11:43 am
Sean
I think the height distribution of corners in the NFL supports the assumption that height and agility are independent. Cornerback is almost purely an agility position, in man coverage he’s got to stay in the receiver’s hip pocket without knowing where the receiver is going to go. Agility being equal you’d love to have a tall corner (to defend better once the ball is in the air), but preferences are nearly lexicographic in agility. Nearly every corner in the NFL is between 5’9-6’2, with the average around 5’11 (none taller than 6’2). The average height of a U.S. male is 5’10. As Jeff mentioned in a reply to a previous post, to get a super-rare draw on agility, most likely the individual will not be too far from the mean on height. NFL corners skew about an inch high due to a subsidiary preference for height, but there is not much variance at all.
January 25, 2011 at 4:33 pm
Jonathan Weinstein
As Matt said, height and other skills do correlate negatively within the NBA. Each inch of height matters quite a lot even as you go from 6’6″ to 7′ (contrary to what Jeff said) and this creates a substitution. The class of NBA players who just make the cutoff lie on some negatively sloped height/skill curve. The very best lie above the curve.
Another way to look at it: the ratio of 7′ to 6’6″ NBA players is *much* higher than the general-population ratio. So you are taking people from further down the ranks in skill.
January 26, 2011 at 9:52 am
MikeY
extreme height (6’10″+) is exceedingly rare, but also extremely valuable in basketball. That’s why so few teams win championships (not enough skilled big men to go around) and also why basketball has the most international players (a tall player in another country has a bigger advantage on americans than, say, a skilled pitcher in baseball).
Agility has got to be something like power/momentum, and since weight increases geometrically compared to muscle power, it will be somewhat negatively correlated with height, no? That’s why the biggest vertical leaps are all on small guys (could be selection, but I doubt it). This is based on a vague notion I have from elementary school describing the maximum size of dinosaurs, so maybe I have this wrong?
January 26, 2011 at 2:00 pm
jeff
that is a nice point about the scaling, i hadn’t thought about it.
January 27, 2011 at 1:10 am
Ryan
It comes from the fact that with linear increases in height you get ^2 increases in surface area and ^3 increases in weight. Hence the pressure in joints, etc. is much greater for a tall person than a short person, which has direct effects on effective strength/power. Conversely, very small creatures such as ants can lift 10-50X their weight or bugs can stand on water without breaking the surface tension, but surely this would not hold true if they were scaled to our size. Finally, exceptionally tall people in recent history could not stand without braces.
So, your theory neglects that things like height are not just a random distribution but are also in a sort of evolutionary equilibrium.
January 27, 2011 at 9:18 am
jeff
of course the forces that bear on this tradeoff in nature are different than those that would produce the optimal basketball or tennis player. at the margin would a basketball-player designer be willing to sacrifice more or less agility for an inch of height than a “tree-climber/predator-escaper/nut-gatherer”-designer?
February 8, 2011 at 12:47 am
itovertakesme
agreed, the maximization problem is different so it doesn’t guarantee height/speed tradeoff is merely an evolutionary equilibrium, but i think the physical constraints make a significant push in this direction. i.e. as height increases past a certain point, you lose more agility per inch for each added inch of height. hence unless height becomes unusually important (like in basketball and maybe tennis), these freaky-tall dudes aren’t all that useful because they move like kids on stilts. but that’s not just because the maximization problem over random distributions of height and agility happen to pick people with extremes in each category but not both.
February 8, 2011 at 12:55 am
itovertakesme
theoretically you could test this if you could find two *supply-side independent* variables, say X and Y, that are easily measured, which both help a player succeed at a sport, and see if players in that sport basically max out on both of these variables, or if there are players that have so much X that it makes up for their lack in Y or vice-versa. anyone have ideas on what variables would work? i don’t think height/speed are good because i think height has an intrinsic speed disadvantage.
January 26, 2011 at 4:40 pm
~Q
Is it possible that tall, fast guys get selected into other sports (e.g. basketball), and tall slow guys get selected into tennis (where height can compensate for speed?) Or is that too cute, or not relevant somehow?
January 27, 2011 at 1:00 am
Ryan
Interesting… similar logic would predict that the best looking politicians are not the brightest.
May 23, 2011 at 1:39 pm
How Selection Creates Tradeoffs « Cheap Talk
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February 7, 2012 at 9:10 am
Anonymous
Usain Bolt