An Omenti minipost

A reader sent sent a chart showing height vs weight for three major professional sports. It's immediately obvious that some clustering is going on. NFL football tends to favor taller and heavier players than soccer (football for most of the world) and NBA basketball strongly favors height. While it's a nice example of how a specific sport will favor certain body types at the elite level, it's not as dramatic as photographic comparisons of Olympic athletes. Taller and larger isn't always better - gymnasts and divers tend to be short, basketball and volleyball players tall, distance runners and soccer players are closer to average. Sports involving pure strength, wrestling and weight lifting for example, have weight classes. Why?

Height in volleyball and basketball seem pretty obvious and gymnasts are lighter so they can change direction more easily. Away from elite levels it's possible to have some success in a sport if your size isn't optimal. Some high schools have successful tall gymnasts and short basketball players, but as competition tightens having the right body type becomes an important factor. Body size and shape have a large influence in how fast they came move their limbs and how strong they are for their weight.

For the sake of argument imagine two athletes with the same body proportions but one is 60 inches tall and the other 70. The ratio of their weights is the cube of the ratio of their heights (7/6)^{3 } - the taller one would be about 1.6 times heavier. Muscle power is proportional to the cross sectional area of the muscle - the length doesn't matter much. Here the taller athlete would be (7/6)^{2} or about 1.36 times stronger. The big difference if you want to move your body quickly is the shorter athlete has a larger strength to weight ratio - 1.6/1.36 nearly 18% higher in this example. This is critically important in gymnastics and diving. As those sports became more specialized, elite athletes became smaller. Simone Biles, arguably the best athlete in the world, stands four feet eight inches tall.

Another factor is how easy it is to move a limb. What is the limb's inertia. Inertia is usually defined as the resistance of a physical body to an change of velocity. Something not moving just sits there and something moving, assuming no other forces like friction, just keeps moving at the same velocity. Acceleration is just the change of velocity and this is where force equals mass times acceleration comes into play. For many sports you need to consider rotational inertia. Think of a volleyball player or gymnast swinging her arm. There's an inertia to the rotational motion - her arm muscles need to generate a torque to move the arm. A physics 101 course will have the details, but for the power her muscles have to generate will be roughly proportional to the mass of her limb times the square of its length. Long limbs not only require more strength to move, but their mass increases as the cube of their length while the muscle strength only increases as the square. It is very difficult for taller athletes to be as agile as shorter athletes. To compensate volleyball and basketball players focus on building the muscles in their arms and legs while being lean.

Sports like soccer require an optimal mixture of agility and height. It turns out that an average stature is generally the best although goalies tend to be taller for obvious reasons. The best distance runners are a bit shorter than average and very lean. (heat dissipation is also very important and shorter athletes have an advantage). In swimming upper body strength is more important than weight so tall athletes with long torsos are favored. Rowing requires strength. Added weight doesn't change the drag of the boat much so the best crew athletes are have lots of muscle cross section area.

Beach volleyball is interesting as there are two specialized positions. Height is favored for blocker at the net while defenders need great agility moving around the back court. The best teams tend to have a tall blocker and a shorter defender, but blockers need as much agility as possible and the defenders need some height, so it's a bit of a mix. The best women's teams tend to average around six feet tall and the best men's teams about six feet five.

It needs to be said again these height differences aren't that important if the competition isn't at an elite level as many other factors are involved. Only the elite levels demand that you need most or all to win. People should play whatever sport they enjoy and it's possible to have success if their body they don't look like a professional or Olympian. And consider the impact of certain rule changes in some sports. Lower the basket a foot in basketball and the women's game suddenly sees a lot of dunking and the men's game would probably see somewhat shorter and more agile players. Would either be more interesting? Who knows - you would have to run the experiment for some time to see how those with the new right body types (arguably it might be the same women) would rise to the top. It makes you wonder if and when some athletes will consider body modifications to compete. We've already had a taste of that with running blades.