Watch Kobe or LeBron on the court. There is an incredible awareness of the shifting context of the game and the available moves. In the greatest athletes it is faster and more fluid than in most athletes.
It's a constantly shifting analytical mode that leans heavily on training and instinct, but is full of novelty. Consider that opponents spend weeks watching tape in hopes of understanding how to anticipate what Kobe will do.
In terms of physical metrics (size, speed, etc.) professional athletes are pretty close to average. I think it is a combination of intellect and general desire to win that makes some people become great athletes.
Because of what I like to call Cartesian Blindness (viewing the world through the mind/body duality) we assume it's simply a matter of great athletes having superior muscle fibers, etc.
David Epstein's "The Sports Gene" covers this topic with some depth.
Many people are brilliant, talented, and have a strong desire to win but lack the physical aptitude to support that at elite levels of play.
The examples in the "Sports Gene" are mostly about the kind of genetics that allow some to run micro to milliseconds faster than others, oxygenate slightly better, and so on. These things might help in the olympics where such minor distinctions matter but are certainly not a key or deciding factor in many sports.
Totally, true, but the number of people who are good at professional football is a very tiny subset of the people who can run a 4.4 40.
http://journals.plos.org/plosone/article?id=10.1371/journal....
http://discovermagazine.com/2010/apr/16-the-brain-athletes-a...
https://en.wikipedia.org/wiki/Theory_of_multiple_intelligenc...
I also don't think the stereotype is accurate. We tend to confuse interest in pursuits that are perceived as intellectual with actual intelligence.
You might be surprised to learn that there is a negative correlation between obesity and IQ.
The basic idea is that while you are learning to do challenging gymnastic (or other physical) skills, the brain is releasing growth hormones to learn the skill. But they aren't targeted. It's hard to grow the part of the brain that does a cartwheel on a balance beam without also growing the part of the brain that does calculus.