One of my favorite answers in SXSE is this one which addresses subtler effects of low gravity on sports that one might not anticipate. There are other answers there, and other questions and answers about swimming here as well.
This question about jumping was recently re-opened and I think it's a good question, and the answer there almost qualifies as a mini scholarly work in itself. The human musculoskeletal system is (roughly) optimized for a certain combination of inertial and gravity, and playing sports in a very different gravity might result in some unexpected differences.
A simple case in point - ISS astronauts and lots of other people as well know that it takes time to learn to carefully and safely move heavy objects in microgravity without injury. Weight lifters would have to learn this as well - what new kinds of injuries will result from an overzealous jerk (motion) in the clean and jerk?
On the other hand, maybe the shot put would not need quite as much interplanetary cross training as it is more about inertia and Newton's Laws of Motion than it is gravity - from the point of view of the mechanics of the athlete.
And of course there are questions of bone loss in low gravity, but there is not much known about long term effects in reduced gravity yet.
So I'd like to know: has there been any scholarly or serious work in Sports Science for the low surface gravity of Mars or the Moon?
I almost changed this question to "how would the clean and jerk have to be done differently on Mars". It's a really good question as well and not so simple. If you have a good quantitative answer, you could ask and answer yourself, or someone could just ask it! But it deserves a thorough treatment.