I certainly hope this is not offensive to anyone, as that is surely not my intent. I simply hear this statement a lot and would like to be able to give an educated response.
The assertion is that slave owners would select slaves to reproduce based on their traits of strength, speed, and endurance, all of which would result in theoretically superior workers. It is said that this, over time, resulted in the black race (in early America as well as other places where slaves were brought to from Africa) as a whole becoming more athletic. This is stated as the reason why black people are so highly represented in many professional sports (especially sports that require a combination of size, strength, and speed, such as basketball - I believe almost 80% of current NBA players are black.)
Is there any truth to this, or do we have historical evidence that any perceived athletic differences between the races is a result of some earlier branching in our evolutionary tree?
No. There is no correlation between skin color and athletic ability. The overrepresentation of black athletes (pre-1995, of course, though it might be suspected that the tend would continue) is entirely the result of career paths in sports being utilized as a method of escaping poverty. That is, the overrepresentation of black athletes is the product of socio-economic, not biological, factors.
See, inter alia:
"do we have historical evidence that any perceived athletic differences between the races is a result of some earlier branching in our evolutionary tree?"
To be clear, all modern humans are one species, but that doesn't mean some cultures can have a higher relative "athleticism." As a prime example, the average height of one region of people can be notably shorter than those in another region. As Wikipedia notes, these small differences play a part in a group's relative "athleticism." How large of a role does this play? Depends on the sport, I'd wager! And I imagine sociological factors play a huge role as well, if not the more important component in this question.