The TV show The Nature of Things on CBC this week talked about man's (homo sapiens) evolutionary adaptations, which make us long-distance runners (able to run down animals until they have to stop from heat exhaustion - suggested we ought to be called 'homo cursor', "running man", instead).
Part of that show mentioned the first Ethiopian who won an Olympic gold medal for running: barefoot.
The show then took us to modern Ethiopia.
The people who do well (as runners) there come from similar backgrounds: really really poor (and, motivated). The fact that children of poor farmers don't wear shoes was asserted to be one of the reasons why they're stronger runners as adults.
If nature (e.g. 'black' or 'white' skin) might be a part of it, so might nurture.
Also this program wasn't talking about "the average": it was talking about athletes, and elite athletes at that.
This doesn't answer your question, which is explicitly about the average: but maybe that's the wrong question. "White men can't jump" might be more of a statement about elite athletes (e.g. the NBA) than about the average.