Here's a good article by Anthony Bradley of the Acton Institute on why he thinks sports do not build character.
The whole problem falls back, in large part, to having a short time horizon. When it's all about winning right now, the incentives to account for future effects is diminished. So the New England Patriots stole signals; they've got 3 Super Bowl titles (who's to say they wouldn't have them anyway?). Now the Pats will pay a fairly steep price. Jason Giambi took steroids and got a huge contract from the Yankees out of it. Then his body started breaking down. There was a complete and total lack of long term thinking in both situations. It is the same basic ailment that causes people not to save enough for their retirement.
Then you have situations like Travis Henry. Henry has nine children by nine women because the only time period he obviously thinks about is right now. (Incidentally, how about sending him over to Russia. He's already repopulated several NFL cities. He could really do some good for humanity in Russia.)
Maybe the problem isn't entirely one of time horizons. These folks obviously thought long term sometime otherwise they wouldn't have worked hard enough to get to the professional level. Maybe they are just too stupid to realize all the consequences of their actions. Either way, the short time horizon plays a role in the sports cheating incidents and many other social phenomenon, especially on college campuses. And I have no idea what could be done about it.