As all academically alert chessplayers know, however, this is far from the whole truth. Social Psychology Quarterly published a paper in 1992 entitled "Testosterone and Chess Competition", which revealed not only that winners of chess games show greater post-game increases in testosterone levels than losers, but that such rises even occur before the game has begun.
In other words, it's not just winning that raises your testosterone level, it's also raised testosterone levels that help you win.
So now we have it: football teams win because their spectators have higher testosterone levels and cheer more loudly. And Garry Kasparov bangs his pieces down and slams doors because he knows he is winning. It's all testosterone.