Another example, what I've found interesting reading some of the NBA statisticians blogs is this argument about "clutch". Most fans and media insist that Kobe Bryant, a player who shoots a lot of shots at the end of games and makes spectacular shots sometimes is the best closer in the game. Meanwhile almost all statistical evidence points to Chris Paul, a player who runs boring routine plays down the stretch, as by far the best closer in the league in terms of actually winning close games.
Until the NBA stats can predict winners like baseball, the public will always go by the "look." The teams themselves however, are almost all hiring statisticians now.