Last night, an NBA announcer indicated that “Game 5 is of the utmost importance – in series tied 2-2, the winner of game 5 wins the series 83% of the time.” WOW! 83% eh? Let’s consider the possibilities:
Suppose the teams are evenly matched at each game is a 50-50 coin flip. A team up 3-2 (having won game 5) has a 75% chance of winning one of the next two games, and thus the series. Of course, we could presume that having a 3-2 advantage means that the leading team actually has a 60% chance of winning any given game. This would make their chances of winning the series 84% – just on random draws.
So there you have it. The two most reasonable bounds on system performance are 75% and 84% chance that the team up 3-2 wins the game. So, this shocking statistic is exactly what one would expect. It’s too much to ask sports casters to understand probability though.