Archive for the ‘Mathematics’ Category

Is a 7-game series really fair?

Posted: August 16, 2010 by gwopdn in Mathematics

I know it’s better than just 1 or 2 games to determine the better team…but how reliable it is to indicate that the winning team of a 7-game series is indeed the better one? (Yup, I have a calculator with me all the time, so I can figure things out at work)

If one team can warrant a win against another 55 percent of its games, the probability for the weaker team to win a 7-game series is calculated as following:

– weaker team wins 4 games out of first 6:
wins first 4: (0.45)^4 (then the winner is determined)
loses first one, wins the next 4: (0.55)*(0.45)^4
wins from the 3rd to the 6th game: (0.55)^2 * (0.45)^4

– weaker team wins 3 games out of the first 6, and the last game:
(6c3)*(0.45)^3*(0.55)^3*0.45=0.136448296

So the weaker team can win a matchup about 4 times out of 10: ( _____) . There is a pretty good chance for the weaker team to win. To fairly determine its winner, a matchup would need far more games, number of games depending on the winning edge of a team, so that the chance for a weaker team to win a series would be 5 percent or less of the time (depending on statistical significance). In conclusion, the crowned champion in a series final is probably not actually the best team. – A well known fact. =P

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