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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Comments
  1. kdawgz says:

    Factor in some human error, under-the-table cash, and poor calls, and the probability that the winning team is not the best team will be even greater – referring to soccer.

    I don’t quite understand the math…most likely because it’s definitely not my forte.

    How do factorials help in determining probability (I guess it saves writing out extensive formulas)?

    Does 6c4 mean there are 20 possible events where the weaker team will likely win? (with the continued probability of the stronger team winning with two matches remaining of course)

    And aren’t the two scenarios independent events? I don’t understand the addition.

    Please explain =)

  2. gwopdn says:

    That’s why soccer is so fun! (and irritating) btw. the Spanish team was actually the No.1 choice of the gambling companies (lowest yield), and they ended up winning! It’s intriguing to consider how much luck/competency they’d need to achieve that, factoring in all the unpredictable circumstances that affect game results. I have always been very interested in soccer betting… (Well, because it’s nice and simple, basically 0-0, 0-1, 1-1, 2-1)

    So in a 7-game series, there are two ways to determine the winner:
    A. two teams played 6 games and one won 4 out of 6
    B. two teams played 7 games, each won 3 games in the first 6, and the winner also won the last one

    So for one team to win, its EITHER A OR B. A and B are mutually exclusive (they can’t happen at the same time), so that the probability of EITHER occurring is the sum of the probabilities of each occurring.

    It’s the same logic for the calculation under A or B. But sadly, I just realized that I was wrong because its not possible for one team to win more than 4 games LOL. I’d correct that soon (*>__<*), but still, there's still a sizable chance that the weaker team wins the series.

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