I have not always been a baseball fan.  It took me a while to appreciate the fact that there are a lot of strategic moments in between periods of watching the grass grow.  I have, however, always wondered about 5-game series versus 7-game series.  Given that any game can be won by the weaker team, it is more likely that the weaker team can defeat the better team in a 5-game series.   I believe that a contest should be setup to determine the best team.  As such, I have always thought that 5-game series are not great for the game, especially in the opening round of the playoffs.  Today, I try to support my opinion with facts.

Say that you decide to completely remove the fun of baseball by just thinking about the games as random events, in which teams have certain probabilities of winning.  Let’s compare the probabilities that the underdog pulls the upset in 5 versus 7 game series.

Thanks to the University of Minnesota’s School of Statistics, I do not have to write my own program for this.  Professor Geyer offers a “Playoff and World Series Probability Calculator” on his website.  The program, which solves the answer analytically rather than through the use of simulations, allows the user to control a few variables:

  • The probability that a team wins at home
  • The probability that a team wins on the road

Note, this program assumes that weaker team plays first game on the road.

Table 1: Probability That Underdog Pull Upset in a 5-Game Series

Table 1 above provides the probability that the underdog pulls the upset in a 5-game series.  For example, an underdog that has a 45% chance of winning home games and a 35% chance of winning away games will pull the upset nearly 30% of the time.

Table 2: Probability That Underdog Pulls Upset in a 7-Game Series

Table 2 above provides the matching probabilities in a 7-game series.  The same team will pull the upset 27.5% of the time in a 7-game series.  This really surprised me, as playing a 5-game series only improves the chance of pulling an upset by 2.43%.

Table 3 - Differences in Probabilities

Table 3 provides the difference in the probabilities, or the gain that the underdog has in playing a 5-game series instead of a 7-game series.  These are a lot smaller than I would have guessed.  As it turns out, I think that I was wrong.  Having a 7-game series over a 5-game series does not really seem to have a tremendous play on the outcome of the series.

Category: CAIA, CFA, CIMA

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October 2011
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