For most of the 20th century only two teams made the playoffs in baseball: the NL pennant winner and the AL pennant winner. There were only one playoff series--the World Series. In 1969 that changed to four teams--one from each division (East and West) of each league. In 1995 it changed again to include eight teams--three division winners and two wildcards.

The changes have made baseball more exciting. Every year there are a lot of teams in the hunt for a wild card or division spot. In the 1920s and 1930s the Yankees often wrapped up the AL pennant by early September and baseball was dull until the Fall Classic. Not anymore. I wouldn't do away with the wildcard or combine divisions.

But one thing did bother me. The first round of the MLB playoff is a short best of five series. And baseball teams have more parity than most sports clubs. For any given game even a bad team has a good chance of beating a good team. A worse team is less likely to win a best of 3 series than just a single game, and even less a best of 5. In general the longer the series the more likely the better team will win the series. My suspicion is that because the first round of the MLB playoff is so short there is an unreasonable large chance that the worst team will win in the first round.

You could make a case that's how it should be. Sports are about chance. They're about showing up and performing well on a specific day, not being the best on average. But, on the other hand, most people feel a sense that the rules should be designed so that "the best man (team) wins."

I decided to explore numerically how much of a difference it makes that the first round is a 5 game series as opposed to 7, 9, or 11. Longer series are better because give fans more games to watch and the better team is more likely to win, but they have a cost in sucking some of the drama out of the playoffs. I wanted to quantify the gain from the better team being more likely to win.

Call the probability that the better team, say the Rays, will win p. Then you can model the Rays chance of winning with a mathematical construct called the Binomial Distribution. I used that model in Excel to simulate the Rays chances of winning for p = 0.42, 0.44, ..., 0.60 for a 5, 7, 9, and 11 game series. To my surprising the length of the series doesn't make much of a difference for teams that are relatively equal (which is true for playoff teams). The graph below shows the effect of lengthening the series.**

I'd still like to see longer series. 9 for the first round and 11 for later rounds. But at the same time I can see why one can't complain too much. In football the playoff "series" are just one game rounds and we think that amount of chance is acceptable--even exciting.

But I'm still bitter than the Rays got bumped by a vastly inferior team.

* - This averages out pitcher effects. What I mean is that the Phillies might have one great pitcher that makes winning Game 1 likely, but the average of their likelihood of winning Games 1, 2 and 3 is probably < 60% against another playoff team.

** - This model leaves out the effect on pitching rotation choice. If the playoffs could potentially go 29 games a manager that might use a 3-man rotation under the current system might switch to a 4 or 5 man rotation. That effect could be large in some cases (e.g. 2001 Diamondbacks).