Major League Baseball has adopted a new playoff format. Each of the National and American leagues is divided into three divisions. This won’t change, but five teams from each league will make it to the postseason: the three division winners, and two wild cards, the best two teams among the non-division-winners. The two wild cards in each league will play in a one game playoff;. Then there are four teams left. The wild card will play the division winner with the best record, and the two remaining division winners will play each other, in a best-of-five series; the winners of those two series play best-of-seven in the League Championship Series; the winner moves on to the World Series.
mlb.com indulges in a little how would history be different with the new playoff format, mostly to draw the eyeballs of fans of, say, the 2005 and 2006 Phillies. (Readers of this blog’s former incarnation will know I’m a Phillies fan, in exile now in the Bay Area, which made 2010 hard.) In a fourteen-team or sixteen-team league it’s not surprising that there are a lot of teams that just barely miss the playoffs; the difference between the fourth-best and fifth-best team is likely to be pretty small. (The difference between the fifth-best and sixth-best team is probably even smaller on average, being closer to the middle of the distribution.)
The natural question from a probabilistic/statistical point of view, I think, is “what’s the probability that the best team wins the World Series”? As you add more layers of playoffs, this seems like it would go down. But on the other hand, this wrinkle seems like it might push up the probability of the best team winning the World Series. The best team is likely to have the best record in its league (“be the first seed”). This previously would have meant they faced the wild card team in the first round. Now the first seed’s first-round opponent is actually slightly worse than previous, on average. They face a team picked essentially by a coin flip between the fourth seed (the former wild card, i. e. the best non-division winner) and the fifth seed (the second best non-division winner), and that team will have likely used its best pitcher in the play-in game.
So somewhat paradoxically it seems that this helps the very best teams, at the expense of those slightly-above-average teams that somehow manage to slip in. However this argument seems handwavy enough that I don’t know for sure. One thing to do would be to look at old data, but I suspect the effects are fairly small and hard to see in MLB’s hundred-year data set. The new system is suppoedly based on simulations but I’m not sure what that means; I may just have to do my own simulation to be sure.
God plays dice 