August 27, 2014

BP Unfiltered

Playing Favorites

by Russell A. Carleton

I do love me some Wednesday e-mail show Effectively Wild. Today, someone asked a fantastic question about the playoffs. How good would a team have to be in the regular season to, before the first pitch of the playoffs is thrown, be considered the mathematical favorite to win the World Series versus the field. There will be ten teams that make the playoffs this year (OK, fine, lest we defile the sanctity of the Wild Card, there will be eight). One of them will have the best chances of the eight/ten, and would theoretically be the favorite, but its chances might be somewhere in the neighborhood of 20 percent to be taking a champagne championship shower in late October. That means that the best team has an 80 percent chance of winning a participant trophy instead.

How good would a team have to be in order to have a 50/50 shot of winning the World Series at the beginning of the playoffs?

Warning! Gory Mathematical Details Ahead!

In order to win the World Series, a team must first survive a best-of-5 Division Series, and then a best-of-7 LCS, and a best-of-7 World Series. In a scenario where all teams were exactly equal, and each series was a legitimate 50/50 coin flip, then each team would have a 12.5 percent chance of winning three consecutive series (50 percent raised to the third power) and emerging as champs. Using the same logic, in order to have 50 percent chance overall of winning all three series, we take the cube root of .50, which is .7937. Our team would need a 79.37 percent chance of winning each series.

Now, to win the division series, our team needs to win three out of five games in the Division Series first. A simple binomial calculator can tell us that if a team wants to have at least an 80 percent (rounding) chance of winning 3 of 5 games, in each individual game, it would need roughly a 67 percent chance of winning each game. For a best 4 of 7 series, they would need a 65 percent chance of winning each game.

Let's just use 65 percent as our benchmark. How good would a team have to be in order to have a 65 percent chance of winning an individual game... against a playoff quality team? Let's assume that their opponents in all three series are 90-win teams (a .555 winning percentage).

Using the log5 formula for predicting the chances in one specific game, we can plug in .65 as our expected outcome and .555 for the opponent's win percentage. What sort of team would be needed to maintain a 65 percent chance of winning one game against a 90-win team. Doing some algebra, the answer is actually just shy of a .700 winning percentage.

That translates into a regular season record of 113-49. A team would need to be on par with some of the all-time greats before we would consider them to be even a 50/50 shot to win the World Series.

Excremental Ineffectiveness

I realize that I vastly over-simplified some things in these calculations, but they wouldn't affect the big picture conclusion all that much. This is a mathematical abstraction. A team that somehow went 113-49 probably snagged some insane amount of luck along the way (or were just super-human robots playing baseball with guns) and the model probably wouldn't hold any more. But that's not the point.

Russell A. Carleton is an author of Baseball Prospectus. Follow @pizzacutter4
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