Come shed a tear

[Snowman]

Originally Posted by raulus

Just out of curiosity, what does the math say about the difference between a 5-game and a 7-game series in terms of the probability of a major underdog knocking off a favorite? Just for fun, let’s say a hypothetical team with 89 wins was facing another hypothetical team with 111.

There are a few ways to estimate the probability that team A will beat team B for any given game. Bill James uses a logistic rating model that he dubbed the 'Log5 method'. It's basically the same thing as the Bradley-Terry model or the Elo rating system in chess. That formula looks like this:

Let P(A) = team A's true win%
Let P(B) = team B's true win%
Let P(A,B) = the probability of team A beating team B for any given game (yes, this ignores the variance incurred through specific pitching matchups and would need to be adjusted for home field advantage, but it is still a useful estimate over the course of a series)

Then,
P(A,B) = [P(A) - P(A)*P(B)] / [(P(A) + P(B) - 2*P(A)*P(B)]

In this example, the Dodgers win% = 0.685, and the Padres win% = 0.549. So, plugging those values in for the Dodgers vs Padres, we get:

P(A,B) = 0.641

In order to estimate the probability for a 5-game or 7-game series, we can use binomial expansion. The formula looks like this, where p is the win% of team A and q is the win% for team B (or 1-p) for any given game:

win%_7game = p^4 + (p^3)*(q)*choose(4,3)*p + (p^3)*(q^2)*choose(5,3)*p + (p^3)*(q^3)*choose(6,3)*p

win%_5game = p^3 + (p^2)*(q)*choose(3,2)*p + (p^2)*(q^2)*choose(4,2)*p

So, in our example here with the Dodgers having an expected win% of 0.641 vs the Padres, the likelihood of the Dodgers winning a series against the Padres could be estimated as:

Dodgers 5-game win% = 75.0%
Dodgers 7-game win% = 78.5%

I didn't look this up for the series, but it's probably a good estimate for what the Vegas line might have been for the Dodgers to win the series against the Padres before any games were played.

Also worth noting is that this is a pretty wide win% gap for baseball. The Dodgers were an historically elite team this year. Most series odds are going to be a lot closer than that. Baseball playoffs nearly is a game of flipping coins for the most part. Luck plays a much larger role in the MLB than it does in the NBA and NFL.

Originally Posted by brianp-beme

How about NFL playoff where you lose once and you are gone? And flipping coins is a ritualized part of every football game.

Brian

That actually doesn't matter nearly as much as you'd think because in the NFL, the better team beats the weaker team far more often than in baseball for any given game. If you look at the win% for the best team in the NFL, it's usually pretty close to 90% for any given season, whereas in the MLB, it's typically only around 60%. In the NBA, it's closer to 80%.

The best teams win the championship far more often in the NBA and the NFL than they do in the MLB. It's just the way it is. There's a LOT of luck in baseball, and it takes a very long time for that to even out.