During and after the ALCS, even Sox fans were declaring the Rays the "better team." I caught a lot of guff (and was even compared to John Lackey) for saying that by advanced baseball analysis (that is, looking at things beyond the record), the Sox were better. Runs scored, runs allowed, equivalent averages, whatever you wanted to use, would lead you to believe the Sox were about 5 games better than the Rays.

But yet, because the Rays won the season series (including playoffs) 14-11, they were definitely better?

Please. Without Mike Lowell and with an ailing David Ortiz and Josh Beckett, I would go so far as to say the Rays were probably the better team in the ALCS. But by no means was it clear from the results.

By the way, in the adjusted standings the Rays are about 10 games better than the Phils. Wow.

I think you've still got the wrong idea of "better" here. There is a lot of variance in a baseball game that is unrelated to skill. If you were to play a game 100 times it might come out 50-50, or 51-49, or whatever. Unfortunately we can only play it once, so the temptation is to say that the winner would've been the same every time.

It's just not true. That's not how baseball works. It's like saying that if I flip a coin and it comes up heads, then it was absolutely, positively certain to come up heads. But if I'd waited a second, or used a different coin, or flipped infinitesimally harder or softer, it could've come out differently.

"Anyway, what I really want to know is: How many games should a series have to really determine the best team?"

If the better team has a 55% chance of winning any given game, which is actually quite a bit better when we're talking about playoff baseball, you'd need to play a best 134-out-of-269 series to determine the better team with 95% certainty.

A 7-game series determines the "better" team 60.8% of the time, assuming these relative skills.

To determine the "better" team with 95% certainty when it's pretty obvious - say 70% chance to win - then you'd need to play best 8-out-of-17.

All this is by way of saying a 7 game series is fine to determine a champion, but it's not even close to being able to determine the better team.

1. Rich people

2. Isle of Davos

3. Atlas Shrugged

In my previous post, I used Bill James's log5 method to determine the expected winning percentage in one game. The 55% number corresponds to a 97-win team against a 90-win team, which is close to what we see in this series. (The Phillies' actual win total was 92, but advanced metrics put their skill level at around 87 wins. 90 is a good compromise.)

The 70-30 split roughly corresponds to a 97-win team against a 65-win team. With advanced metrics we're talking about a Rays/Mariners series. And we'd need a 17-game series to figure out the "better" team between those two, even!

(Note, I also was off by 1 in "number of games necessary to win," but the series length was right.)

It's the Binomial Distribution.

It tells you the probability of a certain number of positive outcomes (wins) in a certain number of trials (games) given a certain outcome probability (win percentage).

So, for the probability of .55, in 7 games, the probability that they'd win 4 games plus the probability of winning 5 plus the probability of winning 6 plus the probability of winning 7 was, whatever I said, 60.8%. That's the probability they'd win the series.

I kept adding this up for longer and longer series until I reached 95%, which is generally accepted as being "statistically significant."

Regarding your comment about the hypothetical 17-game series between the Rays and Mariners, note that we're not allowed to stop the series before 9 wins are reached. If we're playing best 9-out-of-17, then we're playing best 9-out-of-17. The probability accounts for ANY series outcome, not any specific one. If there were such a thing as a "mercy rule" in a series, we could end this Rays/Mariners series at 3-0, and say the Rays are 97% likely to be the better team. Assuming, of course, we know by how much one of the teams is better than the other.

In reality what we'd have to do is say we want to detect a difference of (some skill level) with (some probability, which I'm setting at 95%). Because think about it, you can't play a series long enough to determine the "better" of two perfectly equal teams with any certainty.

So here is the statement we could say with mathematical certainty (assuming all our assumptions are sound): "If one World Series team is a 97-win team and the other is a 90-win team, the winner of a 269-game series is 95% likely to be the better team."

Indeed.

@ Commander_Xander, I guess we can say definitively that Evan Longoria is a .000 hitter, too, then. I mean, it was proven in the experiment that is the World Series. He is, in fact, the worst player in Major League history.

@ Tom, I calculated the probability of the better team winning, which is also the probability that the winning team is the better one. The winner of the entire 269-game series is 95% likely to be the better team.

We have to define the series and the "series winning" criteria ahead of time, which accounts for every probability from 135-0 to 135-134. In order to give us the power to declare the winner if it's 135-134, we have to eliminate the opportunity to declare a winner at 134-0.

What you COULD do is declare a winner at any point where there's a 95% probability of the better team being ahead. So you could declare a winner if it happens to be 4-0. But if you're tied 134-134 going into the 269th game, you're likely to have another couple hundred games ahead of you. So pick your poison.