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January 28, 2004

One in 1,654
by Larry Mahnken

I got an email from a reader Monday about the postseason and luck, and I'll reprint most of it here:
I just have one statistical tidbit that you might want to consider.

You know how sabermetricians always claim that the postseason is just a matter of luck? No? Well here's a sample (the bold type is mine):

But the truth is that winning the World Series isn't about being the best, it's about being the luckiest.
--Rob Neyer ESPN column, 4-2-2003

"Four postseason series is like two weeks in the regular season, and anybody can go through a rough couple of weeks." In other words, Dierker thinks the Astros were unlucky. And I happen to agree with him.
--Rob Neyer ESPN column, 7-8-2003

All [baseball fans] care about was how you fared in the post-season crap shoot.
--Michael Lewis, New York Times Magazine, 3-30-2003

Nobody ever said that it's ALL luck. Nobody.
--Rob Neyer via e-mail, 7-22-03

That last quote was for irony. Anyhow, as a casual Yankees fan - as you were a casual Blue Jays fan in the early 90's, I'd noticed a certain magic about the Yankees team that was, of course, unquantifiable but impossible to ignore. So then I start going to all of these websites that dismiss the postseason as if it were some appendage for retards, like putting a shiny cover on a DVD or something, useless and dismissable. I recalled many declarations that the postseason was all luck, in addition to the easy-to-find quotes printed above, and I was bothered by it.

Bothered by these snobs because I believe that there is such a thing as the heart of a champion. I believe that Jason Kidd, while statistically inferior, is a better point guard than Stephon Marbury. Lots of these beliefs that I really hadn't even doubted were, I realized, being spasmically mocked by the emerging powers. Maybe I haven't the time and creativity to totally defend my beliefs, but I'd certainly do something.

So, I thought, if the postseason is all luck, that the odds of one team winning a given series would be 50%, right? Well, the odds of, for example flipping a coin and having it land on heads X times in a row is .5^X. The odds of a 40% three-point shooter making three consecutive is (.4)(.4)(.4).

Well, the Yankees had won 11 straight postseason series between 1998 and 2001. If the sabermetric guys were right - and they seem to have little desire to debunk themselves - then the odds of the Yankees achieving that would be .5^11, or (approximately) .00049. That's one in 2,041. Once every 2,041 years should the Yankees feat be duplicated.

Well, I mean, maybe I'm easy to please but those odds seem too ridiculous to be true, so, by my standards, this proves that the postseason isn't luck.

Moreover, why would they want to believe that the whole objective of baseball - winning a championship - is based on chance? I mean, if that were true and they'd figured out this great secret, then why not just get out from following baseball and pick a hobby more based upon reason, ya know? It just seems like they hate their own sport, so get another, that's all.

-David B.
Thanks for the email, David, but your premise is wrong:

Rob Neyer's last quote wasn't ironic, it was correct. Neyer never claimed or implied that the postseason was all luck, he implied that it was mostly luck, which is something I agree with.

Here's how it goes: the odds of any team winning a postseason series are NOT 50%. These aren't evenly matched teams we're talking about, they're all good teams. The worst team the Yankees played during their streak was the 1998 Texas Rangers, who had a .543 winning percentage, the best team they played was the 2001 Mariners, with a .716 Winning Percentage, and the worst team the Yankees put out there was the 2000 team, with a .540 winning percentage.

So, what are the odds of the Yankees winning any particular series? Wouldn't you know it, Bill James figured that one out for us. James' log5 formula* tells us the Yankees should have been expected to beat the '98 Texas Rangers 2/3 of the time. The entire expected Winning Percentages are:
'98 Yankees vs. '98 Rangers   : .666
     "      vs. '98 Indians   : .661
     "      vs. '98 Padres    : .608
'99 Yankees vs. '99 Rangers   : .519
     "      vs. '99 Red Sox   : .526
     "      vs. '99 Braves    : .467
'00 Yankees vs. '00 Athletics : .475
     "      vs. '00 Mariners  : .478
     "      vs. '00 Mets      : .460
'01 Yankees vs. '01 Athletics : .462
     "      vs. '01 Mariners  : .367
Now, outside of the '98 Yankees and the 2001 Mariners, these numbers are all pretty close to 50%. The '98 Yankees dispatched their first and last opponents without a single loss, and took care of the Indians in six games (which was almost exactly the expected winning percentage, interestingly, but meaninglessly).

Now here's the thing (</John Madden>), none of those expected winning percentages mean anything. Even the ones for the '98 Yankees or the 2001 Mariners. Now, if the '98 Yankees played the '98 Rangers 162 times, they'd win the series 108-54. But in a five game series, they'd be expected to win 3-2. A margin of one game.

And that's what statisticians mean when they say "luck"--that the sample size is too small to draw a conclusion. The Detroit Tigers beat the Yankees in one game last season. Would you look at that game and say that the Tigers were better than the Yankees last season? Of course not, the sample size is too small. The '98 Anaheim Angels went 6-5 against the '98 Yankees. Would you look at those eleven games and conclude that the Angels were better than the '98 Yankees, and if so, are you on crack? Or are you Shredder?

If eleven games is too small a sample to draw a conclusion about which team is better, which it clearly is, then how can five or seven games be enough of a sample size?

Yes, the odds of the Yankees winning eleven consecutive series' is one in 2,041, but their odds of winning under their particular circumstances was much higher--one in 1,654. That's still very long odds, but...

Has anyone else done it? Has anyone else come even close to doing it? The Yankees did win 8 consecutive postseason series' over a 13 year span in the twenties and thirties, but the odds of that happening were much better--1/256 in evenly matched series', 1/93 in the matchups they actually had. The long odds of the Yankees' streak don't prove anything, they merely show how incredible a feat it was.

And it was incredible, and saying that they were lucky to do it is not taking credit away from them, but rather not giving them credit for things they weren't responsible for. The Yankees were lucky that the '99 Boston/Cleveland ALDS went five games, so they only had to face Pedro once instead of twice, they were lucky that the 2001 Seattle/Cleveland ALDS went five games so they were able to get the favorable pitching matchups. They were lucky that Jeremy Giambi didn't slide, they were lucky that strike three to Tino Martinez was called a ball, they were lucky that Jim Thome's HR got blown back in by the wind, they were lucky that Timo Perez stopped running hard when Todd Zeile's ball hit the wall. Luck is anything good that happens that you don't have any personal control over, and the Yankees didn't have control over any of those things. They were lucky.

Baseball games are played by two teams, and the outcome is decided by the performance of both teams, not one. The Yankees could play their best possible game, with the heart of a champion and clutchness and all that stuff, and still lose because the other team played better--or just becuase you got unlucky. You can do everything right and still fail, the perfect pitch that saws off Luis Gonzalez could still drop over the infield and win the World Series. That's how it works.

So, if we know that the playoffs don't decide who the best team is, why do we still watch?

Are you serious? Because we don't know what's going to happen. We watch because baseball is the greatest game ever invented, and seeing the best teams in the game playing each other every October is one of the most fun things we could do with our time, even if the best team doesn't always win. It's just fun to see who will win. If we already knew that, if we knew going into the '98 postseason that the Yankees would win, it wouldn't be fun, and we wouldn't watch.

* Bill James' log5 formula is:
A = Team A's Winning Percentage
B = Team B's Winning Percentage
C = Team A's Expected Winning Percentage vs. Team B

C = (A-A*B)/(A+B-2*A*B)