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For all intents and purposes, the World Series is over. No team has ever come back from a 3-0 deficit –

Scratch that. It was less than a week ago that David Ortiz busted about a 250-pound hole through that particular argument. But to hear the pundits talk, you’d think that the Red Sox had pulled off a one-in-a-million feat.

Cardinals fans can rest assured that their odds of pulling off a similar miracle are substantially better than that. A naïve model, which simply assigns each team 50 percent probability of winning each game, would conclude the odds of a Cardinal comeback are 15-to-1 against, or exactly the same as having a coin come up tails four times in a row. Clay Davenport’s model, which is anything but naïve and takes into account relative team strength (and regards the Cardinals as the better team), puts the odds at a more palatable 12-to-1 against.

Neither of those estimates would seem to take history into account. The Red Sox, after all, were the first team ever to come back from a 3-0 deficit to go on and win the series. How amazing is that?

Actually, it’s not all that amazing. The Red Sox might have been the first team to pull off the feat, but only 25 teams before them had had the opportunity. If the team leading the series and the team trailing series were of equal strength–meaning a team trailing 3-0 has a 1-in-16 chance of going on to victory–we’d expect the trailing team to have come back to win the series 1.625 tries in 26. Instead, they’ve come back one time out of 26. We can’t draw any conclusions from that.

In fact, there’s no reason to think that the teams ought to be of equal strength. That a team has won the first three games of a series provides some prima facie evidence that it is, in fact, the stronger club. For example, suppose that, if the two teams played one another an infinite number of times, Springfield would win 55% of the time, and Shelbyville would win the other 45%. Shelbyville will jump out to a 3-0 lead in a seven-game series approximately 9% of the time (figured as .55^3), while the Isotopes will manage the feat around 17% of the time, or almost twice as often.

Similarly, if a team trailing 3-0 in a series is at an intrinsic 45-55 disadvantage, we’d expect it to go on to sweep the last four games and win the series about 4.1% of the time, or one try in 24. Instead, the trailing team has gone 1-for-26. The empirical results have been exactly what we’d expect them to be.

I should point out that I’m not going to consider data from other sports. I realize that we have a lot more trials to work with if we include NBA and NHL results–and basketball and hockey teams have done remarkably poorly when facing 3-0 deficits–but I don’t think that it tells us anything. The difference between two “good” basketball teams is a couple of orders of magnitude greater than the difference between two good baseball teams. If you pitted the 2002 Lakers against the 2002 Nets say 100 times, I’d expect the Lakers to win something like 75 of those games. If you did the same thing with the 1989 A’s and the 1989 Giants, it’s hard to imagine the A’s emerging with more than 60 victories. It’s also my belief that momentum plays a greater role in basketball, though I’m sure someone like John Hollinger could shoot a few holes in that theory. As for hockey, I don’t know the sport as well, but I do know that it places intense physical demands upon its combatants, and it’s easy enough to imagine a team trailing 3-0 collapsing from exhaustion.

We do, however, have some additional baseball-specific data to work with. Let’s look at the 26 post-season series in which a team has trailed 3-0 in a little bit more detail:

Year   Series     Ahead      Behind     Game 4 Result   Series Result
1907     WS       Cubs       Tigers          2-0             4-0
1910     WS       A's        Cubs            3-4             4-1
1914     WS       Braves     A's             3-1             4-0
1922     WS       Giants     Yankees         5-3             4-0
1927     WS       Yankees    Pirates         4-3             4-0
1928     WS       Yankees    Cardinals       7-3             4-0
1932     WS       Yankees    Cubs           13-6             4-0
1937     WS       Yankees    Giants          3-7             4-1
1938     WS       Yankees    Cubs            8-3             4-0
1939     WS       Yankees    Reds            7-4             4-0
1950     WS       Yankees    Phillies        5-2             4-0
1954     WS       Giants     Indians         7-4             4-0
1963     WS       Dodgers    Yankees         2-1             4-0
1966     WS       Orioles    Dodgers         1-0             4-0
1970     WS       Orioles    Reds            5-6             4-1
1976     WS       Reds       Yankees         7-2             4-0
1988     ALDS     A's        Red Sox         4-1             4-0
1989     WS       A's        Giants          9-6             4-0
1990     ALDS     A's        Red Sox         3-1             4-0
1990     WS       Reds       A's             2-1             4-0
1995     NLDS     Braves     Reds            6-0             4-0
1998     NLDS     Padres     Braves          3-8             4-2
1998     WS       Yankees    Padres          3-0             4-0
1999     NLDS     Braves     Mets            2-3             4-2
1999     WS       Yankees    Braves          4-1             4-0
2004     ALDS     Yankees   Red Sox          4-6             3-4

What stands out is the number of sweeps. The team with a 3-0 lead has gone on to win Game Four and bring out the brooms on 20 of 26 occasions. The series has been extended to five games just six times, and six games just three times. The 2004 Red Sox, of course, are the only team to force a Game Seven and the only team to win it.

All told, teams trailing 3-0 in a postseason series have managed an 11-25 record in the games that follows. That seems, at first glance, to be a non-random result. Is it?

Once again, the answer depends on the skill advantage of the team that holds the lead. If you take two teams of equal strength, Team A will win 25 or more times in 36 games about 1.4% of the time (this is estimated using a binomial distribution. If instead Team A has a 55-45 skill advantage–a much more realistic assumption–it will go 25-11 or better about 5.6% of the time.

The latter figure is just on the cusp of statistical significance. But it’s also worth looking at the scores of Game Fours when a team trails 3-0:

1 run: four times
2 runs: four times
3 runs: seven times
4+ runs: four times
Lost game: six times

In 14 of 26 Game Fours, the leading team has won by one run or two runs, or has lost the game. If the trailing team were laying down and setting its golf schedule for the winter, you’d expect a lot of blowouts. Instead, the games have been quite competitive: just four times has the game been decided by more than three runs.

None of this is likely to provide much comfort to Cardinal fans. St. Louis has to win four games in a row, and that no easy feat in baseball, especially against a team a good as the Red Sox. But history provides no compelling evidence that the feat is any more difficult than that.

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