The Boston Red Sox’s odds of reaching the playoffs peaked on Sept. 3. Following a 12-7 win against the Texas Rangers, they held a 9-game lead over the Tampa Bay Rays with 24 games to play, giving them a 99.6 percent chance of making the post-season.
The Red Sox, of course, once had a reputation for elevating improbable collapses into the routine, dealing their opponents one inside straight after another.
There was the Bucky Dent game in 1978:
The Aaron Boone game in 2003:
And there was Game 6 of the 1986 World Series, when Mookie Wilson’s grounder skirted through Billy Buckner’s legs, bringing Ray Knight around to score.
But following their victory in the 2004 World Series, their first in 86 years — naturally, it had required an improbable comeback of its own, as the Red Sox had recovered from a 3 games to none deficit to defeat the Yankees in the A.L.C.S. — the Red Sox’ luck had finally seemed to turn around.
Until Wednesday night.
It’s hard to describe just how epic the Red Sox’ collapse was — something on the order of Mr. Buckner’s play multiplied by itself two or three times over. Numbers and graphics may do the most adequate job.
This is a chart, from FanGraphs.com, showing the Red Sox’ probability of winning their game against the Orioles on Wednesday night. According to FanGraphs, it peaked at 95.3 percent, when the Orioles had two outs and nobody on in the bottom of the ninth inning.
That’s probably an underestimate, in fact. FanGraphs tracks these numbers on a play-by-play basis, but not a pitch-by-pitch basis, and the Orioles’ Chris Davis was down to his final strike. Moreover, the Red Sox had Jonathan Papelbon on the mound, one of baseball’s most unhittable pitchers. A more realistic estimate might have been that the Orioles had about a 2 percent chance of coming back at that point. (By comparison, the Red Sox’ chances of winning Game 6 of the 1986 World Series had peaked at about 99 percent.)
And that is only part of the story. More unlikely still was the Rays’ comeback against the Yankees, without which the Red Sox would have had an opportunity to redeem themselves in a one-game playoff. Trailing 7-0 in the 8th inning, the Rays’ winning chances were all the way down to 0.3 percent — about 300-to-1 against — before they scored 6 runs in the bottom of the inning.
Although the rally revived the Rays, giving them about a 15 percent chance of winning, they were in nearly as much trouble in the 9th, after Ben Zobrist and Casey Kotchman made outs to start the inning, bringing their odds back down to 4.2 percent, according to FanGraphs.
This, however, also understates the magnitude of the Rays’ accomplishment. Like Chris Davis in Baltimore, the Rays’ Dan Johnson had two strikes against him. Granted, he wasn’t facing Jonathan Papelbon (or Mariano Rivera, whom the Yankees held out of the game). But Johnson was hitting just .108 on the season — and had just 1 hit in 45 at bats with a two-strike count. A 2 percent chance of a comeback at that point would be a generous estimate.
But Johnson poked Cory Wade’s pitch around the fair side of the right field foul pole, tying the score. Then in the 12th inning, Evan Longoria hit a home run that was virtually its mirror image, but this one to left field, winning the game for the Rays just moments after the Red Sox had lost theirs.
The following is not mathematically rigorous, since the events of yesterday evening were contingent upon one another in various ways. But just for fun, let’s put all of them together in sequence:
The Red Sox had just a 0.3 percent chance of failing to make the playoffs on Sept. 3.
The Rays had just a 0.3 percent chance of coming back after trailing 7-0 with two innings to play.
The Red Sox had only about a 2 percent chance of losing their game against Baltimore, when the Orioles were down to their last strike.
The Rays had about a 2 percent chance of winning in the bottom of the 9th, with Johnson also down to his last strike.
Multiply those four probabilities together, and you get a combined probability of about one chance in 278 million of all these events coming together in quite this way.
When confronted with numbers like these, you have to start to ask a few questions, statistical and existential.
The statistics that Web sites like FanGraphs use, for instance, usually assume that that outcome of each game or at-bat is independent of the next one. They don’t account for things like streaks or clutch hitting, above and beyond what arises naturally from random chance.
That’s probably a good assumption under most circumstances. There are volumes of literature suggesting that the notion of clutch performance is vastly overrated in baseball and in most other sports — and that what we think of as streaks are usually just tricks that random numbers are playing upon us.
xkcd.com But perhaps there is an exception once in a while — I’ll spare you the lecture about Bayes’ theorem — and this may have been one of them.
There is some evidence, for instance, that the Red Sox’ pitchers may have “choked” in key situations during the final few weeks of the season to a degree that withstands some statistical scrutiny. Their bullpen, also, was extremely fatigued, as their starters averaged only 4.2 innings per start in September.
One should also have the license in situations like these to turn to various divine and karmic explanations. I have a couple of these.
First, perhaps the baseball that unfolded on Wednesday evening — which also featured a dramatic and season-ending collapse by the Atlanta Braves — was God’s way of telling Bud Selig that baseball ought not add an extra wild card, which would have rendered yesterday’s games relatively meaningless.
The second explanation involves Mr. Buckner.
On Sept. 4, the day after the Red Sox’ playoff probability peaked, H.B.O. aired an episode of “Curb Your Enthusiasm.” The show is the brainchild of Larry David, the creator of Seinfeld.
In the episode, “Mister Softee”, Mr. Buckner was featured prominently. Jeered by Red Sox fans everywhere he went, he dropped a baseball autographed by Mookie Wilson out a window. But he restored his reputation after catching a baby dropped from a burning building.
Since the Red Sox’ curse already seemed to have been lifted after 2004, Mr. Buckner’s redemption was superfluous: a case of two 180-degree rotations turning the Red Sox’ karma all the way back around. From the day that the episode aired, the Red Sox went 6-18.
The program was fiction, of course. But you couldn’t have scripted what happened last night. And Mr. David is a Yankees fan.
A version of this article appears in print on 09/30/2011, on page B9 of the NewYork edition with the headline: The Buckner Effect: Outcomes That Defy All Reason and Odds.
