By Nate Silver, BaseballProspectus.com

9) 2003 Red Sox lose ALCS to Yankees

What the math says: 26-to-1 against. Those were the Yankees' odds, down by three runs with no one on base and five outs remaining in Game 7.

Aggravating circumstances: Grady Little refusing to remove Pedro Martinez when it was obvious to 56,279 fans that he was wiped out. The Red Sox blowing the opportunity to tell Roger Clemens where to shove it after knocking him out of the game in the fourth inning. And Aaron Bleeping Boone's home run off of Tim Wakefield to end it.

Mitigating circumstances: The Yankees did not win the championship in a somewhat anticlimactic World Series against the Marlins, while the Red Sox did not need long to redeem themselves.

Aftermath: Little was summarily dismissed and Martinez has never quite been the same.

8) 1969 Cubs lose pennant to Mets

What the math says: 47-to-1 against. The Cubs had as much as a nine-game lead on the Mets, only to lose the division by eight.

Aggravating circumstances: The standings swung a total of 18 games over six weeks, as a black cat ominously circled Ron Santo near the on-deck circle at Shea Stadium.

Mitigating circumstances: The Cubs' collapse, at least, allowed the Miracle Mets to be miraculous.

The aftermath: This preserved the Cubs' curse for at least 27 more seasons and counting and has quite possibly denied Santo a place in Cooperstown.

7) 2004 Yankees lose ALCS to Red Sox

What the math says: 58-to-1 against. The Red Sox entered the 9th inning trailing 3-0 in the series and 4-3 in the game against Mariano Rivera. They could expect to win the game 16.9 percent of the time. And even if they managed to do so they were still 9-to-1 underdogs to pull out the series, with two of the remaining three games to be played on the road.

Aggravating circumstances: The Red Sox had just gotten over a 19-8 drubbing in Game 3. And Game 5 was every bit as good, with Boston making a two-run comeback and winning 5-4 in 14 innings.

Mitigating circumstances: The World Series itself was a snoozer.

Aftermath: Ortiz began to build his clutch hitting resume. Baseball Prospectus wrote a book.

6) 1986 Angels lose ALCS to Red Sox

What the math says: 196-to-1 against. The Angels not only held a 3-run lead to start the 9th inning -- a situation in which the visiting team could expect to win about 1.6 percent of the time against a pitcher like Donnie Moore -- but they also had a 3-1 lead in the best-of-seven series.

Aggravating circumstances: The Angels came back to tie the game in the bottom of the 9th, only to go on to lose in extra frames. Mauch was involved in another choke job.

Mitigating circumstances: Games 6 and 7 were fairly ugly, with the Angels losing by a combined margin of 18-5.

Aftermath: Moore killed himself on July 18, 1989, his blown save in Game 5 believed to be a major factor.

5) 2007 Mets miss playoffs

What the math says: 499-to-1 against. The Mets' playoff probability peaked at 99.80 percent after the action of Sept. 12, when they held a 7-game lead over the Phillies with 16 games to play, and some favorable wild-card permutations as a backup.

Aggravating circumstances: Willie Randolph's clubhouse imploding; for better or for worse, this team will be used for quite some time as the example of the importance of clubhouse chemistry. Most of the damage came at the hands of the lowly Nationals and Marlins, and much of it before record-setting home crowds, while Tom Glavine finished things off with the least -- and hopefully not last -- start of his career.

Mitigating circumstances: Mathematically (as in every other sense) this was a catastrophe: The Mets' 99.80 percent chance to reach the playoffs was the second-highest figure ever by a team that failed to do so. However, there was perhaps no one signature moment or game; the loss to the Marlins in Game 162 was a symbolic in a way, but it was also an anticlimactic affair that was over by the middle of the 1st inning. Nor was the National League a great league; the Mets' only real enemies were themselves.

Aftermath: We shall have to see. Randolph's job is probably safe; this list is remarkable for the lack of managerial firings associated with it, perhaps because when a team blows a lead that looks this secure, management recognizes that there's plenty of blame to go around.

4) 1995 Angels miss playoffs

What the math says: 8,332-to-1 against. As far as the numbers go this was by far the biggest choke job in baseball history. Following games of Aug. 20 the Angels held a 9 1/2-game lead on a mediocre Rangers team and a 12-game lead on the Yankees for the wild card. They finished out the season at 12-26 while the Yankees and Mariners -- in third place at the time -- each went 26-13 to secure playoff spots. The odds of all these things coming together are longer than 8,000-to-1.

Aggravating circumstances: After suffering through two separate losing streaks of nine games each, the Angels then won five straight to close out the regular season, only to succumb to the Mariners in a one-game playoff.

Mitigating circumstances: Quick -- name five members of the 1995 Angels. Chuck Finley, Tim Salmon ... it's getting hard, right? As disastrous as this collapse was from a mathematical standpoint, I cannot in good conscience put it ahead of the top three on this list because of the lack of singular dramatic moments.

Aftermath: Manager Marcel Lachemann kept his job but only to the midpoint of the 1996 season, as the Angels got off to a 52-59 start. The Mariners went on to defeat the Yankees in one of the more underrated postseason series in recent memory.

3) 2003 Cubs lose NLCS to Marlins

The Steve Bartman play was surreal, but it wasn't the main reason the Cubs lost Game 6 of the 2003 NLCS to Florida. AP

What the math says: 107-to-1 against. Somewhat contrary to its reputation, the Bartman Ball does not play the lead role here. The Cubs' chances of winning actually peaked one batter earlier in that unforgettable eighth inning, with no one on, one out, a three-run lead, and Juan Pierre at the plate against Mark Prior. At that point the Marlins were at 2.5 percent to win the game, which increased to around 5 percent after Pierre doubled. Even if Moises Alou had caught the ball that Steve Bartman grabbed instead -- and it isn't a sure thing that he would have -- the Marlins' chances of winning at that point would have been higher than they were before Pierre reached base. The Cubs also had to blow Game 7 to lose the series, a game that they were favored to win 52.1% of the time.

Aggravating circumstances: Shortstop Alex Gonzalez making a key error that could have prevented most of the bleeding. Dusty Baker pulling his own Grady Little by leaving Prior out for too long. Bartman being led out of Wrigley Field under police protection and migrating to Florida. Bartman not holding onto the ball anyway. Baker accusing Bartman of being a Marlins fan in the postgame press conference.

Mitigating circumstances: Not many. This, along with the Buckner error, was one of the great stranger-than-fiction moments in baseball history.

Aftermath: The Cubs suffered through another ugly collapse in 2004 and then just flat-out ugly seasons in '05 and '06 before getting back to the dance this year. In other ways, however, 2003 worked out fantastically for them. Forbes valued the franchise at $335 million in April 2003, but the team is now expected to fetch nearly $1 billion when it is sold. Perhaps 2003 will ultimately be remembered for the death of the warm-and-cuddly Cubs and the birth of the corporate Cubs.

2) 1986 Red Sox lose World Series to Mets

What the math says: 140-to-1 against. Analogous to the Bartman game, Game 6 was of course remembered for Buckner's error, but that wasn't the low point from the standpoint of the Mets' win probability -- by that point the score had already been tied. Rather, there were a pair of low points that had come moments earlier. The first was when Gary Carter came to the plate against Calvin Schiraldi with the Mets trailing by two runs in the bottom of the 10th with two out and no one on. At that point the Mets' chances of winning the game were 1.4 percent. Then, after Carter and Kevin Mitchell had reached base to preserve the inning, Schiraldi had an 0-2 count on Ray Knight; at that point the Mets had about a 3.5 percent chance of winning the game. And even after the Game 6 comeback they still had to win Game 7 at home.

Aggravating circumstances: The wild pitch that allowed Mitchell to score during Mookie Wilson's 10-pitch at bat. The Red Sox having blown a 3-2 lead in the eighth to allow the Mets to force extras. John McNamara's refusal to use Dave Stapleton as a defensive replacement for Buckner. The RBI Baseball recreation.

Mitigating circumstances: None.

Aftermath: The Red Sox suffered a real hangover in 1987, going 78-84; Buckner was released in July.

1) 1951 Dodgers lose pennant to Giants

What the math says: 384-to-1 against. The Dodgers' chances of winning the pennant peaked at 99.84 percent on Aug. 12, at which time they held a 12 1/2-game lead over the Giants.

Aggravating circumstances: The Dodgers rank No. 1 on this list because no other team can combine such a profound collapse in a pennant race with a profound collapse in a deciding game. That game, of course, was made famous by Bobby Thomson's "Shot Heard Round the World", which was preceded by the Dodgers holding a 4-1 lead to start the bottom of the ninth inning. Under those circumstances the Giants could only be expected to win 1.8 percent of the time. To have come back from a 50-to-1 shot after coming back from a 400-1 shot -- and the Giants had to put the pedal to the floor to do it, going 37-7 to close out the regular season and force the playoff -- was very special.

Mitigating circumstances: There is some evidence that the Giants were stealing signs from opposing batteries at the Polo Grounds throughout this pennant race, but as Kevin Baker points out in It Ain't Over 'Til It's Over, the Giants' run scoring at home actually dropped during the stretch run.

Aftermath: The Dodgers, so often forced to play second fiddle in New York to the Giants and the Yankees, finally won their first World Series in 1955, only to be relocated to Los Angeles three years later. Ralph Branca, then 25, won just 12 more games over the balance of his career.

Ultimately, the lesson is that misery loves company: many of the same teams that have vanquished a choker have been the victim at another point in time. That could mean that the Cubs are due to make a big comeback at some point in the 2007 playoffs.

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