And that led us to toss together a salad of data around 12 game units. We wanted to get to the point where teams would start making the playoffs...and we figured (correctly) that no team starting the year 0-12 had done so. These five teams (plus the team that had a tie game in the bunch and went "only" 0-11...) were all uniformly horrible...no one remotely near .500.
Of the 26 teams that started the year 1-11 (heck, let's throw in the three more who, again, had a tie and went 1-10) only one team got to .500--the 1973 St. Louis Cardinals.
So we figured it might come down to the 2-10 teams. And this turned out to be true. Two teams actually made it to the post-season after a 2-10 start: the 1951 New York Giants and the 2001 Oakland A's. In fact, 27% of the 30 teams that started 2-10 since 1901 have wound up with a .500 or better WPCT at the close of the year.
But what about at other points during the year? Are there any teams that limp into the post-season by posting a 2-10 record over the final dozen contests in a year? We took a look--and discovered that the answer is no. Only six of 43 teams since 1901 that finished their year 2-10 (in either a 154-game or 162-game schedule) managed to play .500 or better at season's end (14%) and none of them made it into the post-season.

So the moral of the story seems to be: if you are going to swoon, swoon early. That's the only way to stage a recovery, and have a shot at the post-season.