Thanks to Baseball Prospectus' postseason probabilities, available daily on MLB.com, it's possible to track those changes. These probabilities are based on thousands of Monte Carlo simulations of the rest of the season and take into account each team's run differential, roster composition, playing time projections and remaining schedule.
Here is a look at each division race:
The Yankees won seven of their last 10 before the break, opening up a 3 1/2-game lead over the Rays, who had the Orioles and Blue Jays nipping at their heels. Their division-title odds stood at 60 percent. New York stayed hot after the All-Star Game, opening up a seven-game lead -- and an eight-game lead on Toronto -- by July 28. The Yanks' odds of winning the division peaked at 85 percent.
But the dynamics of the race changed considerably before the July 31 non-waiver Trade Deadline, with the Jays acquiring shortstop Troy Tulowitzki from the Rockies and pitcher David Price from the Tigers, among others. Since that low point on July 28, the Jays have won 14 of 15 games, including 11 in a row, overtaking the slumping Yankees. Toronto's division odds, which were at 14 percent a month ago, now stand at 56 percent, while the Yankees have tumbled to 39 percent.
The reign of the Tigers is all but over. After four straight AL Central championships, Detroit has seen its odds of a five-peat drop from nine percent to zero since the All-Star Game. Cleveland, Minnesota and Chicago also have odds near zero, with Kansas City more or less locking up its first AL Central title. By going 16-12 in the second half while the Tigers and Twins have scuffled, the Royals have increased their division odds from a solid 76 percent to a near-certain 99 percent.
The Astros entered Friday having lost seven of their past nine games, yet their prospects have brightened significantly over the past month. At the break, they held 36-percent division odds, trailing the defending-champion Angels (57 percent) by a half-game.
A strong start to the second half pushed Houston ahead by as many as four games, and while the recent slump has cut into that advantage, the Astros enjoy 66-percent odds. The Angels, meanwhile, have dipped to 30 percent.
The Nationals, heavy preseason favorites, got off to a rocky start and trailed the red-hot Mets by as many as eight games in late April. But going into the break, it seemed that order had been restored. Washington won 14 of 20, built a two-game edge over New York and pushed its division odds up to 72 percent.
Then things got crazy. Before the Deadline, the Mets nearly traded for Carlos Gomez, then actually traded for Yoenis Cespedes, among other reinforcements. From July 31 on, they have reeled off 11 wins in 13 games, suddenly finding themselves 4 1/2 games ahead of the reeling Nats (18 percent). As things stand now, it's the Mets (82 percent) who are the heavy favorites.
The Cardinals have traveled a similar road as their in-state neighbors to the west, taking strong odds into the break (72 percent), then watching them rise further thus far in the second half (86 percent). St. Louis, looking for its third straight division title, holds MLB's best record. The Pirates have the second-best mark in the NL, yet their chances of taking the division have dropped from 20 percent to 8 percent. The upstart Cubs, just 1 1/2 games behind the Bucs, are at 6 percent.
Not much has changed here over the past month. On the day of the All-Star Game, the Dodgers held a 4 1/2-game lead over the Giants, with 89 percent odds. That lead now stands at 2 1/2 games, and those odds at 81 percent. The odds for San Francisco, meanwhile, have crept from 10 to 17 percent.
Biggest second-half risers
1. Mets: +55 percentage points (27 to 82 percent)
2. Blue Jays: +42 percentage points (14 to 56 percent)
3. Astros: +30 percentage points (36 to 66 percent)
4. Royals: +23 percentage points (76 to 99 percent)
5. Cardinals: +14 percentage points (72 to 86 percent)