On August 7, 2013, the Yankees' record stood at 57-56. They were 11. 5 games back in the division and seven games back for the second wild card spot. They would need to pass four teams in the standings for the final playoff spot. Since that time, the team has gone 12-5, putting them seven games back in the division and just three and a half games from the final wild card spot. If the Yankees were to continue their run and sneak into the playoffs, it would rank among the greatest in-season comebacks in Yankee history.
According to coolstandings.com, there have been three previous Yankee teams with odds of making the postseason at lower than ten percent after the All-Star Break and still made the playoffs.
August 22, 1964 (6.2% chance of making the playoffs)
With just 40 games left in the regular season, the Yankees were staring up at both Chicago and Baltimore, five and a half games behind the league-leading Orioles. As late as September 4, the odds of making the playoffs were still only 9.9%. The team featured Mickey Mantle, Roger Maris, and Joe Pepitone in the lineup with Jim Bouton and Whitey Ford in the rotation. The team got hot to end the season, winning 22 of its final 29 games. They clinched on the second to last day of the season and finished one game ahead of the White Sox.
Their opponent in the World Series, the St. Louis Cardinals, completed a more improbable run to the playoffs. They had just a 0.2% of making the playoffs on July 24, 1964, when they were ten games back and in a tie for seventh place. The Cardinals comeback rated third all-time. Thanks to an epic Phillies collapse, the Cardinals were able to ride their way to the pennant and eventual World Series Championship in seven games over the Yankees.
August 26, 1995 (1.7% chance of making the playoffs)
At 53-58 and 15.5 games back of the Red Sox for the division, the Yankees had no shot at winning the division, and slim odds of making the playoffs as a wild card. They sat 5.5 games in back of the wild card-leading Rangers and needed to pass five teams to get to the postseason. With Don Mattingly and much of the group that would win the Series the following year, the Yankees finished the season on a 26-8 run that allowed them to get the wild card on the second-to-last day of the season. They wound up losing the Mariners in the division series, Mattingly retired, Joe Torre was brought in to replace Buck Showalter, and they no longer needed to make regular season comebacks to get into the postseason.
July 18, 1978 (0.6% chance of making the playoffs)
At 61-28, the Boston Red Sox appeared to have the division sewn up, leading by eight games over the Milwaukee Brewers, as well as a 12.5 game lead over the Orioles and a 14 game lead over the Yankees. The Yankees, at 47-42, played extremely well over the next month, upping their record to 75-54 by August 29 yet still had just a 5.1% chance of making the playoffs as the Red Sox were still seven and a half games ahead. The Yankees surged, grabbing the lead for good on September 13. They slipped into a tie on the final day of the regular season, but then Bucky Dent happened, followed by a World Series win over the Dodgers.
August 7, 2013 (1.8% chance of making the playoffs)