After the trade deadline, no one thought that the Tigers would be in the position they're in now. They were 52-57 at the beginning of August, fourth in the division, and eight games behind the Royals and Twins, who were tied for third. Jack Flaherty and almost all of the veterans were gone, with just a handful of prospects picked up in return. They'd all but waved the white flag on the season.
The Tigers only had two healthy starters. Jace Jung and Trey Sweeney being called up was more of a "screw it" measure to give them some run at the major league level rather than a bid to turn the Tigers into a winning team by the time the season was over. Detroit was still gunning to put up a better regular season record than last year, but that was just about the only plausible goal they had before trying to come back better next season.
But the Tigers' record since the deadline is 33-23, the best in the American League. They're chasing history in not only becoming the first Tigers team to overcome such a deficit going into the second half to make the postseason, but to also become the first "MLB team ever to make the playoffs in a non-shortened season after being 8+ games under .500 in August or later" since the Mets did it in 1973.
Tigers poised to join 1973 Mets and overcome massive playoff deficit as they push toward the Wild Card
The 1973 Mets were 62-71 at the end of August, but by Sept. 21 they had clawed their way up to a half-game division lead off of the Cardinals, which they extended to 1.5 by the time the season was over. They made it all the way to the World Series against the Athletics that year, even getting out of Game 5 with a 3-2 lead before falling to Oakland in Games 6 and 7.
The Tigers aren't fighting for a division title here, and thanks to the addition of the Wild Card and expanded playoff format, they have a few more hurdles to get over if they're going to get to the World Series. However, after their sweep of the Royals their playoff odds went up to 36.4%, with a 1% chance of winning the World Series. 1% is still 1%, but it isn't zero.
Jake Rogers said it best: "Don't let the Tigers get hot." The rest of the league underestimated them, and they started to roar back in August to make an unprecedented push. If the Tigers keep winning and the Twins keep losing (and it certainly looks like both might happen), this team could do the unthinkable.