What had been the greatest season in Bengals history took a regrettably Bengals-like turn Sunday, when Cincinnati quarterback Andy Dalton fractured his thumb, likely putting him out for the season. Although the Bengals are still practically certain to make the playoffs, the team’s Super Bowl chances have suffered a major setback. According to our back-of-the-envelope calculations, the loss of Dalton’s passing productivity is enough to cut the Bengals’ championship hopes by between two-thirds and three-quarters. Or, more bluntly, from dark horse range down to a Hail Mary.

To sketch out what the Bengals might look like without Dalton, we can turn to Football Outsiders’ defense-adjusted yards above replacement (DYAR), a stat that measures performance relative to a backup-caliber player. By adding up the passing, rushing and receiving production for each team and combining the result with a team’s defensive SRS rating, those DYAR counts can be used in a regression model to predict how many games it will win. (This model does a reasonably good job, too, with an r-squared of 0.72 and a standard error of +/- 1.6 wins per 16 games.) This is especially useful when a certain amount of production gets removed from the team’s ledger, as it has with Dalton.

Going into Week 14, Dalton had been the NFL’s third-most-productive QB according to DYAR. Meanwhile, A.J. McCarron, Dalton’s stand-in, hasn’t made a compelling argument that he should be accounted for as anything but a zero-DYAR backup. Dalton’s performance this season has vastly exceeded his own track record, so we’ll regress his numbers some toward his previous standard of play — the mean of his two-year average going into this season and his per-16-game rate this year (before Sunday’s game). Even then, with this lesser version of Dalton plugged in, replacing him with McCarron figures to cost Cincinnati about two wins every 16 games.

To express that in Elo ratings, Cincy should now effectively play to a rating of 1545 instead of the 1654 mark Elo had assigned the Bengals before their loss to Pittsburgh. A 109-point Elo dip is significant: It’s enough to hack 4.4 points off a team’s point spread each game, or the equivalent of turning the formerly AFC-leading Bengals into, say, the much less dominant Minnesota Vikings.

EXPECTED TEAM DYAR (2015) QB PASSING RUSHING RECEIVING TEAM DSRS WINS PER 16 EQUIV. ELO Dalton 1000 220 732 +3.3 10.9 1654 McCarron 0 220 269 +3.3 8.8 1545

Cincinnati remains more likely than not to secure the AFC’s No. 1 or 2 seed, and therefore a first-round bye. But a team carrying a 1545 Elo is also about three times less likely than a 1654-rated squad to rattle off the three consecutive victories against a typical playoff-caliber opponent (averaging an Elo of 1650) necessary to win the Super Bowl from a top-two seeding, falling from roughly 13 percent to 4 percent. And if the Bengals can’t hang on to one of those bye weeks, their odds of ripping off four straight against playoff opposition drop from 7 percent to 2 percent at the post-Dalton rating.

Perhaps Dalton will somehow be able to return for the playoffs, or maybe McCarron will prove better than the typical backup. If not, the Bengals’ Super Bowl chances will find the same final destination as a trough of Skyline Chili.