The Redskins’ playoff chances have climbed to about 47 percent heading into the final three weeks of the season. Their easiest path to the playoffs is by winning the NFC East. About 30 of that 47 percent is by winning the division, and the other 17 percent is by qualifying for a wildcard berth.

All season long, my prediction model tracks key team efficiency statistics for all teams and estimates the outcome probabilities for every forthcoming game. These estimates form the basis of a Monte Carlo prediction model, which simulates the season thousands of times and assesses each team’s chances of making the playoffs according to the NFL’s sometimes-arcane tiebreaking procedures. (This model was developed in cooperation with Chris Cox, whose season simulation application is available at his site,

Winning out and finishing 10-6 would virtually assure Washington its first playoff berth since 2007. There is a less-than-one-percent chance that 10-6 might not be enough. Finishing 9-7 would still likely be enough for a berth, depending on which team the Redskins lose to. (It would be best to lose this Sunday against Cleveland, their sole remaining out-of-conference opponent.) Should the Redskins wind up at 9-7, they’d have about a 62 percent shot at the postseason.

To win the division, the Redskins need to beat out both the Giants and Cowboys. They need win at least one more game than the Giants to achieve a tie in overall record. At that point the tiebreaker becomes division record, because the two teams split their head-to-head games. The Redskins own a 3-1 division record with two more games to play in the division. The Giants are 2-3 with one more to play.

The Redskins also need to at least keep pace with Cowboys and, in all likelihood, have to beat them in the final week of the regular season to win the head-to-head matchup and keep an edge in division record against their rivals.

Things are setting up well for the Redskins in terms of strength of schedule. The Giants face two winning teams in the final three weeks — at Atlanta and at Baltimore — before hosting the Eagles. The Redskins face only one winning team, at home against the Cowboys in Week 17. Their two other games — at Cleveland and at Philadelphia — could still be dangerous. The Cowboys might have the toughest road schedule, facing the Steelers and the Saints before their final showdown with the Redskins at FedEx Field.

A wildcard is the less likely path for Washington. First, the Redskins must best the Cowboys in overall record or tie them with a better division record. Next, they must catch either the Bears or Seahawks, both of whom they trail by a game. Without a head-to-head game among those three teams, the tiebreaker will be conference record. Both the Redskins and Seahawks have a 6-4 conference record, while the Bears have a 5-4 record. The Vikings are also a threat, but the Redskins have the head-to-head tiebreaker.

The chances of the Redskins catching the Giants might not be very high, and their chances of catching the Bears might not be very good. And catching the Seahawks might not be so likely. But the Redskins don’t have to catch all three. They just need to catch any one of them, which is much more likely than may be intuitively apparent.

Of the Redskins’ three remaining games, the biggest is going to be against the Cowboys. Measuring the difference between their playoff chances, assuming a win and assuming a loss against each remaining opponent, we can estimate the leverage of each game. For example, if the Redskins beat the Browns this Sunday, their playoff chances would go to 64 percent, pending the rest of the results from Week 15. But should they lose to the Browns, the Redskins’ chances would drop to 30 percent, for a net potential swing of 34 percent. The Eagles game has a similar potential swing of 37 percent. But the Cowboys game is by far the most critical, with a potential swing of 55 percent.

Brian Burke is the creator of Advanced NFL Stats, a Web site about football, statistics and game theory.