Redskins Coach Mike Shanahan recently denied that his postgame comments meant he was giving up hope his team would make the playoffs. Even if he was only admitting the obvious, he gained nothing from forfeiting the motivational edge that chasing a playoff spot can provide a team.

But I don’t think it’s certain that the Redskins don’t have a realistic shot at a playoff berth. Here’s why I say that.

It starts with an estimate of each team’s ability to beat any of the others. The model I use is based on team statistics which have been demonstrated to be the most predictive of future outcomes weighted according to how well they correlate with winning. These numbers are adjusted according to past strength of schedule and then applied to all forthcoming regular season games to produce a probability each opponent will win. Home field advantage is also accounted for.

Then the season is simulated to see which teams end up in the playoffs. This simulation is repeated thousands of times, enough to reliably see how often each team tends to end the season in the playoffs. This kind of brute-force approach is known as a Monte Carlo method, which is well suited to complex systems like the NFL’s convoluted tie-breaking rules.

When we put the numbers through this grinder, the Redskins come out with a 5 percent shot at a playoff spot at any seed. If this seems high to you, it probably is. During Shanahan’s defense of his postgame statement, he cited the fact that only three 3-6 teams went on to make the playoffs. But there are some good reasons why this year might be different.

First, there are no NFC divisions with dual juggernauts this season. Often, there can be two or more elite teams gumming up the same division, where one of them is a virtual lock for a wildcard slot. Currently there are only three NFC teams not leading their divisions with winning records. Of those three teams, only one is more than a single game over .500.

Even winning the division is not completely out of the question. Don’t get me wrong. It’s very unlikely, to be sure, but the Redskins have a slew of division games remaining on their schedule, and the breaks may go their way. They have their bye this week, which will allow them to heal somewhat, plus they have one more home game than away game.

Despite their losing record, the Redskins are not a bad team. They have scored the fourth-most points in the NFC, but have given up the most points to opponents. Considering their strength of schedule to date, they are right in the middle of the pack. Average teams sneak into playoff spots nearly every year. Whether we call it sample error, uncertainty or randomness, luck plays a much larger part of the NFL season than we realize, and one of these seasons the ball is going to bounce the Redskins’ way.

Five percent isn’t much, but it’s real. It’s too soon to give up on the playoffs, either realistically or as merely a matter of motivation.

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