Kidding aside, it’s not really about systems or play-calling or even injuries. Those things do matter, but the heart of any sport is about having better players than the other team. Rebuilding a team takes time and requires patience.

At the moment, there’s not much the Redskins can do with their current offensive roster. There are some solid players, just not enough of them. The system the Shanahan brain trust is so fond of might work well for John Elway and Terrell Davis or for Matt Schaub and Andre Johnson, but it doesn’t work as well for John Beck and Jabar Gaffney. No system in the world can make up for a lack of talent and depth.

But there is something they can do to instantly improve their offense.

The Redskins have to understand that their offense enters every game as an underdog, and if they keep doing the same things in the same way, they’re very unlikely to score enough points to win. Put simply, the offense needs to take more risks and have a more aggressive game plan, and there is a solid mathematical reason.

Risk is at the heart of football strategy. Conservative game plans result in relatively consistent low-variance outcomes, with teams performing close to their average. Aggressive, risky game plans result in boom-or-bust, high-variance outcomes, sometimes scoring lots of points but sometimes scoring very few. This is exactly what an underdog offense needs to do to win.

Think about it this way: If a better team is facing an underdog, and both teams perform exactly at their typical level, the favorite will win every time. To maximize its chance of winning, an underdog needs variance, even if it means risking a blowout. The reason for the extra risk involves the math of relative score distributions, and those interested can find a more complete analysis here.

This is something poker players understand very well. With a dwindling pot of chips, a poker player often goes all in, betting everything. This is an example of a high-variance strategy — a big risk, but also possibly a big payoff that’s necessary to even the odds.

Underdogs should employ a high-variance strategy from the first kickoff. They shouldn’t wait until the fourth quarter and become desperate. Roll the dice from the get-go. Bad offenses should play as if they are down by a touchdown or two at the start of the game because, in effect, they are.

The real question is, what is the optimum level of risk? I’m not sure, but I do know NFL coaches are operating far from it.

In a study I did a couple years ago, I discovered that underdog NFL teams do not increase their variance. For example, for games in which the point spread is between 6 and 7.5 points, the standard deviation of the underdog’s score is 9.8 points, slightly less than the overall league average of 10 points. Ideally, it should be much higher. The favorite’s standard deviation is 10.4 points, when ideally it should be lower.

This result suggests coaches are not maximizing their team’s chances of winning as much as they are delaying elimination from contention — that is, trying to “stay in the game” for as long as possible. Underdog coaches like Mike Shanahan minimize risk all game long, hoping for a miracle along the way. They seem to be reducing the chances of being blown out, but this is not consistent with giving their team the best chance to win.

Overnight, the Redskins’ offense can get better, or at least yield a better chance of winning. Here’s what they need to do:

 1. Pass more often, particularly early in the game and on 1st and 2nd down. Passing has a much higher variance than running. Sure, the Redskins’ passing game stinks, but their running game has become even worse lately.

2. Take more chances on defense. Jump routes occasionally. Call more risky stunts and blitzes.

3. Go for it on 4th down more often than not. The math is clear on this, and every analysis I’m aware of agrees that the NFL convention of kicking on everything up to 4th and an inch is hyper-conservative.

4. Install a variety of trick plays, practice them, and use them—fake punts, fake kicks, flea flickers, etc. Trick plays are all about high variance.

5. Attempt the occasional surprise onside kick. Similar to 4th downs, the math here is just as convincing.Study the tape of opposing receiving teams and whether they respect the possibility of a surprise onside kick.
 Note that I’m not calling for going for it on 4th and 15 from the Redskins’ own 5-yard line, and I’m not suggesting a trick play on every other down. But if the Redskins offense is going to score enough points to win, it should take some aggressive yet measured risks. They can’t wait until their last few chips to go all in.

Brian Burke is former Navy pilot who has given up his F/A-18 for the less dangerous hobby of football analysis. He is the creator of Advanced NFL Stats, a website about football, statistics, and and game theory.