Variance and the Broncos

The Broncos, led by Tim Tebow, have pulled off yet another amazing last second win. This will convince many, probably including the Broncos' front office, that they need to stick with Tebow as their QB-of-the-future. He took a team in last place to a division championship and a playoff win. What's not to like? If the Broncos want to have a good shot at winning pretty much any game they play, keeping Tebow is the right move. If they want to become one of the best teams in the league and win Super Bowls, they need to dump him and find a real quarterback as soon as possible.

That doesn't make sense, does it? Isn't having a shot to win every game and being a good team the same thing? You put a good team on the field, you have a better chance to win, you put a bad team on the field, you have a worse chance to win, right? Well, not necessarily, and here's why.

The Green Bay Packers score 35 points per game, while the Kansas City Chiefs score about 13 points per game. So obviously a Packers-Chiefs game would see the Packers win by a score of 35-13 right? Of course not, because scoring 35 points per game doesn't mean you score 35 points in every game, it means that on average you score 35 points per game. Some days the Packers score 49 points, some days they score 14, but overall the average is 35. That is an example of one of the most underrated forces in life; variance.

Variance is the measure of, predictably, how much things vary. Sets with high variance vary a lot, while sets with low variance vary very little. So a society where all men are 6-feet tall would have low variance in height, and a society where lots of people were 4'6" and many other guys were 7' would have a high variance in height. They could both have the same average height, but the variance would be very different.

The idea behind variance is pretty simple, but many interesting effects come out of it. Because it is often easier to effect the variance than it is to change the mean, these effects can become very important. For example, making your house less likely to be robbed is very difficult. But you can change the variance in how much you can expect to lose from a robbery by simply buying insurance. Without insurance, you either lose nothing (you aren't robbed) or you lose a lot (you are robbed). But with insurance, you either lose a little (you aren't robbed but still pay premiums) or you lose a little bit more but still not much (you are robbed, but insurance gives you some money to help cover the damage).

In football it is also often easier to change the variance rather than change the mean. In this case, instead of money, we're measuring point differential. Teams with a high average point differential are good while teams with a low average point differential are bad. To improve your mean, you have to improve the team. This is very difficult, because you are competing against 31 other highly competitive teams in a zero sum game. But increasing or decreasing variance is relatively easy, since nobody cares about variance (even though they should).

So the question becomes how do we change our variance in point differential and should we try to move it up or down? The answer to the first question is pretty intuitive. To increase variance in point differential in a game, you want lower scores and fewer possessions, while decreasing variance means higher scores and more possessions. That means that a team that wants higher variance should run the ball and stop the pass, while a team that wants to pass and stop the run.

The answer to the second question is that it depends. If you're a good team, you want the variance to be low, while a bad team wants the variance to be high. If a good team has an average point differential of +6, then a variance of 0 would mean that they always win by 6, which would mean they always win. But a team with that same average but with a high variance has a chance of being upset in a given game. So a good team reduces their chance of being upset by reducing the variance in point differential, while by similar logic bad teams increase their chance of upsets by increasing variance.

And this brings us to the Broncos. As a bad team, the Broncos want to increase variance by running the ball and stopping the pass, and that's exactly what they've done. In fact, by starting Tebow, they can now run the ball more than any other team in the league, which means their chances of pulling off upsets are far higher than what you would expect from a team of their quality.

If you don't believe me, consider the Big 3 teams (Packers, Patriots, and Saints). They all have great offenses and not so great defenses, which means that each team has several drives, decreasing the variance and decreaing their chances of being upset. These three teams have been upset 6 times, and only once can you really describe the game as a shootout (Buffalo over New England). All the other times the good team was held far bellow their normal score. In fact, when we beat the Packers, this is exactly what we did. By running the ball effectively and not scoring too quickly, we limited Green Bay's possessions and gave ourselves a better chance of winning.

But building your team to increase variance is a bad idea. Sure, you'll be able to pull off more upsets, but the ultimate goal is winning Super Bowls, and thus you don't want to build a mediocre team that can occasionally pull off an upset, but build a good team that doesn't get upset. That means building a team that passes well and can stop the run, not one who can run well and stop the pass.*

*Actually, this isn't true for other reasons. You actually want to build a team that can pass and stop the pass. The short version is that even if not being able to stop the run causes you to get upset every once and a while, you're still very likely to make the playoffs if you're a good team, and so you should focus on being able to beat other playoff teams rather than beating bad teams. And, for reasons I won't explain here, good passing teams are more likely than good running teams to be good overall teams, so you need to be able to stop them with a good pass defense.

But won't this mean your bad team will be even worse? If you inherit a 2-14 team and build a lower variance team, won't you reduce your chances of winning? Yes, bud that doesn't matter. Even after their win today (notice that they won against another high variance team), the Broncos have very little chance of winning the Super Bowl. They have virtually no chance of beating the low variance Patriots and the low variance team they'd likely see in the Super Bowl (the Ravens or Texans they would have a better shot against).

When a bad team invests in the passing game, however, they either become good, which was the goal in the first place, or stay really bad, which gives them higher draft picks to continue to improve their passing game until they get good. A team like the Broncos is doomed to be like those mediocre NBA teams who are good enough to make the playoffs and miss out on the lottery yet have no chance at the title, making them perpetually mediocre. But a bad team who invests in their passing game ends up like the Colts or Lions, who both dug their way out of the bottom of the barrel in just this way, while teams like the Titans depend on their running game and stay mediocre forever.

In short, the Broncos are making a mistake if they stick with Tebow. They may pull off an upset every once in a while, but they can't expect to win as many close games as they did this year, and will likely end up at around 6-10 next year. The Chiefs, meanwhile, need to get rid of Cassel and Orton and take a risk on either Manning, Stanzi, or some other QB who has a shot at being above average. Sure it may backfire, but it's better than being mediocre.