Variance is a measure of how much the data are scattered about their mean. Usually we want to minimize it as much as possible. A manufacturer of screws wants to minimize the variation in the length of the screws. A restaurant owner doesn't want the taste of the same meal to vary from one day to the next. And they might not know it, but most football coaches choose a low variance strategy when they make 4th down decisions!
For example, take the following situation: It’s 4th and 2 at the 50 yard line. If a coach punts, the other team will most likely start with the ball anywhere between their own 1 and 20 yard line. Using the model for expected points, the coach (if they’re playing on the road) can expect their opponent to score between 0.65 and -0.77 points, depending on how lucky they get with the punt. If the coach goes for it, their expected points will be approximately 2.4 if they convert and -2.9 if they fail.
So one decision has a range of 1.42 expected points and the other has a range of 5.3. The low-variance option is clearly to punt. And coaches are choosing the low-variance option mainly because they want to avoid the worst-case scenario (failing on 4th down and giving their opponent the ball at midfield). They are making choices that minimize their risk.
But what if they wanted to maximize their points instead?
Creating a Cheat Sheet for 4th Down Decisions
Using the model for expected points and the model that calculates the probability of converting on 4th down, I was able to create a simple image that shows the decisions that maximize your expected points on 4th down. If a distance is on or below the line, you should go for it. Any distances above the line should result in a punt or field goal. The following chart assumes a punt nets 40 yards (the Big Ten average last year) until a team gets passed midfield, then it assumes the punt is downed at the 10 yard line.
The statistics say to go for it on 4th and 2 and less, no matter where you are at on the field. As we reach field goal range, there are different decisions depending on whether you’re playing at home or on the road. Home teams should be much more aggressive than road teams, as the numbers say they shouldn't attempt a field goal on 4th and 5 or shorter. And on 4th and goal, teams should be going for it inside the 5 yard line every time, no matter if they are at home or on the road. The reason being that even if you fail, the other team is starting so deep in their own territory that you’re likely to be the next team to score anyway. It’s a win/win!
Now a lot of these decisions favor choosing the high variance strategy. Fourth and 2 on your own 10 yard line? You can imagine what the range of possibilities are there. But it’s important to remember these are just general guidelines, they’re not meant to be written in stone. Some teams should choose the low variance strategy even if it decreases their expected points.
For example, take Ohio State. They will have more talent than almost every team they play. As Virginia Tech found out earlier this week, you may be able to keep it close for a while, but sooner or later the talent gap will be too much to overcome. For a team to beat Ohio State, they’re going to need some lucky breaks. Something like Ohio State failing on 4th down multiple times deep in their own territory. So if you’re the Buckeyes (or any heavily favored team), when you’re deep in your own territory, the best decision is to choose the low-variance strategy and punt. If you avoid giving your opponent easy opportunities to score, odds are your talent alone will be enough to get you the win.
But the opposite is true if you’re a heavy underdog. Then, you should actually be more aggressive than the previous chart suggests. Your best chance of pulling an upset is to hope you get lucky converting a majority of your 4th downs. Of course, this also gives you the best chance of being blown out. But if you’re not likely to win playing conventionally anyway, what do you have to lose?
Indiana Hoosiers, are you listening?
The Indiana football program has had a pretty rough go of it. And that’s putting it mildly. Their last Big Ten Championship was in 1967. The last time they won a bowl game was 1991, and they’ve had exactly two winning seasons since then (both resulting in bowl losses). Clearly, playing conventionally hasn’t gotten Indiana very far. Perhaps it's time for Indiana to adopt a new strategy. Let's dig deeper.
The past 5 seasons, here is where the Indiana defense has ranked in football outsiders S&P+ ratings:
And things don’t seem to be turning around this season. In week 1 Indiana gave up 47 points to Southern Illinois, a FCS team that went 6-6 a season ago. Southern Illinois had 411 yards passing, another 248 yards rushing, and had 5 different touchdown drives of 72 yards or more. What exactly is the point of punting if the other team can score from anywhere on the field?
The lone bright spot for Indiana is their quarterback, Nate Sudfeld. With Sudfeld at the helm in 2013, Indiana had the 16th best offense according to the football outsiders S&P+ ratings. He completed only five games last year before his season was ended by an injury. But this season he’s back for his senior year, ready to lead what should be an above average Indiana offense.
So let’s recap. A defense that is so bad, teams will be able to score on it no matter where they start with the ball. An offense led by a senior who previously quarterbacked one of the top offenses in the country. And a history of losing trying to play the same way the rest of the Big Ten plays. It only leaves one more thing to say.
Hey Indiana, stop punting!