Big Play Margin

How often have you heard, “the team that forces more turnovers will be the team that wins this game”?

Now how often have you heard, “the team that makes more big plays from scrimmage will be the team that wins this game”?

I haven’t kept an official tally, but I’d guess that the first assertion is made more often than the second. In fact, my impression is that when big plays are mentioned, it’s big plays on special teams that get more attention than big plays from scrimmage. It could be that people don’t mention big plays from scrimmage because it’s assumed that they’re important. Or it could be that people really believe that turnovers are more important.

I find this interesting becuase in many situations, a big play from scrimmage is exactly analagous to a turnover. If your running back rips off a 40-yard gain on 3rd-and-2, that’s the same result as if he had been stuffed, you punted, and then your defense forced a turnover on the next play. And we’ve all seen those interceptions 45 yards downfield that are the same as a punt. Granted, those are contrived examples and the correspondence isn’t always so clean, but it seems reasonable — at least to me — that the value of a big play from scrimmage is roughly comparable to the value of a turnover. Some theoretical evidence for this position can be found in The Hidden Game of Football, where the authors conclude that a turnover is, on average, worth about 40 yards of field position.

I decided to see how this plays out in practice. So I ran a regression with team wins as the output, and turnover margin and big play margin as the inputs. I defined a big play as any play from scrimmage that gained 30 or more yards. I didn’t include big plays on special teams simply because I don’t have that data in an easily-accessible format. This is based on data from 2003–2005. Here are the results:

Estimated Team Wins = 8 + .165 * (TurnoverMargin) + .163 * (BigPlayMargin)

What this says is that, over the course of a season, an increase of one in turnover margin will add about .165 to your win total, while an additional big play from scrimmage is worth .163 wins. To put it in less absurd terms, you can expect to gain an extra win in a 16-game season by forcing six extra turnovers. Or by allowing six fewer.

If you found the discussion above convincing, you shouldn’t be surprised to see that the two coefficients are so close. A big play is about as valuable as a turnover; no more, no less.

Or is it? It could be that big plays aren’t important at all. It could be that big plays are simply the byproduct of good offenses (and prevention of big plays is the byproduct of a good defense). In other words, it could be that good teams have good big play margins and good teams win games, but that big plays are incidental to the process. To check for this, I included the teams’ season yardage margin: total yards gained minus total yards allowed.

Estimated Team Wins = 8 + .163 * (TurnoverMargin) + .070 * (BigPlayMargin) + .0017 (YardageMargin)

The important thing to note here is that the BigPlayMargin coefficient is significant. That says that big plays do matter, even over and above the yardage they provide. A 50-yard play adds 50*.0017 + .070 = .155 to the win column, almost the same as a turnover.

3 Responses “Big Play Margin”

  1. jason says:

    Your formulas do not appear to be consistent…

    .070 * (BigPlayMargin) + .0017 (YardageMargin)

    A 50-yard play adds 50*.0017 + .070

  2. Aaron says:

    I don’t see how that’s not consistent. YardageMargin=50 and since 50>30, BigPlayMargin=1.

    I was wondering if a linear model is necessarily the best for something like this. It seems like 30 yards is an arbitrary cutoff and that, in general, the effect might be more continuous and less binary. Like there might be a more descriptive function for the marginal effect of additional yardage in a given play.

    Did you ever think of running different cutoffs, seeing how the coefficients varied with each mark? Like maybe in seeing how the BigPlayMargin and YardageMargin coefficients move with cutoffs of 20, 30, 40, etc. we could get an idea of the marginal impact of each additional big play yard.

    If, for example, 30 yard plays are twice as important as 20 yard plays and 40 yard plays are twice as important as 30 yard plays, we could be looking at some kind of exponential effect.

  3. jason says:

    I see why I’m confused, the formula isn’t written in the same order. The bold lettering is
    while the example is

    Same formula, just written differently.