Friday, March 9, 2007

Passer ratings?

Most football fans pay attention to statistics, at least a little bit. Some statistics are very basic and understandable even by a novice. Others are a lot more complex and obscure. Some positions (offensive line) have no real statistics to gauge performance. Most of the stats you see are of the simple variety. It's pretty easy to know what "yards" means when talking about a running back. It's pretty easy to know what "completion percentage" means when talking about a quarterback. The "passer rating" falls into the opposite category.

How many times have you seen "passer rating" or "quarterback rating" discussed or mentioned? You've probably heard it quite a lot. How many times has anyone in the media actually explained what it is? Personally, I can't swear I've ever heard a television talking head actually discuss how passer rating is formulated. I don't understand why this is so, but I am here to educate you about it.

College and pro football each have their own ratings, and you can't really compare the numbers to each other. I'll focus on college. For college football, here is the formula for passer rating:
(100*Completions/attempts) + (8.4*yards/attempts) + (330*Touchdowns/attempts) - (200*Interceptions/attempt) = Passer rating
That clears it all up for you, doesn't it? Well, let's do some algebra and go a little deeper. If you do some factoring, here's what it comes down to:
8.4*(Yards passing + 11.9*Completions + 39.3*Touchdowns - 23.8*Interceptions)/(Number of attempts) = Passer Rating
I think this is a much more useful way to show it. It shows the rating for what it is. It's a measure of yards per pass attempt, with certain bonuses and penalties. There is a 39.3 yard bonus for throwing a touchdown, a 23.8 yard penalty for throwing an interception, plus a weird 11.9 yard bonus every time the ball doesn't fall incomplete. All of that is then multiplied by 8.4, apparently for no other reason than to multiply by some arbitrary number.

Part of this makes a lot of sense. Yards per attempt has a pretty clear meaning to a quarterback, and I think everyone can grasp its importance in evaluating a player. Likewise, the number of touchdowns and the number of interceptions a player throws are also extremely important.

There are a number of weaknesses in this statistic, however. The most important weakness is that it does not reward a quarterback for escaping the rush and gaining yards on the ground, a key part of many modern quarterbacks' games. Consider the following scenario:
Quarterback drops back to pass. The defense gets a good rush and the quarterback escapes out of the pocket. He continues looking for his receivers, but the receivers aren't getting open and the QB will be sacked if he doesn't do something. Should he a) stand there and take a sack, or b) try to get out of the pocket and run for positive yardage? Assume that playclock effects are not important at this stage of the game.
Any good quarterback will try to run for it and get whatever he can get. Some will be better at it than others. However, the passer rating will not reflect these differences. As far as the passer rating is concerned, the quarterback who runs for an electrifying 50 yard touchdown will get the same result as the one who trips over his own feet in the backfield.

This problem can and should be fixed by taking out the "yards per attempt" and using instead a "yards per designed pass play", which would include passing yards as well as yards gained or lost on the ground, with the number of attempts changed to include all times the quarterback drops back to pass. Go ahead and count rushing touchdowns among the number of touchdowns as well.

Another weakness is that second term. I don't understand the second term, which seems to reward a quarterback simply for completing a pass, even if the pass made no yardage, or even lost yardage. Consider the above scenario, but changed in this way:
Quarterback drops back to pass. The pocket collapses before the receivers break open. The quarterback is surrounded, unable to escape the pocket. Should he a) stand there and take a sack, or b) throw the ball away? Assume that playclock effects are not important at this stage of the game.
While no quarterback will simply take the sack in this situation if he has a choice, his Passer Rating will suffer for his decision to throw it away, because it will increase his number of pass attempts. In that scenario, your passer rating will stay the same if you simply take the sack. In fact, you can actually improve your passer rating by throwing a completed pass that loses yards, so long as it loses less than 11.9 yards.

I'm not suggesting that a quarterback, mindful of his "rating", will deliberately take an action that will hurt his team. I am merely saying that in this common situation, where a player has two choices, the primary statistic that gauges his performance will actually suffer if he makes the correct choice. That, to me, is a serious deficiency in the quarterback rating, and renders it almost unusable.

I would recommend removing this term and instead have a term that gives a quarterback a bonus not for simply completing a pass, but for gaining a first down. After all, it's a lot better to get 11 yards on 3rd-and-10 than it is to get 9, but your passer rating will hardly notice the difference.

Lastly, I don't like the magnitudes of the bonuses. Is a touchdown really worth the same as a 39 yard pass? Is an interception the equivalent of 24 yards lost? I don't buy it. For one, it means that a quarterback who throws almost twice as many interceptions as he does touchdowns is about as good a quarterback as one who throws none of either. Of course, you'll be hard-pressed to find a quarterback who throws neither touchdowns nor interceptions, but it implies a quarterback who throws 1.65 interceptions for every touchdown pass is statistically "neutral". And here I was thinking that Rex Grossman's 23 touchdowns and 20 interceptions last year was bad. Shows you what I know; his passer rating was helped more by the touchdowns than it was hurt by the interceptions. A lot more.

When you hear about Passer Ratings, realize that it is a measure of yards per pass attempt, with a 40 yard bonus for touchdowns and a 24 yard penalty for interceptions, plus another factor that makes little sense, all multiplied by an arbitrary number. Realize also that it fails to reward quarterbacks who help their teams through running out of trouble. Realize further that it actually penalizes a quarterback for throwing the ball away to avoid a sack, and artificially puffs up a quarterback who throws a lot of short completions. I don't like it as a measure of quarterbacks.

I prefer giving the quarterback a 20 yard bonus for a touchdown, and a 30 yard penalty for an interception. It means that a QB who has a 1.5:1 touchdown to interception ratio is statistically neutral in that regard, and I think it more accurately reflects the field position lost be a typical interception. And while we're at it, let's count the times a quarterback loses a fumble the same way we'd count an interception. It just makes sense.

Here's the formula I would use (I'll take out the 8.4 factor just on principle):
Passer Rating = (yards passing + yards rushing - yards lost by sack + 5*First down completions and runs + 20*Number of Touchdowns - 30*Number of Turnovers)/(Number of called pass plays).
My formula ha the features I talked about, plus it gives a 5 yard bonus for making a first down. After all, a pass that goes for 11 yards on 3rd-and-10 is much better than a pass that goes for 9 yards, but the conventional passer rating will hardly notice the difference.

It all makes so much more sense to me to use this measure than it does to use the traditional Passer Rating, but it isn't going to happen. This formula isn't even particularly useful to me because they don't keep track of 1st down throws (and runs). I can't compile these numbers even for my own benefit. I can, however, use it if I take out the 1st-down bonus, leaving the following formula:
Passer Rating = (yards passing + yards rushing - yards lost by sack + 20*Number of Touchdowns - 30*Number of Turnovers)/(Number of called pass plays).

Next time, we start compiling some numbers.


Anonymous said...

Very interesting. I would not have known that, probably because I wouldn't have done the research.


Anonymous said...

I must say that I'm impressed by the analyses on the blog, but I'm even more impressed that you can eek out time to formulate them. Cudeaux's to the author.


Anonymous said...

Por que no:)