Passer Rating Explained

One of football's least understood metrics is the Passer Rating. It's an attempt by the statisticians to quantify a quarterback's performance, but how does it work? What does it take into account? Why the hell is the maximum rating 158.3? Given the evolution of the position, is it really a good measure of a quarterback's ability?

The QB's passer rating looks at four elements: completions, yards, interceptions, and touchdowns, all on a per completion basis. It does not include fumbles, sacks, or any type of rushing statistics. The maximum rating is 158.3 as opposed to a more logical 100.

The first element, Completions, "C" uses the formula: C = (COMP/ATT * 100 - 30)/20.
The third element, Interceptions: I = 2.375 - (INT/ATT * 25)
The fourth element, Touchdowns: T = TD/ATT * 20
The second element, Yards: Y = (YDS/ATT - 3)/4

The maximum possible value for each category is 2.375 and the minimum is 0; if COMP/ATT = .8, then C = 2.5. Since the maximum is 2.375, C equals 2.375, not 2.5. If COMP/ATT = .2 then C = -0.5. Since them minimum is 0, C equals 0. If COMP/ATT = .6 then C = 1.33. Finally, plug the values into the formula: (C+I+T+Y)/6 * 100. The result is the passer rating.

Using Tony Romo as an example, from the heartbreaking DAL-ARI game, we see that Romo had 24 completions, 38 attempts, 321 yards, 3 touchdowns, and 0 interceptions.

Therefore:
C = (24/38 * 100 - 30)/20
C = 1.66

I = 2.375 - (0/38 *25)
I = 2.375

T = 3/38 * 20
T = 1.58

Y = (321/38 - 3)/4
Y = 1.36

Rating = (1.66+2.375+1.58+1.36)/6 * 100
Romo's Rating = 116.2

That wasn't too tough.

The passer rating was developed by Don Smith and was first used in the 1973 season. Smith was a statistician and executive with the Pro Football Hall of Fame.1 The odd 158.3 limit came about when he decided that the average QB rating should be 66.6. That was pretty close to reality back in '73 when the average passer rating was 64.7, but last year, in '07, the average passer rating was 82.5, an increase of 28% over the decades. The idea behind his calculations was that he wanted a way to compare all QB's to the average QB at the time. Perhaps Smith's rating made sense 35 years ago when the numbers he used to calibrate the formulae were relevent, though obviously circumstances have changed since then. Completion % has gone from 51% to 61%, yards per game from 140 to 214, TD's from 1.0 to 1.4, etc.

That's a basic overview of passer rating. Once you get through the numbers, it starts to make sense. From now on when your buddies complain about that ridiculous stat, impress them with your knowledge of C.I.T.Y (comp, int, td, yds).

For you stats-minded people out there, maybe this gives you some ideas on how to make a modern formula that makes sense. When you do make one, post it for some peer review, it will be interesting to see what everyone can think up. I'm working on a formula of my own now, so stay tuned.


1. www.baseball-statistics.com/Greats/Century/passer-rating.htm