Quarterback Rating

The NFL has a QB rating, a composite statistic that combines yards, pass attempts, completions, touchdowns, and interceptions. Unfortunately, it's kinda arbitrary. In an effort to fix that I present an estimated points added statistic, which includes all of the above.

The basis for EPA is that at any given point on the field a team has an average number of points they'll get. At their own 20, it's about 0, at their opponent's 20 it's around 4 (for first and 10). 15 yards adds about a point. A turnover at the line of scrimmage is then -4 points (so -3 for a 15 yard interception). Similar values can be obtained for the other achievements. Here's the components:

One yard: 1/15

Interception: -3

Touchdown: 3

Attempt: -2/5

Completion percentage-60 (average): completions/150

It doesn't make total sense at first, but the results do. Here they are:

Player	EPA	PPG	Wins
Philip Rivers	160.54	10.7	4.01
Tom Brady	158.89	10.6	3.97
Aaron Rodgers	129.14	9.23	3.23
Drew Brees	104.64	6.98	2.62
Michael Vick	101.44	8.47	2.54
Peyton Manning	100.3	6.69	2.51
Matt Cassel	99.6	7.1	2.49
Joe Flacco	97.22	6.48	2.43
Matt Schaub	93.38	6.21	2.33
Josh Freeman	85.41	5.69	2.14
Ben Roethlisberger	79.82	7.24	2
Jay Cutler	78.63	5.62	1.97
Kyle Orton	74.99	5.77	1.87
Matt Ryan	71.58	4.77	1.79
Eli Manning	71.25	4.76	1.78
David Garrard	66.95	4.77	1.67
Carson Palmer	51.13	3.4	1.28
Jon Kitna	50.41	5.05	1.26
Ryan Fitzpatrick	43.86	3.38	1.1
Tony Romo	43.17	7.21	1.08
Jason Campbell	37.89	3.16	0.95
Donovan McNabb	30.22	2.33	0.76
Shaun Hill	24.14	2.42	0.6
Chad Henne	21.06	1.51	0.53
Alex Smith	20.9	2.09	0.52
Mark Sanchez	18.96	1.26	0.47
Sam Bradford	15.32	1.02	0.38
Kerry Collins	13.71	1.52	0.34
Matt Hasselbeck	7.29	0.52	0.18
Brett Favre	0.93	0.07	0.02
Derek Anderson	-11.48	-0.96	-0.29
Jimmy Clausen	-40.12	-3.35	-1

The best quarterbacks in the NFL are right at the top, as they should be. The PPG column accounts for some quarterbacks (Vick, Romo) not playing all their games. Most useful though is the wins column, which divides EPA by 40 (as shown earlier in the week) to get the expected wins added by a player over a replacement quarterback. For example, with his 4 wins added Tom Brady has taken the Patriots from the border of the playoffs to being the best team in football. Sounds like an MVP to me.