## Checkdowns: Adjusted Net Yards per Attempt “FIP” for Quarterbacks

I’ve been on a major QB kick lately, and there’s no reason to stop now. Today, I want to look at a method that might tease out a quarterback’s “true talent” better than if we simply use his raw stats from the season.

Three years ago, our colleague Jason Lisk had a post on the old PFR Blog about which rate stats stay consistent when a QB changes teams. Basically, he grabbed QBs who were still in their primes and changed teams, looking at how their key rate stats correlated from one year to the next. Here’s what Jason found:

[…]I looked at the correlation coefficient for our group of 48 passers, for the year N advanced passing score compared to the year N+1 advanced passing score in each category. This should tell us whether the passers who were good in a performance area (or bad) tended to be the ones who remained good in that performance area the following season, even with the uncertainty of team changes (some positive, some negative for the quarterback).

```Sack Percentage:  0.31
Completion Percentage: 0.25
Yards Per Attempt:  0.20
Touchdown Percentage: 0.12
Interception Percentage: 0.10
```

What do those correlations mean, exactly? Well, take sack percentage as an example. In general, a correlation of 0.31 means you can expect 31% of a QB’s difference from the mean to be repeated next year when he changes teams. In other words, you have to regress the QB’s sack rate 69% towards the mean to get the true rate that “belongs” to him. If the average sack rate is 6.1%, and a QB has a rate of 4.0% (like, say, Drew Brees this year), his “true” sack rate is probably something like 5.4% — 31% of the distance between .061 and .040.

The same concept applies to the other stats listed above. Tony Romo’s observed 66.7% completion percentage is really more like 62.5% after regressing to the mean, and so forth. Do that for every QB who had a reasonable number of attempts this year, and you get these rate stats:

PlayerTmGGSAttA-Sk%A-Cmp%A-YPAA-TD%A-INT%R-Sk%R-Cmp%R-YPAR-TD%R-INT%
Matthew StaffordDET14146294.359.56.82.72.45.560.77.04.02.6
Drew BreesNOR14145744.062.07.66.33.15.461.47.24.52.7
Tony RomoDAL14145685.366.77.53.92.85.962.57.24.22.7
Andrew LuckIND14135646.254.67.13.53.26.159.57.14.12.7
Carson PalmerOAK14145624.460.97.13.92.55.661.17.14.22.6
Matt RyanATL14145394.468.57.85.02.65.663.07.24.32.7
Peyton ManningDEN14145113.967.97.96.12.05.462.87.24.42.6
Brandon WeedenCLE14144985.057.26.62.83.45.760.27.04.02.7
Joe FlaccoBAL14144876.559.17.14.12.16.260.77.14.22.6
Eli ManningNYG14144873.060.47.44.13.15.161.07.14.22.7
Matt SchaubHOU14134764.064.77.54.62.15.562.07.24.32.6
Aaron RodgersGNB14144748.766.77.66.81.76.962.57.24.52.6
Andy DaltonCIN14144727.562.57.05.53.06.561.57.14.42.7
Josh FreemanTAM14144694.354.87.45.32.65.559.67.14.32.7
Ryan FitzpatrickBUF14134445.961.76.65.03.46.061.37.04.32.7
Christian PonderMIN14144256.663.15.93.32.86.261.66.94.12.7
Ryan TannehillMIA14144245.858.76.92.42.86.060.57.04.02.7
Cam NewtonCAR14144237.258.28.24.32.46.460.47.34.22.6
Mark SanchezNYJ14144187.354.86.43.14.16.559.66.94.12.8
Ben RoethlisbergerPIT11113985.764.17.35.51.56.061.97.14.42.6
Jay CutlerCHI13133778.559.77.04.53.76.860.87.14.22.8
Russell WilsonSEA14143536.962.97.65.92.56.361.67.24.42.7
Robert Griffin IIIWAS13133517.466.48.35.11.16.562.57.34.32.5
Michael VickPHI993167.958.56.93.52.86.660.57.04.12.7
Blaine GabbertJAX10102787.358.36.03.22.26.560.46.94.12.6
Matt CasselKAN982776.458.16.52.24.36.260.47.04.02.8
Jake LockerTEN992695.657.67.03.33.35.960.37.14.12.7
Matt HasselbeckTEN852216.062.46.23.22.36.161.56.94.12.6
Nick FolesPHI652176.559.46.22.31.86.260.76.94.02.6
Alex SmithSFO9921710.070.08.06.02.37.363.47.34.42.6
John SkeltonARI762016.954.25.61.04.56.459.46.83.82.8
Kevin KolbARI6518312.959.66.44.41.68.260.86.94.22.6
Colin KaepernickSFO1151548.365.68.44.51.36.862.37.34.32.5
Ryan LindleyARI631416.651.14.30.04.36.358.66.53.72.8

(“A-” before a stat means the actual observed rate; “R-” means the regressed rate.)

Now we just need to reconstruct the player’s raw passing line as though he posted those rate stats instead of his actual rates. Cmp%, YPA, TD%, and INT% are easy (just multiply by attempts), and Sack% can be derived via simple algebra:

Sacks_new = (-reg_sk% * Attempts) / (reg_sk% – 1)

(Sack yards can be assumed by multiplying raw sack yards per sack by the new sack total.)

Finally, we plug the new totals into the Adjusted Net Yards Per Attempt formula, and we have a QB stat that is sort of like baseball’s Fielding Independent Pitching (FIP), which also seeks to reduce the noise and teammate interactions in a pitcher’s ERA by reducing his performance to only those elements he has control over — strikeouts, walks, and home runs.

Here are the 2012 leaders in QB-FIP (along with their regressed totals):

RkPlayerAgeTmGGSCmpAttYdsTDIntSkSkYdsQB-FIP
1Peyton Manning36DEN141432151136972313291916.22
3Robert Griffin III22WAS13132193512568159241666.15
4Colin Kaepernick25SFO1159615411307411766.11
5Ben Roethlisberger30PIT111124639828361710251416.11
6Matt Ryan27ATL141433953938932314322256.11
7Eli Manning31NYG141429748734762013261656.09
8Drew Brees33NOR141435257441182616332376.08
9Josh Freeman24TAM141427946933502012271816.08
10Aaron Rodgers29GNB141429647434022112351976.06
11Cam Newton23CAR141425642330861811292036.05
12Russell Wilson24SEA14142173532539169241486.05
13Alex Smith28SFO99138217157510617976.04
14Matt Schaub31HOU141329547634072012272286.01
15Tony Romo32DAL141435556840712415352555.97
16Andy Dalton25CIN141429047233362113331765.94
17Joe Flacco27BAL141429548734532013322095.93
18Carson Palmer33OAK141434356239802315332545.92
19Ryan Fitzpatrick30BUF141327244431011912291515.89
20Andrew Luck23IND141333656439902315372305.89
21Matthew Stafford24DET141438262944132517372565.88
22Jake Locker24TEN991622691900117171085.88
23Michael Vick32PHI991913162223138221245.84
25Brandon Weeden29CLE141430049834772014301985.80
26Ryan Tannehill24MIA141425742429871711272055.78
28Philip Rivers31SDG141430248834222113352215.77
29Matt Cassel30KAN98167277192811818975.75
30Jay Cutler29CHI131322937726611610281875.74
31Christian Ponder24MIN141426242529121711281645.70
32Nick Foles23PHI65132217150096141025.70
33Matt Hasselbeck37TEN85136221152596141055.70
34Mark Sanchez26NYJ141424941829031712291785.68
35Blaine Gabbert23JAX10101682781907117191385.61
36Kevin Kolb28ARI6511118312708516965.61