Building on my previous efforts to devise a better passer rating, and on my analysis of Air Yards, I've created a more complete passer rating formula.
Most fans are familiar with the NFL passer rating, and all its flaws. The formula itself is almost too complex to type out, so I won't bother, but you can find it here. Its shortcomings are also almost too long to list. But here are a few I've mentioned before:
It is incomplete because it does not consider sacks.
It is redundant because it includes both completion percentage and yards per attempt. Because yards per attempt is strongly dependent on completion percentage, it is double counted in the formula.
It is arbitrary because each of the four components are not weighted in any meaningful way. The components of the formula are based on multipliers and constants selected to give the rating a nice scale rather than based on their importance to scoring or winning. They also use arbitrary maximums.
Lastly, it includes touchdown passes. They should not be included in a passer rating because they are the result of many other factors in addition to QB passing proficiency. Factors such as a great defense that produces turnovers in an opponent's territory, a solid running offense that sustains drives, or spectacular recievers who generate large amounts of YAC are strong contributors to passing TDs. Further, TD passes are the culmination of all the other attributes of the passer including accuracy, avoiding interceptions, and avoiding sacks.
This improved QB rating system is primarily based on Air Yards per Attempt. Air Yards is what I call the yardage gained by the pass through the air. It's essentially total passing yards minus YAC. I've learned that YAC is largely independent of passer ability and it should be credited to the receiver more than to the QB.
Sack yards per pass attempt are also included. Although partially dependent on pass protection, sacks are also dependent on a QB's pocket presence, ability to read open receivers, decision-making, and mobility. Pass attempts are defined as throws and sacks.
Interceptions are obviously crucial to a passer's performance as well. I include interception rate (INTs/Att) in the formula.
The components of the new passer rating are weighted according to how important they are in terms of team wins. The formula is based on a multivariate regression model of team wins. Using data from the past five NFL regular seasons, the regression model estimates team wins based on the efficiency stats of each team including passing, running, turnovers, and penalties. Regression models can hold all other factors equal, so by only adjusting the factors of interest (passing performance) we can calculate the effect on the estimate of season wins. Arbitrary weighting is not necessary.
1. Is not arbitrary. Each component is weighted exactly as much as their relative importance to winning games. These weights are derived from a regression model using data from all teams since the 2002 expansion.
2. The result is stated in units of team wins over a 16-game regular season. The regression model allows the passer rating model's component weights to translate directly into how many additional wins a QB's performance would yield, on average, over 16 full games.
3. Is not redundant. The components do not double count passing stats.
4. Includes only the passing stats primarily controlled by the QB. Factors such as passing yards after catch are not included.
After some quick algebra to simplify the equation, the resulting formula of the improved new passer rating is:
QB Wins Added = [(Air Yds - Sack Yds) * 1.56 - INTs * 50.5 ] / Pass Attempts - 3
Basically, every additional yard of passing/sack efficiency yields an additional 1.56 wins on average. That is, assuming an average running game, and an average defense, a team whose passing efficiency is 1 yard/att above average will win 9.56 games.
The average interception rate is about 0.03 interceptions per attempt. So if a QB throws 0.04 INTs/Att, he'll cost his team 0.01 * 50.5 = 0.5 wins, all other factors being equal.
I subtract 3 because 3.01 was the average score of a QB in 2006. Better than average QBs have positive wins added, and vice versa.
The table below ranks the QBs of 2006 in Wins Added:
|Player||Cmp Pct||Yds||AY||YAC||YPA||AY/ Cmp||YAC/ Cmp||AY/ Att||TAY/ Att||Int%||SkYd Rate||YAC%||+Wins|
AY = Air Yards
YAC = Yards after Catch
YPA = Yards per Attempt (sacks not included)
TAY/ATT = 'True' Air Yards per Att (Includes sack data)
SkYdRate = Sack Yards per Attempt (Attempts include sacks)
YAC% = Percentage of passing yards obtained from YAC
+Wins = Wins Added by QB over a 16-game season
Manning tops the list, which should be a surprise to no one. But Romo's numbers are very impressive. Manning beats him by virtue of his low sack and interception rates.
Campbell's numbers are bad news for Redskins fans. Not only is his completion percentage very low, he's also throwing very short passes. His average completion only goes 3.7 yds down field.
Notice how much better Huard fared than Green. They had the same team around them, but Huard distinguished himself thanks to his very low interception rate and his above average down field passing ability.
Perhaps Vick's passing ability will be missed in Atlanta after all. When he does hit his receiver, it's usually for a good chunck of yards.
Rivers appears to be genuinely talented and was not relying on the talent around him to pound out YAC. He was successfully throwing deep in 2006.
There are many more observations that can be made, but if you're like me you look right for where your favorite QB ranks, and then decide if you buy the formula. Next, I'll expand it further to include fumbles and rushing yards.