http://www.bookofhook.com/Article/Football/RevisitingtheQBRating.html
Revisiting the QB Rating
Tuesday, December 23, 2003
According to the NFL, the
official QB rating formula is as follows:
max( min( ( completion % - 30 ) x 0.05, 2.375 ), 0 ) +
max( min( ( yards/attempt - 3 ) x 0.25, 2.375 ), 0 ) +
min( TD% x 0.2, 2.375 ) +
max( 2.375 - INT% x 0.25, 0 )
Take the above, divide by six and multiply by 100.
Hmmmm, how do I feel about this? Tphtphtphthtt. It's crap. It's a bunch of minutiae that doesn't tell the whole story. What about sacks? Does the QB hold the ball too long? Does he fumble a lot? Does he choke on third down? According to the NFL, right now Vinny Testaverde is the 6th rated passer in the league -- but you think the Jets don't want Pennington in there? Hidden stat #1: Pennington has twice the number of TDs per attempt inside the opponent red zone over Vinny. Hidden stat #2: Pennington converts on third down on 44.4% of his attempts, whereas Vinny does so on 34% of his attempts. Other than those two stats, Vinny is technically the better QB (higher completion percentage, fewer picks).
How could we improve this? Well, the first, and most obvious approach (in fact, the one I felt was going to be the right one) is to sit down and factor in yet more variables, including fumbles, fumbles lost, sacks, third down conversion and red zone TD%. But then you just have an equation with a ton of variables and a lot of people arguing about the relative merit of each stat.
In the end, though, what everyone asks is "Is he a winner?" Now, that's a bit vague, and it doesn't take into account a team's defense and QBs that win despite their best attempts to screw things up. So what we really want to know are two things: does a QB put up points, and does he throw a lot to get those points? Of course, we also want to make sure that we factor in the number of opportunities he gets -- QBs that benefit from turn-over heavy defenses shouldn't automatically rank higher.
The two criteria then really boil down to points per possession and passing yards per possession. These two values give a gestalt view of a quarterback's capabilities without getting down into microscopic and subjective details. Interceptions and lost fumbles are automatically factored by making a possession worth zero points. Third-down conversions do likewise. A QB that can get into the end zone is going to have a higher scoring average than one that settles for field goals. And a QB on a run oriented team, or who starts with consistently good field position, may still score a lot of points per possession, but will be affected by a reduced passing yards/possession (look at Anthony Wright's stats).
The only other major item I could see factoring is opposing points allowed due to turnover, e.g. an interception or fumble return for touchdown. There is also a slight problem when a possession has very little time associated with it, such as at the end of a half or end of the game.
Just to test out my theory, I went back and looked at the Week 16 games of 2003 and computed the Hook Quarterback Value. I also threw in some of the best and worst games of the season I could find (nothing comprehensive, for this to be 100% accurate/valid I'd need full stats). I normalized the passing yards/possession and points/possession against their average values (averages were slightly biased because of the very strong out-of-week values introduced), and then combined the two with a 60% weight towards points and a 40% weight towards yards. I also clamped max points/possession at 4, since beyond that the delta between 4.5 and everything else is so high that the rest of the range compresses, and for someone with a huge scoring day because of an RB (i.e. Plummer vs. Indy when Portis did a good chunk of the work), it skews it too much in his favor. Suffice to say, that if you're doing 4 points or more per possession, you're pretty much in stratospheric levels. These are my results:
Player Hook Rating NFL Rating Yards Points Yards/Poss Points/Poss Poss Green vs. DET 95.89 158.3 341 45 34.1 4.5 10 Manning vs. NO 87.54 158.3 314 48 26.17 4 12 Favre 86.25 154.9 399 41 33.25 3.42 12 Plummer vs. KC 85.05 105.2 238 45 23.8 4.5 10 Bulger vs. MINN 83.37 106.7 222 41 22.2 4.1 10 McNair vs. HOU 82.27 146.8 421 31 38.27 2.82 11 Culpepper 79.06 117 260 45 21.67 3.75 12 B. Johnson 71.29 84.2 346 28 31.45 2.55 11 Bulger 64.61 86.4 229 27 22.9 2.7 10 Plummer 64.28 113.8 230 31 20.91 2.82 11 Maddox 56.54 129.6 160 34 13.33 2.83 12 McNabb 55.88 72.8 238 28 19.83 2.33 12 Grossman 55.59 91.8 249 27 20.75 2.25 12 Brooks 54.23 100.3 296 19 26.91 1.73 11 Garcia 50.13 100.5 225 31 16.07 2.21 14 Q. Carter 48.88 112.1 240 19 21.82 1.73 11 T. Hasselbeck 48.33 116.9 209 24 17.42 2 12 Delhomme 47.81 104.8 260 20 21.67 1.67 12 Vick 47.03 119.2 119 23 11.9 2.3 10 T. Green 44.65 44.2 224 20 18.67 1.67 12 Leftwich 43.79 58.3 131 20 13.1 2 10 Wright 42.89 64.6 90 28 7.5 2.33 12 McNair 41.58 79.4 268 20 19.14 1.43 14 Pennington 40.09 31.2 229 16 19.08 1.33 12 Carr 39.21 58.7 242 17 18.62 1.31 13 M.Hasselbeck 38.72 88.7 179 21 13.77 1.62 13 Manning 37.96 72 146 10 18.25 1.25 8 Kitna 36.26 49 202 10 20.2 1 10 McCown 33.72 91 274 10 21.08 0.77 13 Brooks vs. TB 29.63 101.2 238 7 19.83 0.58 12 T. Brady 29.61 101.8 138 14 11.5 1.17 12 Bledsoe vs. NYJ 23.42 62.7 202 3 18.36 0.27 11 Testaverde vs. DAL 23.05 93.9 219 0 21.9 0 10 Palmer 22.27 73.7 190 3 17.27 0.27 11 Fiedler 20.29 48.9 46 13 3.83 1.08 12 Carter vs. NE 18.42 38 210 0 17.5 0 12 Carter vs. TB 13.4 42.1 140 0 12.73 0 11 Bledsoe 12.69 36.2 114 3 8.77 0.23 13 Couch 12.26 53 163 0 11.64 0 14 Ragone vs. JAX 5.75 36.7 71 0 5.46 0 13 T. Hasselbeck vs.DAL 4.53 0 56 0 4.31 0 13 Fiedler vs. NE 2.18 25.1 31 0 2.07 0 15
AVERAGE 44.77
209.5 19.57 18.31 1.73 11.69
At a high level, quarterbacks that score well with NFL QB Rating also tend to do well with mine, but there are notable -- and important -- exceptions. Note: arguing about the relative jockeying of two QBs close to each other (within, say, 5 points of HQV) is kind of pointless and subjective. I'm trying to make sure we get the sweeping generalizations correct, whcih I feel the NFL QB Rating does not.
The most striking difference is Aaron Brooks vs. Tampa Bay, where his NFL QB Rating was an impressive 101.0, but his HQV was a fairly abysmal 29.63. HQV implicitly takes into account Brooks's four lost fumbles in that game, which in turn manifested as lower points per possession. When he did throw, sure, he was good, but he was screwing up too much elsewhere to be considered a good QB.
Also of note is Tom Brady's NFL QB Rating of 101.8 vs. his HQV of 29.61. Even though he was efficient when he did throw, he simply wasn't scoring very many points when he had the opportunity. He benefited from good field position -- he traveled a total of 95 combined yards for both his touchdowns -- and took advantage of the running game. So sure, he won, but he didn't really have to earn it too much. On his first TD drive, it was a single pass for 35 yards. On his second TD drive, over half the yards were from the running game. The rest of his possessions ended in zero points.
On the flip side, there were several instances of players with poor NFL QB Ratings that scored relatively well on the HQV. Brad Johnson had an NFL rating of 84.2 but an HQV of 71.29. His NFL rating is hurt by four interceptions, but amazingly enough he still manages to score around 50% more points/possession than the average. He also has a monstrous 31.45 passing yards/possession, which means that he was consistently the prime mover in that offense and dealing with poor field position -- his average TD drive was over 70 yards and he accounted for 78.6% of his team's offense. And that is why he rates well ahead of Vick in the same game, even though Vick had a 119.0 NFL Rating.
Another climber is McNabb, whose pedestrian 72.8 NFL QB rating doesn't really demonstrate how much value he provided to his team. While his HQV is only above average (55.88), it's still considerably better than eight other quarterbacks with 100+ NFL QB ratings. Once again, the reason is pretty simple --he had a higher than average passing yards/possession, and a significantly higher points/possession than, say, Tom Brady that same day.
When you look at Green's performance against Detroit, it's just mind boggling. It's better than Favre's performance against Oakland and Manning's against New Orleans, both of which stand out as some of the best of the year. Yet Green threw for more yards per possession and scored more points per possession than either of those two.
McNair's performance against Houston was awe inspiring because of the sheer number of bombs that were thrown, but while he had the most dominant passing yards/possession, he didn't score nearly as well per possession as some of the other notable performances.
Plummer was a scoring machine against KC, and while people might say that performance shouldn't be ranked so high because Portis did all the work, the numbers actually indicate otherwise -- Plummer was still averaging 23.8 passing yards per possession, well above average. Not only that, but Plummer was the key contributor on many drives. On the first touchdown drive he contributed 29 of the 74 yards, and Portis contributed 18 yards. On their second TD drive Plummer was responsible for all three first down conversions. On their third TD drive Plummer was responsible for 2 out of 4 of their first down conversions, and also threw into the end zone for their TD. The fourth TD drive was all Portis. The fifth TD drive had Plummer getting a first down twice, and Portis converting once and getting the 28 yard TD run. The sixth TD was all Portis again. The field goal was Plummer with 44 yards passing and Portis -2 rushing (but 30 of the pass yards were to Portis).
The point here isn't that Plummer was more important than Portis, it's too illustrate that even on a day when it looks like the running back may have done all the work, it's often misleading -- in this case, Portis was directly responsible for 14 points, but even if you take those away, Plummer
still has an amazing 3.1 points/possession. Without Plummer, they likely would not have made several key first downs that sustained drives. The HQV demonstrates this pretty vividly (as compared to Anthony Wright's HQV, where even though he scored quite a bit, he benefited heavily from field position and a running game).
I like Vick's ranking. His passing numbers were rather mediocre, but he was still able to get 2.3 points per possession, well above average, and that puts him squarely "average" as a QB, which is probably about right for that day's work.
A lot of arguments can be had when dealing with quarterbacks that are rated near each other, but that's missing the point. The important thing, to me, is allowing the guys that carry a team on their shoulder to show up, and efficient guys that aren't scoring points ("dinkers") to get exposed for what they are. I can go either way as to who had the truly worse day -- Brooks vs. TB or Brady vs. NYJ, but the fact remains that they have nearly identical HQVs but for different reasons (Brady scored more points, Brooks had to throw for more yards).
With this system, scoring points matters a lot, and they don't have to be TDs. Yardage is still important, but that's mostly judging you as a passer, not your intangibles. Because of the bias towards scoring, Maddox ranks higher than McNair this week even though he had over 100 fewer yards passing, but that is as it should be in my opinion.