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For more from Chase and Jason, check out their work at Football Perspective and The Big Lead.
What quarterback rate stats stay most consistent when a quarterback changes teams?
What happens when a quarterback changes teams? Which performance stats remain most consistent, suggesting they are more the responsibility of the quarterback himself, and which are least consistent, suggesting that outside forces (such as teammates, game situation, and random luck) play a larger role?
To examine this, I took all quarterbacks since the merger, between ages 25 and 35, who threw 14 or more attempts per team game in consecutive seasons, but did so for a different team in year two. The result was 48 different quarterback seasons (a handful of players appear on the list more than once). I examined the five basic performance rate stats: yards per attempt, completion percentage, touchdown percentage, interception percentage, and sack percentage. Other stats, such as passer rating or net adjusted yards per attempt, are derivative stats that rely on some combination of these underlying performance measures. Oh, and I used the advanced passing ranking in those five categories, rather than the raw rate stats, to avoid any era bias affecting the results, and to be able to compare between statistics (so we can compare a change of 5% in completion percentage to a 2% drop in sack rate).
I've tried to look at the data from several different angles. First, 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
Sack percentage checks out on top, primarily because those quarterbacks who were good at avoiding sacks tended to remain good at avoiding sacks. Of the top 21 in sack rate in year N (the top 20 and ties), 17 of them were above average in sack rate the following year on a different team. This probably understates the difference, because consider that we have three relatively rare event stats (sacks, touchdowns, and interceptions) that each occur infrequently. Even the most careless type typically throws an interception on about 3% more of the passes than his counterparts (over a large season sample) and the most prolific touchdown passer is only a few percentage points above league average. On the other hand, completion percentage and yards per attempt are not defined by rare events--one dropped pass is not going to impact completion percentage or yards per attempt nearly as much as an unlucky tip will influence interception rate.
Next, I looked at the absolute value difference in the advanced passing score from year N to year N+1. This measure is not concerned with direction, but magnitude of change. Here are the results in ascending order (remember that here, the smaller the number, the less average change in that category) when looking at change in advanced passing score in each category.
Completion Percentage: 13.44 Sack Percentage: 13.63 Yards Per Attempt: 14.15 Touchdown Percentage: 14.35 Interception Percentage: 15.90
Here, we see roughly the same order, except completion percentage moves just ahead of sack rate at the top. Interception percentage is still dead last, and moves even further away. The difference between interception percentage and touchdown percentage is now larger than the difference between the other four.
Next, to evaluate where each quarterback changed the least or most, I assigned an ordinal ranking of 1 to 5 to each of the five categories, with "1" representing the category where the quarterback was most similar to the previous year, and "5" representing the category with the largest change. Individual results varied greatly. Here are the composite scores (lowest means most consistent).
Completion Percentage: 2.79 Sack Percentage: 2.92 Touchdown Percentage: 2.98 Yards Per Attempt: 3.08 Interception Percentage: 3.22
Finally, I looked at the total change in a quarterback's performance with a new team (as measured by the sum of the absolute value differences in each category), and divided each category to assign a percentage of change. This last summary lists the number of times that each category represented 20% or less of the total change in a quarterback's performance from the previous year, after a team change.
Sack Percentage: 31 of 48 Completion Percentage: 30 of 48 Touchdown Percentage: 29 of 48 Yards Per Attempt: 28 of 48 Interception Percentage: 22 of 48
It's pretty clear which performance category is least consistent from year to year and probably belongs to the individual quarterback the least. It's probably the one the general public uses to judge a quarterback the most--interceptions. You rarely hear after a game about how the receivers caused the interceptions, or the bad luck of it all, or the game context dictated the interceptions.
At the other end of the spectrum, two performance measures stand out at the top--completion percentage and sack rate. One of those, of course, is the one passer performance measure that is not currently included in the NFL's passer rating formula.
Back in the 1985 Bill James Baseball Abstract, James talked about how the old sources never included walk information for hitters, and that a walk was generally thought of as "something that the pitcher did; the batter was just the guy who was standing there when he did it." I think that walks in baseball are a nice parallel to sacks in football some twenty years later. The common wisdom of sacks is that they are the fault of the offensive line or the accomplishment of the defensive player. The quarterback is "just the guy who was standing there".
While sacks can be the fault of the offensive line or the accomplishment of the defensive player, the evidence is pretty clear that the quarterback is at least as responsible for his team's sack rate as other passing performance measures that we readily attribute primarily to the quarterback. It's time that the NFL passer rating reflect as much. I suppose the argument against change would be that the passer rating is only measuring quarterbacks as passers, and a sack isn't a pass. This, to me, makes about as much sense as having a hitter rating in baseball that ignores walks and called third strikes, because, well, the guy wasn't swinging at the ball.
I recognize that I'm not the first the make an observation that quarterbacks might be more responsible for sack rate than we believe. In an article written in 2003, Michael David Smith, formerly of Football Outsiders, observed that quarterbacks on the same team showed different sack rates, when looking at a three year period. Those numbers weren't put into context with other statistics (to compare with changes at, say, yards per attempt or interception rate when teams change quarterbacks), so I'm going to do a post in the near future to look at quarterbacks on the same team, in the same season, and look at the same five categories I looked at here.
This entry was posted on Monday, October 5th, 2009 at 8:37 am and is filed under Statgeekery. You can follow any responses to this entry through the RSS 2.0 feed. Both comments and pings are currently closed.

Outstanding stuff, Jason.
Here's an article I wrote for Footballguys on interception rates that came to the same conclusion that you did.
I'm glad I include net passing yards in my Greatest QB of All-Time formula. That said, it's important to note the correlation between sacks and rushing yards. So a QB Rating that includes sacks -- while it would be better than one that ignores sacks -- is going to hurt rushing QBs even more than your usual QB rating. Of course, the official QB rating is a bunk statistic and I'd prefer the formula I use in GQBOAT-III. But that's just me.
Cool stuff. Of course, I've been pushing sacks in my rating system for a while now (which I won't link to now, having self-promoted it enough
). We give all the credit to the QB and receiver for a long pass completion (ignoring the contributions of the O-line), yet give all the blame for a sack to the O-line, while ignoring the "contributions" of the QB (and, to some possible extent, the receivers).
There's another part to this analysis. How much does team matter. Seeing that QBs have carryover in certain rates is great, but how much carryover does a QB have if they don't change teams? I'd expect all the correlations to be higher, but by how much? What does this say for how much of an offense is the qb and how much is everything else?
Thank you, Jason! This post validates what I've intuitively known for years about interceptions. Formulas like Passer Rating and even this site's ANY/A assign way too much blame to the quarteback when a pass is intercepted. Here's why:
His receiver could run the wrong route, fall down, or bobble the ball into the air. The pass could be batted at the line of scrimmage, or it could be a hail-mary throw at the end of the game. The team could be down 21 in the 4th quarter and ask the QB to take more chances than normal. Also, how many potential INTs hit a DB in the chest only to be droppped? There are so many variables that determine whether or not a ball is intercepted that have nothing to do with the QB, that I would estimate maybe only 35% of INT's are the fault of the QB.
Red, while I agree that not all INTs are a QBs fault, I think 35% is a little bit low of an estimate. Yes, a reciever can bobble a ball, but more often than not, a pass that is intercepted after hitting the reciever is usually because it is thrown poorly. (Romo's int that took a freak bounce off Witten's foot would not have happened had Romo made a good throw). The old cliche' about a QB putting the ball only where his reciever can get it makes sense. A majority of interceptions I see are from throwing too high over the middle, throwing late on an out route, and totally ignoring the linebacker that stepped in front of a drag route.
I think, that although there are times that an INT is clearly not the fault of the QB, every QB experiences those things, so they even out in the long run. The bottom line is that if a QB is good at avoiding INTs, then he will end every season with a relatively low INT rate.
Red I disagree with that conclusion. Also if you want to lessen the penaltyfor throwing an INt you should lessen the reward for a TD since by the same argument a lot of times a QB throws a short pass and a WR makes some nice moves to take it for a long TD.
There are a lot of holes with this post. THe main one is the following
1. The correlation coffiecients for all passers in year N+1 is not given.
Chase Stuart ran a post over at football guys showing that the correlation for interception rate for ALL Qb's is 0.1. That's the exact same number as for those that switch teams.
http://subscribers.footballguys.com/2009/09stuart_qbintrates.php
To me that says that the rate of interceptions in any one season has a LOT to do with luck.
Whoops I missed that Chase made the very first post. Ha Ha.
These numbers reflect a combination of how random a stat is (in terms of varying a lot from year to year) and how much the QB contributes to it (compared with the rest of the offense & the scheme). It would be interesting to look at other data to try to tease those apart. The articles from Chase & Michael David Smith help with that, but another thing you might do is to directly compare the correlations with those for QBs who stayed on the same team or with teams that switched QBs.
Actually, you could use these same 48 data points, where a QB switched from Team A in year N to Team B in year N+1, and look at how well Team B's stats in year N predict their new QB's stats in year N+1. What happens when a team that gave up a lot of sacks adds a QB who did not get sacked much, or when a team that didn't throw many interceptions adds a QB who threw a lot of picks? You could just run a regression, with the QB's year N stats and the team's year N stats as predictors, to find out.
Great post. I agree with Vince on the point about overall randomness. Let's say that of all the variance in YPA, the random component is r=0.25. That leaves r=0.75 that could be explained by all contributing factors. If, as you found, that QB YPA correlates at r=0.20 when they switch teams, that equates to .20/.75 = 27% belonging to the QB himself.
If Int% has a high random component of r=0.60, then the QB correlation of 0.10 is .10/.40 or 25% of the remaining possible correlation. So while it appears YPA is twice as consistent as Int%, they might be really be equally attributable to the QB.
What was fascinating to me about the in-season sack data from MDS where teams switched QBs is that there is no correlation (r=-0.04) between the adjusted sack rates of two QBs playing behind the same offensive line. And now JKL has found that sack rates follow QBs who switch teams pretty strongly. I think it's fair to ask whether the quality of an offensive line contributes at all to sack rates. That is, are there any significant differences among offensive lines in their ability to prevent sacks? Intuitively you'd think so, but we certainly don't see it from this data.
Jason and Chase: this is interesting, valuable research. I think you're being too hard on the official passer rating formula, but your findings on sacks and interceptions are really important to any informed analysis of QB statistics. Thanks.
I agree that sacks (as the QB's 'fault') should be looked at, but I think it has to be a case-by-case basis (something that the film would tell better than the stat line). You could have a QB whose system has him make short, quick, throws. If he has a good enough OL, the sacks will probably be minimal. On the other hand, you could have a system with a lot of deep routes, that would force the QB to hold the ball longer until the play develops. An average, or below average OL, would hurt the deep-ball QB more than the short-pass guy. However, a bad enough line would get any QB driven into the ground.
Jim A.,
I think it's absurd to suggest that the O-line has no contribution at all to sack rates. I mean, we can see with our eyes that some lines are lousy at pass-blocking (constantly allowing free pass rushers) and some consistently create sustained pockets. If the math doesn't reflect that *at all*, then you have to strongly consider that you're doing the math wrong.
Andy,
I'm not necessarily convinced that short routes have much quicker releases than long routes. Sure, there are some very quick plays in which the receiver doesn't have time to get more than 10-12 yards down the field, but a lot of short routes seem to take longer, and a lot of long routes feature a fairly quick throw where for most of the route the ball is already in the air.
I agree with Bowl Game Anomaly .... 2 examples of that this year would have to be the orton cutler trade and the signing of matt cassel by KC .... I predicted that orton would be good with den .... den has always had a very strong o-line that carries over from year to year and so sack rates also depend a lot on the o-line. The reason orton had troubles in chi every now and then was because the o-line let people through .... same with matt cassel .. i believe he is among the league leader in sacks ...
While sack rates had the strongest correlation, a 0.31 correlation coeffecient is very low. While a QB may have more control over sack rates than the other stats, they're ALL mostly controlled by the nebulous "everything else".
What I draw from this post mostly is that a QB's stats are largely controlled by outside influences, so drawing conclusions on the quality of a QB based on his stats is dicey at best.