Tom and Mike have climbed to the top of the Hill of Nonsense and unleash another wave of insane wagering on the world.
29 Jul 2007
Guest column by Zac Hinz
One of the problems with statistical analysis in the NFL is that more than half the positions have few or no official stats associated with them. Offensive skill players have touchdowns and yards, defensive backs have interceptions and pass defensed, and defensive linemen have sacks and tackles. Each of these stats at least gives you some idea about whether Player A is better than Player B -- although Football Outsiders readers know that these stats can sometimes be misleading. Nonetheless, think about the poor offensive linemen. The NFL.com Player Pages are basically worthless for them. Flozell Adams' page, for example, tells us that he has started 130 of the 134 games he's played in. That's all we have to describe his ability as an offensive lineman.
But there is one number that exists for every player in the league, the number that the player cares about most: his salary. Right away, I have to admit that there are a lot of cases where a player's salary doesn't accurately describe his ability. The most obvious involve players playing under their rookie contracts. Some of these players are underpaid and some are overpaid. But there are plenty of veteran players who are being underpaid or overpaid too. (Most of the overpaid players are on the Redskins.)
Another challenge in judging players by salary is that some teams use of roster bonuses in place of signing bonuses. The Minnesota Vikings are especially known for this.
If every player signed a new one-year contract every season, then we'd really have something here. Then the USA Today database, which I used for the salary information, would be a perfect resource. However, just because they don't, and it's not, that does not mean that trying to tie salary to performance is worthless. I compared the amount of money a team spends on each position to each team's DVOA (explained here) in various categories. The data runs from 2000 to 2006, and therefore includes 222 data points. Salaries from before 2006 are adjusted upwards by a small amount so that the total amount of all NFL salaries on each year equals the total of all 2006 salaries.
Let's start basic: Is there a relationship between a team's overall salary and its overall DVOA. Yes, in fact, there is. The correlation between a team's overall salary and its overall DVOA is .22. A correlation of 1 signifies a perfect match; a correlation of 0 signifies absolutely no relationship between the two variables. Most mathematicians will tell you a correlation of .22 is pretty small. Given the problems with using salary as a metric, and the relatively small data size, we're going to have to take what we can get. (With a 16-game season, Football Outsiders is used to dealing with smaller correlations when it comes to performance stats.)
Think of the information here as a suggestion of where a relationship may exist. If we had better data, we could very well come up with quite different results -- or a stronger relationship in the same direction.
On the offensive side of the ball, the correlation between Pass Offense DVOA and salary is highest for Quarterback (.27), followed by Receivers (.21), Running Backs (.13), and Offensive Line (.05). That does not necessarily mean that this is the order of importance for these positions, nor does it necessarily mean that the offensive line has nothing to do with the success of the passing game.
First off, remember that we're looking at players' salaries. Quarterbacks have their success rewarded very quickly. Carson Palmer, for example, got a contract extension after three years. If you're a quarterback and you haven't been offered an extension after four years, then the writing is probably on the wall. At most other positions, you aren't going to get a contract extension until you have one year left on your old contract.
Second, the salaries of players on their rookie contracts are based on the positions they were drafted at. And the majority of starting quarterbacks, wide receivers, halfbacks, and offensive tackles are high round draft picks. Tight ends, centers, guards, and fullbacks are more likely to be later round picks. So 100 percent of quarterbacks, 66 percent of receivers, 50 percent of running Backs, and 40 percent of offensive linemen are high draft picks. Notice that this is the same order as the correlation of salary with Passing DVOA.
The positional salary that has the highest correlation with Rush Offense DVOA is Special Teams salary. Special Teams salary includes the salaries of the kicker(s), punter(s), and long snapper(s). It does not include any returners. This is because (1) some teams make it difficult to tell who their returners are, and (2) some returners play a role on the offense or defense as well. Kickers, punters, and long snappers, meanwhile, play a role only on special teams.
It's actually a negative correlation (-.18), which means that the more you pay your three special teams specialists, the worse your rushing offense is. This doesn't seem to make any sense to me. If you've got a possible explanation, feel free to post it in the comments. All the correlations involving special teams DVOA were very confusing and could appear on the cover of Correlation is Not Causation Magazine. For more details, see the section on special teams below.
Rush Offense DVOA in general seems to have very little correlation with any salaries at all. Other than special teams, no other position correlates with Rush Offense DVOA any higher than +/- .10. This could be because the strength of the running game is based more on the offensive line, and offensive line has the highest percentage of players who might be starting as late-round picks -- and therefore are being underpaid, as mentioned above.
So that I didn't have to deal with separating 3-4 defenses from 4-3 defenses, I calculated the salaries of the front seven all together. The numbers showed that the front seven has a larger impact than the defensive backs when it comes to both Rush Defense DVOA and Pass Defense DVOA. Perhaps it shouldn't come as a surprise that seven guys on the defense are more important than the other four guys.
For the front seven, the correlations are -.21 to Pass Defense DVOA and -.15 to Run Defense DVOA. For the secondary, the correlations are basically non-existent: -.12 to Pass Defense DVOA and -.04 to Run Defense DVOA.
Just for fun, though, the 4-3 numbers, in which defensive linemen are separated from linebackers, show that defensive linemen have the highest correlation with Pass Defense DVOA, and linebackers have the highest correlation with Rush Defense DVOA. This seems to suggest that the pass rush (provided by defensive linemen in the 4-3) is more important to Pass Defense DVOA than the coverage skills of the defensive backs.
Stranger is the case of the 3-4 defense. The 3-4 linemen and linebackers have the most ridiculously small sample sizes of anything in this study (there were only 33 teams running the 3-4 in the study's seven years) . However, the numbers for 3-4s are the opposite of those of the 4-3. The defensive linemen have the highest correlation with Rush Defense DVOA, and the linebackers have the highest correlation with Pass Defense DVOA.
I can't explain the relative unimportance of defensive backs. They do have a correlation with Pass Defense DVOA, but it's half as much as the correlation that 4-3 defensive linemen have on Pass Defense DVOA. Total Defensive Salary has the highest correlation with Pass Defense DVOA. That could mean that all parts of the defense need to be working in order to have a good pass defense.
This section is pretty weird. The numbers show that teams that spend more money on special teams specialists (remember, that's only kickers, punters, and long snappers) have better defenses (both passing and rushing), and worse rushing offenses. There are three possibilities here:
1) The numbers are wrong.
2) The numbers are totally unconnected, and the correlation is meaningless.
3) The numbers are not saying that teams which spend more money on special teams have better defense. They are saying the reverse: teams that have good defenses and bad rushing offenses are the ones that are most inclined to pay big money to their specialists. When you are going to punt the ball a lot, and have difficulty scoring touchdowns, your punter and kicker become more important.
The other interesting finding is that Special Teams salary does not have the highest correlation with Special Teams DVOA. Rather, it is defensive backs and linebackers that have the highest correlation. This seems to imply that the coverage and return teams (which have large numbers of defensive backs and linebackers on them) are more important to overall special teams than the specialists are. Defensive backs also often double as return men -- although so do receivers, and the correlation between receivers and special teams is only half that of defensive backs and special teams.
I fully admit that this project represents completely unfinished research. It is a simple first try at answering a complicated question. At a later date, I would like to divide these players up into smaller groups: separate halfbacks from fullbacks, cornerbacks from safeties, and if possible, tackles from guards from centers. I could also separate special teams DVOA into its five components to see if it is important to pay a kicker to get high field-goal value, and what position's salary correlates best specifically with kick and punt returns.
Zac Hinz lives in Oshkosh, Wisconsin, and is currently number 38,151 on the waiting list for Packers season tickets. He expects to receive them the same day he is tragically hit by a bus. If you would like to write a guest column for Football Outsiders, something that analyzes the NFL or college football in a new and different way, please send your idea or rough draft to mailbag-at-footballoutsiders.com.
37 comments, Last at 14 Aug 2007, 6:00pm by steelersalarycap