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Last season I took a cursory look at the importance of depth at offensive line. I highlighted the thinness of the Redskins' line by pointing out that although their total salary spent on their line was in line with most other teams, a large part of their cap space was allocated to a single player, left tackle Trent Williams. Their median salary was less than half of that of the division leading teams at the time, suggesting that the Redskins annual mid-season swoon was due to a lack of replacement talent following inevitable injuries to starting linemen.

This post will go far more in depth and look at correlations between team offensive line (OL) salary and performance. Using salary data from USA Today's database for the 2000 through 2009 seasons, I calculated correlations between OL salary and various advanced offensive performance statistics. (USA Today's database ends at 2009. Additionally, the 2005 season was excluded because USA Today's database appeared incomplete that season, listing half as many players than the other seasons.)

As in my other salary analyses, I relied on cap hit as the truest measure of a player's cost to a team. NFL salary structures are notoriously complex, with base pay, bonuses, guarantees, and other factors. But cap hit comprises most if not all of those considerations, and it represents the cost to most team's most precious resource--its cap space. For each season, I adjusted all salary numbers according to the league's cap for that year to account for salary inflation.

Naturally, we'd expect that the more a team spends on its OL, the better it should do on almost all aspects of offensive performance. They would, in general, tend to both run and pass better, score more, and win more than teams that spend less on their lines. We'd also expect that teams with higher median salaries for their OL will perform better than those with lower median salaries. We'd expect that salary effects on performance would show up in both overall offensive performance and in line-specific metrics, such as sacks, QB hits, and tackles for losses.

Measuring offensive line performance statistically might be the most difficult tasks of all advanced football analysis. My approach has been to measure how little damage an opposing front-7 does (counting linebackers on pass plays only when they are pass-rushing). Still, linemen are central to all aspects of offensive play, so there should be no doubt we'd see a relationship between salary and overall offensive performance.

The results of the analysis were surprising. Most correlations between OL salary and performance were weak or non-significant, but there was an unmistakable pattern to the results. In general, higher total cap dollars allotted to the OL correlated with worse performance, while higher median salaries correlated with better performance.

The table below lists the correlations of team total OL salary and median OL salary with all relevant performance statistics. Stats preceded with a negative sign (-EPA, for example) refer to OL EPA allowed to opposing defenders.

Stat Total OL Salary Median OL Salary Diff
EPA/P -0.04 0.10 0.14
Off EPA -0.04 0.10 0.15
Off WPA -0.02 0.13 0.14
OL -EPA -0.12 -0.03 0.08
OL -WPA -0.05 0.01 0.06
Pass EPA -0.05 0.06 0.10
Pass -EPA -0.14 0.02 0.16
Pass EPA/P -0.05 0.06 0.11
Pass SR -0.07 0.03 0.11
Pass WPA -0.02 0.08 0.10
Pass -WPA -0.09 0.06 0.14
QB Hits* 0.12 -0.10 -0.22
Run EPA -0.01 0.16 0.18
Run -EPA -0.01 -0.08 -0.06
Run EPA/P -0.01 0.16 0.17
Run SR -0.03 0.06 0.10
Run WPA -0.01 0.17 0.18
Run -WPA 0.01 -0.05 -0.06
Sk Yds* 0.14 -0.16 -0.30
Sks Allwd* 0.08 -0.16 -0.24
SR -0.07 0.05 0.12
Tkls Loss* 0.09 -0.09 -0.18

The first thing to notice is that the correlations are all weak. I was expecting a slightly stronger relationship. For comparison, a QB's salary cap hit and EPA correlate at r=0.26 during the same period. Many are not significant at all. With the sample size here, significance is at or beyond a correlation of 0.09 (or below -0.09). Also keep in mind that there are about 40 tests in this analysis, and we should expect a couple Type I errors, meaning that we'd see significance where none actually exists.

Interestingly, the basic stats in the analysis (QB hits, sacks, sack yds, and tackles for losses--each marked with an *) which don't rely on any advanced models are the most telling. Total OL salary correlates positively with these stats, which means the more teams pay their linemen, the more sacks and tackles for losses they tend to give up! But if you look at median salary, we see exactly the opposite. The correlations are all negative, meaning that a higher median salary indicates better performance.

And the same pattern exists for nearly all the performance statistics. Higher median salaries correlate with better performance while total salaries correlate with poorer performance. The Diff column is nearly universally positive, except for the stats in which higher numbers are bad like sacks. And even when the correlations themselves are not significantly different from zero, the correlation for total and median are significantly different from each other. This is the pattern in stat after stat, and only two of the 22 stats analyzed, Run -WPA and Run -EPA, bucks the trend. When drawing an inference, it's this pattern, and not necessarily the strength of the correlations themselves, that I'd hang my statistical hat on.

The pattern indicates that a robust offensive line corps is better than having several star linemen interspersed and backed-up by bottom tier linemen. In other words, on a player scale of 1-10, it's better to have a line of all 6s rather than a line composed of 10s and 2s. The nature of offensive line play might dictate that lines with the fewest weak players are better than lines with the most strong players. Line play is a parallel process, akin to a chain which is only as strong as its weakest link.

The weakness of most of the correlations shouldn't be too surprising after all. Salary cap hit, although the best among  the available options, is still an imperfect measure of the price of a player. And salary is an imperfect representation for actual ability. Veteran free agents are pricier than equivalently performing players serving under their rookie contract. Throw in the unpredictability of injuries, opponent strength, and the randomness of the sport itself, and it's easy to understand why the correlations are weak. Perhaps most importantly, the fact that, due to the salary cap, teams tend to spend about the same total amount on their offensive lines means there isn't going to be a lot of leverage on marginal dollars spent on linemen. That's why how a line is built appears more important than how much is spent building it.

Regardless of the reason, there is a lot of variance in team offensive performance unaccounted for by OL salary.

This analysis is far from conclusive, and as always, further research is warranted. For example, what if we only look at each team's top 5 OL salaries and ignore reserves? What if we only look at the back-ups? Or account for players under their rookie contracts? There are also better ways of looking at the allocation of salary along the line (I'm thinking Gini coefficient maybe?).