How Much Money is a Sack Worth?

I realize it's draft season but I'm still working on building a salary database and combining it with performance statistics. Most of the work in this type of analysis is building the data, but it's harder than it might seem at first. Salary data might use one kind of player identifier while performance statistics use another. Merging them and creating a flat data file to play with is more than half the battle. There's still more I need to do. First up will be segregating free agent years from rookie contract years. But for now, here's some trivia.

Offenses get all the attention, so I thought I'd toy around with what I have so far on defense. Sacks are one of the most visible and tangible defensive statistics. I took the primary sack makers, defined as DTs, DEs or LBs who have averaged over one sack per season in their career, and plotted their career average sack rate against their average cap hit.

A few notes about the data: Only those years with cap hits greater than $1M were included as a crude way to focus on every-down starters. Additionally, only seasons where the player had 7 or more game appearances were included. The data ranges back as far as 2006 for whoever I had salary data for. Cap hit was adjusted for salary cap inflation--All cap hits are in $2012 cap dollars. Lastly, 'sacks per season' is extrapolated for each player to full 16-game seasons.

Sacks correlate well for salaries for sack machines, to a degree of 0.42. The trend line runs at $3.4M + $295k per sack. So teams are valuing sacks at about $300k a pop.

A regression line minimizes variance, but doesn't quite tell the whole story. It seems that teams are paying for sacks at a steeper rate than the trend line shows. A lot of that is likely due to the presence of low-cost rookie contracts in the data, but there is probably either a degree of over-certainty or Gladiator-effect justification for the larger contract values.

One thing to keep in mind is that sack production correlates with other measures of production. The meanest pass rushers are also getting pressures, hits, and probably stopping runs somewhat in proportion to their sack totals. Sack totals can be considered proxies for other, more complete measures of effectiveness.

If we break things out by position, we get similar results. DTs don't tend to have as many sacks as DEs and edge rushing OLBs, so they get more money per sack. The job description of a LB is a bit longer than DTs and DEs, so they aren't valued as much for their sacks as their linemen counterparts.

You'll notice some players appear under multiple positions. For example, Dwight Freeney was reclassified as an OLB this past season when the Colts changed to a 3-4. His DE data point is blue and his OLB data point is quite an outlier. Guys who are toward the top left are the most overpaid per sack, while guys on the bottom right are sack bargains.

But that's not what this post is about. It's just getting an idea for the marginal price of an expected sack. So if we look at Elvis Dumervil's recent contract (chosen solely because he pops out in the top-right of the plot) with BAL that averages $5.2M cap hit per season, we can make a back of the envelope evaluation of the deal. Dumervil has notched 63.5 sacks in 91 career games for an average of 11.1 sacks per 16-game season. That would be worth:

$3.4M + $295k * 11.1 = $6.7M

At age 29, it would be natural to expect Dumervil's sacks to regress as he ages. By virtue of sacks alone, his current contract says BAL expects 6.1 sacks per season over the 5-year term of the contract. In the first two years of the contract, which are the two most likely to be fulfilled, Dumervil's cap hit including dead money totals $13M (averaged to $6.5M/yr). This puts his per year estimate just under the $6.7M estimated above.

As much as an over-over-simplification as this exercise is, maybe it's not too far from reality.

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6 Responses to “How Much Money is a Sack Worth?”

  1. Phil Birnbaum says:

    Brian, if you had to make a gut estimate, how much of that $295K is the sack, and how much is other things that correlate with the sack?

  2. Brian Burke says:

    Very hard to say. Soon I'll have a similar post with cap hit vs. +EPA, which includes all the individual positive contributions of a defender. At first glance it doesn't seem have any stronger correlation, so I suspect teams are tunnel-visioned on sack totals when it comes to contract value.

  3. Anonymous says:

    Hello Brian,

    My name is Theodore and

    The Packers won their 21st straight home game against the Lions Last year.

    So I did a quick estimate on the odds of such a streak happening if every game had the same odds and I came to this conclusion.

    If a team had exactly X% chance of winning every game against an opponent at 1 game a year this is their chances of making the streak last 21 years.

    90% .109418989 9.139

    85% .032945601 30.35

    80% .009223372 108.4

    75% .002378408 420.4

    74% .001794180 557.4

    70% .000558545 1790

    65% 5,517

    60% 27,351

    57% 133,853 average chance of winning a home game

    55% 155,864

    50% 1,048,576

    As you can see only one in 420 teams that keep an exactly 75% advantage would last 21 games unbeaten. And 75% seems a little to high to me and 80% is certainly to high. And besides how many teams in the nfl (where one year the Eagles keep the Giants from the playoffs and two years later they are 4-10 and the Giants have won the SB) have been able to keep a 75-80% chance of winning @home over 2 decades over a divisional opponent. Now of course the Packers were blessed to have Brett Favre then Aaron Rodgers but both of them have lost games (remember who Aaron Rodgers lost to last year?), just not to the Lions at home. And it isn't as if the Lions have never been competitive and the Packers had a few bad years.

    This is the odds of a streak with 18 games @75% and 3 @65%.

    18@.75*3@.65 .001548256 645.9

    So clearly the odds are against something like this happening very often in a nfl with only 32 teams. Most of whom don't have a team that they have 75% of beating in any given game for a couple decades.

    Anyway my question is do you think in things like this once you have a 5-10 game streak over someone you play that much harder so that you don't get headlines like "Lions First Win @ Lambeau Field in 12 Years" "Favre throws 3 int Blame Him" especially with a heated rivalry like Packers vs Lions?

    Also using your prediction model could you please give the stats on Green Bay's chances every year since the streak began or as far back as you have numbers. If it's not to hard. Thank you.

  4. Nate says:

    With a title like "What's a Sack Worth" I was, more or less, expecting an analysis of the impact of sacks on win probability or EPA - that is to say value, rather than price.

    Though I suppose we can do back-of-the napkin calculations here: On average, NFL teams spend about 14 million in salary per win, so, at $300k, each sack is about 1/50 of a win.

    I don't have a handy database, but four of the five single team sack record games listed in Wikipedia are close (less than 7 point difference) so I'm not sure how much sacks end up being worth in terms of winning.

  5. Unknown says:

    Hi Brian,
    I'm developing with my colleague who has developed an Artificial Intelligence-based natural language understanding technology that we are applying to Fantasy Sports and Sports Wagering. We would be interested in having you perhaps write an article about our Fantasy Sports service app. I provided a link to our demo video below. Thanks


  6. Anonymous says:

    Brian, would it be better to use pressures as a statistic instead of sacks? I know you said that players with high sacks usually have high totals, but quite a few sacks are based on opportunity (QB recovering a botched snap, or coverage sacks); there are a lot more pressures to have a bigger sample size, and a pressure results in a loss of down about 54% of the time.

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