Jared Allen and Sack Rate

The biggest transaction this off-season may have been the Jared Allen trade from Kansas City to Minnesota. Allen led the league in sacks last year with 15.5. He'll be going to a Viking defensive line that was impenetrable against the run but featured an average pass rush. The Vikings defense was so good against the run, opponents passed nearly 70% of the time compared to a league average of about 55%. Allen's ability as a pass rusher could have a very large impact. We know the Vikings pass rush will probably improve, but by how much? And how will the improvement affect the Vikes' bottom line?

Importance of Sacks

First, let's look at the general importance of sacks in terms of team wins. Normally when I model team wins, I combine sack stats with passing stats to calculate net passing yards. Along with turnover rates, running efficiency, and penalty rates, net passing efficiency is used in a regression to estimate total season wins for any given team. This method is useful for estimating the overall importance of the passing game compared to other aspects of football. But in this case, we want to specifically know the effect sacks have on total team wins.

By using basic yards per attempt (YPA) and sack rate instead of net passing efficiency, we can isolate the effect sacks have on winning. Using sack rate (sacks per drop back) instead of total sacks is useful for two reasons. First, it is far less susceptible to problems caused by the direction of causation. That is, defenses that face lots of passes would tend to have higher sack totals because they have more opportunities. Secondly, it allows us to compare teams and players that faced vastly different numbers of pass attempts (such as the Chiefs and Vikings).

Jared Allen's Potential Effect

Allen's 15.5 sacks were remarkable because he played in only 14 of 16 games last season. He also played on a 5-11 team that more often than not faced offenses with safe leads more interested in running out the clock than passing. His sack rate was an amazing 3.8%. That's as high as the entire entire Bengals' defense. Had he played in all 17 games and faced the very high number of passes the Vikings defense faced, Allen would have over 26 sacks! But it's unlikely the Vikings' opponents will pass nearly as often in 2008, especially with Allen leading an improved pass rush. If they face the average number of drop-backs, Allen would have about 20 sacks, still a near-record-high amount.

In estimating the number of added sacks Jared Allen could bring to the Vikings, we can't just add 20 to their previous total of 36. The Vikings defense already had 9.5 sacks from the right DE position last year, 5 from Ray Edwards and 4.5 from Brian Robison. A reasonable estimate would be that Allen could add a net of 10 additional sacks, taking them from an exactly average 36 sacks to a solidly above-average 46. This assumes he performs nearly as well as last year and he remains healthy--both fairly big assumptions.

Note that the additional sacks Allen may bring need not be his sacks. By chasing a QB out of the pocket or by occupying multiple pass blockers Allen could enable teammates to get the sack, but the credit would still belong to him.

Sack Rate's Contribution to Winning

Based on a regression of team win totals using sack rates, running and passing efficiencies, turnover rates, and penalty rates, sack rates are fairly important. For every standard deviation improvement in sack rate, a team can expect about an additional half win. That's comparable in importance to offensive running efficiency. The table below lists other important stats in comparison to sack rate and how they tend to impact team win totals.

Importance of Various Factors:
Effect on Wins per Standard Deviation

StatisticWins per SD
O Pass Efficiency1.15
D Pass Efficiency0.97
D Sack Rate0.47
O Run Efficiency0.43
D Run Efficiency0.25

Stated differently, for every percentage point increase in sack rate, a team can expect an extra 0.36 wins. Jared Allen's additional 10 sacks would improve the Vikings' sack rate from 5.0% to 6.4%. That additional 1.4% roughly translates into 0.50 additional wins for Minnesota.

Sacks correlate with other defensive stats, which complicates the analysis. Sack statistics are representative of a defense's overall pass rush. There are hurries and QB hits that are interrelated with other stats such as defensive passing efficiency, interceptions, and fumble rate. (I'll have to make one more assumption--that a pass rush causes the effect on passing efficiency, fumbles, and interceptions instead of the other way around. I realize this is not absolutely correct. A good secondary can cause the QB to hold the ball longer, for example. But it appears to me that the direction of causation primarily begins with the pass rush.)

The fact that sacks correlate with defensive passing efficiency, interceptions, and fumbles means that the benefit of adding a solid pass rusher is stronger than it first appears. Unfortunately, it also means the regression model is less than perfect. Ideally all of the independent variables in a regression are independent of each other as well as independent of the dependent variable. (This is why my normal model does not break out sacks and uses net pass efficiency instead.) However, no model is ever perfect, and I could only hope for a solid but rough 'order-of-magnitude' estimate anyway.

I estimated the effect of sack rate on defensive passing efficiency, interception rates, and fumble rates. I won't bore you any further with regression results, but the correlations were:

Defensive Stat Correlations with Sack Rate

StatisticCorrelation with Sack Rate
D Pass Efficiency0.21
D Int Rate
Fumble Rate

In short, the cumulative effect of sacks on these other stats contributes to an additional 0.41 wins. In total the Vikings could expect about 0.9 additional wins from an extra 10 sacks. Realistically, this estimate should be taken as very rough, but it does provide an idea of the magnitude of impact a premier pass rusher could provide his team.

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10 Responses to “Jared Allen and Sack Rate”

  1. Anonymous says:

    Your forgetting that allen is not replacing edwards, and robinson. He is replacing kenechi udeze, and darrion scott, since ray edwards is moving to LDE. Robinson is still going to get a good amount of playing time backing up everyone across the line. But udeze last years starting LDE, cant play. so allen is replacing his 5 sacks and scotts 0 sacks not edwards and robinsons 10.

  2. Brian Burke says:

    Excellent point. I doubt it's purely additive though. But you're right, the LDE spot should see some more sacks next year.

  3. Anonymous says:

    Don't teams who are already winning get more sacks because of it? It seems to me that when a team is ahead by a lot (or late, or both) then the opponent is passing more than usual and trying to make big plays when they're not there. I would think that would cause big sack totals.

    Just a causation vs. correlation thing. You may have already taken this into account.

  4. Anonymous says:

    Learn to fact check, please. His name is Brian ROBISON.

  5. Anonymous says:

    there are 16 games in a season not 17.

  6. Brian Burke says:

    Good catch. Corrected. Had 'weeks' on my brain.

  7. Anonymous says:

    good read,

    I agree with the addition of Jared many facets of the Vikes D will be on the rise. Sharpers ball hawking will raise 2-3 more pics. Even the CB's might be getting more into the Int column.

    here's another avenue though.

    Jared - PhatPat - Kwill -REdwards
    Greenway Leber
    Ej Henderson

    now that we have natural PassRush. the # of blitz's will go way way down. BUT. here's a thought. the LB crew could add another 10 sacs combined in that total. i mean that if you dbl team. Pat/Jared.. use a Rb/TE to help with kwill, you have ray coming 1v1 all the time. and.. a highway for 1 LB to just rush in..

    now the dbl teams will switch around i know.. 3 ProBowl DL is a very nice thing to have. and will cause problems and headaches for OC's around the league.

  8. Brian Burke says:

    That's a great analysis. No doubt OCs will be dreading game-planning against that D. It's certainly possible that the Vikes could end up with even more sacks than I've estimated (I'm only claiming a rough estimate here), but I did give them a full standard deviation improvement over last year. (They were about 1 SD below average in sack rate last year.) That's a very healthy increase.

    The big take-away point is that for every SD improvement in sack rate, expect between 0.5 and 1 wins added. That's 0.5 wins for sacks alone, plus a bonus for the added effect of fumbles, def pass efficiency, and interceptions (perhaps due to the fewer-blitz effect as you mentioned).

  9. Anonymous says:

    What about "regression to the mean"? Jared Allen hasn't averaged over 1 sack per game during the rest of his career. I think that it's much more likely that instead of 17 or 20 sacks he'll have 12 or something like that (pulled out of a hat, but I'm sure that you can figure out the correlation between sacks in consecutive years for a given player).

    He had a great season and seems to be a great player and a nice addition to the sack starved Vikes but let's be realistic here.

    And what about his affect on the Vikings historically crushing run defense? Anyone have any assessment on what kind of run-D Jared Allen plays?

  10. Anonymous says:

    2008 14.50 sacks
    2009 14.5 sacks
    2010 11 sacks
    2011 22 sacks
    13 FF and 8 FR and 5 INTs over that time period.

    team stats
    2007 38 sacks (before Allen)
    2008 45 sacks
    2009 48 sacks
    2010 31 sacks (yet strangely enough this year they are 10th in passing yards allowed)
    2011 50 sacks (but near last in passing yards)

    Meanwhile, it's a good idea to compare the Cheifs with allen and without
    2007 37 sacks
    2008 10 sacks
    2009 22 sacks
    2010 39 sacks
    2011 29 sacks
    Over a 4 year period after JA trade, Vikings recorded 174 sacks to KC's 100.
    teams are obviously not similar without them, but keep in mind that KC acquired a first and third while Vikings lost a first and third and Chiefs were free to replace JA while Vikings were unable to use the draft picks elsewhere.
    Overall, I have to give the trade to the Vikings, but I think they would be wise to trade Jarred Allen coming off a super high 22 sacks before he regresses to the mean and potentially gets injured as he is now 30 years old. I bet they could get a 1st and a 3rd out of him back now if not more, and I would guess that the next time around trading the player for picks ends up as the better trade this time.. Also, Vikings lost Pat Williams last year, and Ray Edwards the year before, and their LBing core has diminished and secondary as well. Those clearly were not coverage sacks he was getting last year!
    It would be great if you say "what is an average first round worth in terms of EPA and WPA" and then you could perhaps come up with a fair trade, but also consider salary cap? I think Vikings are best off getting younger quickly for the long term sake as the longevity of a rookie's career is likely greater than even a well established player in Jared Allen at this point. Talent level is great, but may drop off after a year or two, and next contract is going to be a big one most likely based on his past performance. He signed a 6 year deal in 2008 which included 2008 season, so he has 2012 and then 2013 he is in a contract year. I believe Vikings would be wise to trade him now or next year to extract maximum value, rather than seeing him depart via free agency or get resigned and overpaid and not getting any value out of him.

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