## The Value of a Sack

Being a Ravens fan makes me appreciate exciting defense. Most football fans are more interested in touchdown passes and long runs, but I've learned to enjoy interceptions, sacks, and safeties. Measuring the values of interceptions and safeties are relatively straight-forward. But sacks come in all shapes and sizes. In my continuing series on things that might only interest me, I'll look at a couple different ways that sacks can be valued. (Hat tip--Buzz)

A sack on 4th and 5 with the game on the line late in the 4th quarter is obviously far more valuable than one on 1st and 10 in the 1st quarter. But players can't control when their sacks, or any other types of plays, come. Otherwise, they'd save up all their best plays for when they matter the most. So I'm not going to worry about all the situational variables. I'll start by looking at sacks in the aggregate, then break them down by field position and down.

One way to measure the value of a sack is by first down probability. On third down a sack almost always forces a kick, either a field goal attempt or a punt. But 2nd down and 1st down sacks change the chances for a 1st down conversion in less direct way. A sack in the NFL results in an average loss of 5.2 yards. We can use the chart of first down probabilities below to estimate the effect of a sack.

For example, knowing that a 1st down and 10 results in another 1st down 67% of the time, a sack that forces a 2nd and 15 changes the chance to 38%. A sack on 2nd and 5, that forces a 3rd and 10, changes the chance of a 1st down from 75% to 35%. Generally, a sack drops an offense's chances of converting a 1st down by roughly 30 percentage points. We can apply the very same principle to any plays for a loss. The effect of a
3-yard loss on a run is very similar to that of a 3-yard sack, but not identical as I'll discuss below.

Field position is important. A sack near the 35 yard line can put a team outside of field goal range, forcing a punt. In other cases, it might force a longer more difficult FG kick. Nothing Earth-shattering here, I'm just quantifying the obvious. So let's look at sacks by field position in terms of expected points.

If we average the expected points of all situations in which there wasn't a sack, and compare it with the average expected points following plays that did result in a sack, we get a difference of 2.0 points. In effect, a sack swings the balance of the game by an average of 2 points in favor of the defense, either by forcing a punt or a longer FG try, or even just putting a team in a predictable passing situation. That's a big swing for a single play. A turnover is generally worth 4 points, so a sack could be thought of as half as good as a fumble or interception.

Two points seemed like a lot, so I dug a little deeper. One reason sacks are so valuable is that they often result in fumbles. In fact, even if a quarterback isn't tackled, if he's forced to fumble, even just by a hair, that's technically counted as a sack. So when we take fumbles out of the equation, sacks are worth an average of 1.7 expected points. It's the possibility of a fumble that makes up the extra 0.3 points.

The three graphs below illustrate how field position affects the value of a sack. There is one graph for each offensive down 1st, 2nd, and 3rd. Field position is in terms of distance from the goal line. For example, the "80" is an offense's own 20 yard line. The blue lines are expected points in situations without a sack, and the red lines are situations following a sack.

One thing to note is how the effect changes on the cusp of field goal range. On 3rd down, sacks on plays that started between the 20 and 30 are especially costly to offenses, probably because this makes a field goal far more difficult. On 2nd down, the effect is slightly different. And on 1st down, there doesn't seem to be any special effect near FG range. Offenses still have 2 more downs to recover any yardage given up.

### 6 Responses to “The Value of a Sack”

1. Unknown says:

I know the guy who invented this stat.

2. Anonymous says:

my uncle invented the cobb salad

3. Brian Burke says:

My grandfather's name was Harold Bingo, and he invented Bingo.

4. Anonymous says:

This is really great information and what I was looking for. I figured that the sack would be worth a heck of a lot, wasnt sure it would be about half as much as a turnover but it doesnt surprise me that it is very high. You look at the things that the Giants have done the last year give or take, winning by putting pressure on the QB and great offensive line play and you win the way that doesn't take one huge star to win. The more teams are able to put value on plays like these seems like the better they can build a team, and getting a strong DE seems to be a good way to spend your money to me.

5. Brian Burke says:

Buzz-Forgot to credit you as I predicted. Rectified.

6. Anonymous says:

Concur, this is incredibly interesting - perhaps you should proprietorize (is that a word, no...I didn't think so) them before you lose out on a profit making opportunity.

Anyhow, I digress, but as Steeler fan (sorry) I found this especially interesting as the Steelers are a team that is excelling both at sacking and being sacked. Which led me to wonder, how well they might be doing if they were average at avoiding sacks.

I used the 1.7 pts per/sack in the following manner(s). First I calculated Pythagorean wins as the season stands now, Pitsburgh is 7.53 estimated wins. Next, I took the NFL average number of sacks allowed and used it for the Steelers and adjusted the Points For total by a factor of 1.7/sack, to yield estimated wins 7.91. So if Pittsburgh could protect the QB (or Ben could protect himself) at the league average, they might have .5 more wins.

Next, I calculated the correlation of sack differential with wins across the league: r = -0.720
and point differential: r = -0.723

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