Not concerned with what it takes to make the HOF or Pro bowls for players only what a sack is worth to the defense.
A sack on 4th and 5 with the game on the line late in the 4th quarter is patently far more valuable than one on 1st and 10 in the 1st quarter. Players can't control when their sacks, or any other types of plays, come. Although it did seem like Charles Haley could summon that talent in his glory days.
I think the best way to measure the value of a sack is by first down likelihood. On a third down the sack typically forces a kick, which can be a field goal attempt or a punt. 1st down and 2nd down sacks change the chances for a 1st down conversion in less direct way. A sack results in an average loss of 5.2 yards.
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%. A sack drops an offense's chances of converting a 1st down by roughly 30 %(easy to remember). 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. A runner is normally in a protective mode for the ball whereas a QB must be more vulnerable for what he needs to achieve.
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. Just appraising the obvious.
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 attempt, or even just putting a team in a expected passing circumstance. Big power for a single play. A turnover is typically worth 4 points, so a sack could be recognized as half as exceptional as a fumble or interception.
One reason sacks are so valuable as you stated is that they often result in fumbles. Even if a quarterback isn't tackled, if he's coerced 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 anticipated points. It's the probability of a fumble that makes up the extra 0.3 points.
So I state once again all sacks are not equal and is not a good way to define a player. How many are cleanup sacks remember...
