# Expected Sacks

Main Takeaway: By capitalizing on a larger sample size, a probability-based metric may offer a much more accurate picture of a pass rusher’s performance than traditional sacks.

Although they have not yet found a solid foothold in football, probability-based metrics are popular across other major sports. In short, such metrics involve multiplying a relatively high frequency event (such as a shot) by its probability of success based on a given variable (such as location) in order to yield an “expected success total” (such as expected goals). In soccer, the infrequency of goals created a demand for a metric based on a larger sample and expected goals provided a natural solution.

A natural application of probability-based metrics to football involves pass rushing, given the infrequency of sacks. Expected Sacks would involve two components:

• Knockdowns broken down by time elapsed between snap and knockdown (“K”)
• While some may justifiably prefer Hurries to Knockdowns due to their greater sample size, I opted for the certainty that the pass rusher made contact with the quarterback and took him to the ground.
• Probability of a quarterback holding onto the ball broken down by time elapsed since snap (“P”)
• As is customary with probability-based metrics, K would be on an individual player basis while P would be based on league-wide performance on passing plays

Expected Sacks would be computed by (I) multiplying a player’s K and the respective P for each time bucket and (II) adding up all of these expected values. Expected Sacks could then be divided by the pass rusher’s number of pass rushes on the season to produce a much more comparable rate metric in Expected Sacks per Pass Rush.

Applied Example (Theoretical Data)

Von Miller (2017)

• Pass Rushes: 320
• Knockdowns (1 Second After Snap): 1
• Knockdowns (2 Seconds After Snap): 7
• Knockdowns (3 Seconds After Snap): 3
• Knockdowns (4 Seconds After Snap): 6
• Knockdowns (5 Seconds After Snap): 2
• Knockdowns (6 Seconds After Snap): 2
• Probability (QB Holding Ball 1 Second After Snap): 95%
• Probability (QB Holding Ball 2 Seconds After Snap): 85%
• Probability (QB Holding Ball 3 Seconds After Snap): 75%
• Probability (QB Holding Ball 4 Seconds After Snap): 50%
• Probability (QB Holding Ball 5 Seconds After Snap): 20%
• Probability (QB Holding Ball 6 Seconds After Snap): 5%

Expected Sacks

= 1*0.95 + 7*0.85 + 3*0.75 + 6*0.50 + 2*0.20 + 2 *0.05

= 12.65

Expected Sacks per Pass Rush

= 12.65/320

= 0.0395