By Kurt Bullard

In March, the NFL instituted a new rule that would move touchbacks on kickoffs to the 25-yard line, a move that received a good amount of backlash from media and fans alike. I wrote an earlier article discussing the possible implications of such a rule, such as increased scoring and an increased rate of touchbacks.

Another possible change in the special teams play that might not be realized, but should be, is for coaches to call more surprise onside kicks.

In another article I wrote a few years back on surprise onside kicks, I found that teams do not utilize the tactic enough. From 2001 to 2010, teams recovered surprise onside kicks 60% of the time. I found that teams should attempt them if they believe they have at least a 37.5% chance of recovering it, meaning that teams should be more aggressiveâ€”the reward is greater than the risk if the recovery rate is 60%.

At the surface, going for a surprise onside kick is simply a choice between an asset with low-risk, low-expected payout and an asset with higher risk, but a higher expected payout. One can either kick it off normally, which is less risky but on average will not gain you much, or you could surprise onside kick, an option that has a higher maximum payout but does not happen that often.

Making this decision is best understood from an expected points modeling perspective, so it might be of use to Jim Caldwell. Under this new rule change, the alternative to a surprise onside kickâ€”that is, a conventional end-to-end kickâ€”is less appealing. Because touchbacks are now brought out to the 25-yard line, the average expected points for the receiving team should increase, because average starting field position should improve. This worsens the â€śsaferâ€ť choice, which should increase oneâ€™s proclivity to go for the riskier option. So, the breakeven point should go down, which should in theory incentivize risk-neutral coaches to go for surprise kicks more often.

One can calculate the breakeven point by seeing how often the recovery would have to happen to make one indifferent between the expected average points of a surprise onside kick and a normal kickoff. There is no empirical data on average starting field position under these new rules, however. So, I calculated the average expected points gained on kickoffs last year as if the touchback was brought to the 25-yard line, which yielded an expected point total gain of 0.775 points over last yearâ€™s 2,559 kickoffs for the returning team. This is the floor for the average expected return, so most likely, kicking it off is even more costly than that number suggests.

To calculate the average expected points for surprise onside kicks, I found the yard-line at which the 63 onside kicks were recovered last season, using NFL Savant data. The following is a histogram of the recovery spots.

I calculated the expected points for each recovery spot, and took the average, which turned out to be 2.22 expected points. Knowing the average totals for each choice, one can then find the expected value of the surprise onside kick.

E(Onside Kick) = P(Recovery) * E(Points|Recovery)+P(Failure) * E(Points|Failure)

E(Onside Kick) = 0.6*(+2.22) + 0.4*(-2.22) = **+0.44 points**

So, under the current success rate, the expected points of the surprise is 0.44 points. This means that, on average, a surprise onside kick is worth that total minus the expected point average of the regular kick, which means that surprise onside kicks are worth **1.21 expected points more than a regular kick.**

How much more should aggressive teams be? In theory, a regular kickoff should be worth as much as a surprise onside kick in equilibrium. To find the breakeven point, you can vary the probability parameter, and the set the two options equal to each other and then solve.

E(Regular Kick) = X * E(Points|Recovery)+ (1-x) * E(Points|Failure)

Solving the equation yields a break even point of **32.5%,** which means teams should be much more aggressive than they now are. It is tough to say, however, how many additional surprise onside kicks would bring the overall success rate down to this level.

Coaches are getting less risk-averse each year nowadays with the advent of analytics. This year, weâ€™ll see if they like surprises any more than they used to.

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