Kicking off with 2:35 left in the fourth quarter and trailing 23-17 with 3 timeouts left, the Patriots attempted an onside kick rather than kicking it deep. The kick went only 7 yards and ended up being illegal, giving the Steelers 1st-and-10 at the NE 42. The Patriots did end up getting the ball back, but with only 19 seconds and no timeouts left, and they wound up losing by 8.

This brings into question whether the onside kick was justified in that situation. Taking a look at the numbers facing Bill Belichick and the Patriots at the time of their decision shows that the onside kick was justified as long as they felt that they had at least a 14.7 percent chance of recovering it.

First off, the assumptions to begin with:

* The probability of recovering an onside kick when trailing in the 4th quarter (an expected, “non-surprise” onside kick) since 2001 is 21.1 percent.

* Suppose that if the Patriots recover the onside kick, they take over at their own 45. If the Steelers recover it, they get it at the NE 40. In either case, suppose 2:32 remains on the clock after the onside kick.

* Suppose that if the Patriots kicked it deep, the Steelers would take over with 1st-and-10 at their own 27, which was their average field position on the 3 previous kickoffs. Assume 2:30 remains on the clock after the long kick.

Now, a look at the win probabilities and math involved in each case:

__Onside Kick__

NE Win Probability if Recover Onside Kick: 21.1%

NE Win Probability if Onside Kick Not Recovered: 4.1%

Estimated Probability of Recovering Onside Kick: 21.1%

NE Expected Win Probability of Onside Kick: 0.211*0.211 +(1-0.211)*0.041 = **7.7%**

__Kick It Deep__

NE Win Probability if Kicking it Deep: **6.6%**

So while the percentages are close, the numbers say that attempting an onside kick is slightly better than kicking it deep in this situation, by a margin of 7.7 percent to 6.6 percent in terms of expected win probability.

Another way to look at it is to use the same win probability numbers as above, but instead of assuming the average onside kick recovery rate, figure out what the break-even point would be -- at what recovery percentage would an onside kick be justified?

Doing this calculation yields a break-even recovery percentage of 14.7 percent. So if Belichick and the Patriots thought that they had at least a 14.7 percent chance of recovering the onside kick, attempting one was justified over kicking it deep, as stated above.