I hadn't seen this discussed anywhere on the boards, but I was drunk for 48 hours after the PSU game (because of the PSU game) so I may have missed it.

I've been thinking about this for a little while now, and my gut tells me that after Kevin Koger's TD catch (and the subsequent facemask penalty on PSU), we should have gone for the onside kick.

Hypothesis: A normal kickoff will result in the opponent starting, on average, about the 25 yard line. Because we got to kick from the 45 rather than the 30, Penn State's expected starting field position from a normal kickoff (touchback) would be only about 5 yards worse. However, an onside kick from the 45 would probably result in PSU's ball at about the 50. Or we get it back, and the chances of us getting it back are actually greater than the increase Penn State gets from 25 free yards.

In order to test my theory, I'm willing to do some math. I'm going to be using the expected points charts found at Advanced NFL stats. I'll be assuming that we'll always force a touchback if we kick off and that whether we're successful or unsuccessful when we onside kick, the ball will be placed at the PSU 45. My goal is to find how often an onside kick needs to be successful to be better than kicking off.

First thing's first: 1st and 10 from the PSU 20 is worth approximately -.5 points to us. It's obviously worth more to any offense facing our defense and thus the negative number would actually be bigger, but for the sake of the argument I'm going to be as conservative as possible.

1st and 10 from the PSU 45 is worth about -1.7 points when PSU recovers. If M gets the ball it's worth 2.2. So we can represent the equilibrium (i.e. the point where kicking away and onside kicking are equal in value) like so: -.5 =2.2y - 1.7(1-y), where y is the likelihood that the onside kick succeeds.

Solve for y to get: .307 so we'd only have to be successful a little over 30% of the time with these parameters to make kicking an onside kick correct. Given that surprise onside kicks are successful 60% of the time in the NFL, it seems like a pretty large mistake not to onside kick in that situation.

In fact, it's pretty easy to imagine a scenario where a team has a very good offense and a very bad defense (just try to imagine such a thing) where we'd only need to be successful 25% of the time or less. For example, if receiving the ball at their 20 is worth a full point for PSU and recovering an onside kick is worth 2.5 for them and 3.5 for us*, the equation would look like: -1=3.5y-2.5(1-y). Then we'd only need to be successful 25% of the time to make going for the onside kick correct.

Add to all this the fact that in this particular game we were down by multiple scores and would have wanted to increase variance, onside kicking in that spot is an absolute no brainer.

*Numbers pulled from my ass