# Empirical Analysis of Onside Kicks

Submitted by Laveranues on October 7th, 2010 at 9:44 PM

In response to the recent discussion of onside kicks, I wanted to look at some empirical data on expected yields.

The main source of the empirical data is from The Mathlete's most recent diary on 4th-down decision making.  In that post (I don't have the link, but if you're reading this, I'm sure you read it), The Mathlete provided a graph of expected offensive point yields for a given starting field position.  That graph showed an approximately linear equation with an (approximate) expected point value of .75 for drives beginning at the offensive team's own 1 yard line and an (approximate) expected point value of 5.0 for drives beginning at the opponent's 10.

Anyway, the resulting equation - and main assumption - is:

Expected Points = .75 + (Starting Position - 1) * .0477528.

Here, starting position is 1 - 99, with 99 being the opponent's 1 yard-line.

The other main assumption is that a successful recovery by the kicking team would result in a drive beginning at their own 42 yard-line, and recovery by the receiving team would result in a drive beginning at their opponent's 42 yard-line (58 yard-line in absolute terms).

For an onside kick with a 25% recover chance, the kicking team's expected net point yield would be:
 Kicking Team Position 42 Kicking Team Probability 25% Kicking Team Expected Pts From Own 42 2.71 Kicking Team Net Expected Pts .68 Receiving Team Position (Onside) 58 Receiving Team Probability (Onside) 75% Receiving Team Expected Pts From Opp 42 3.47 Receiving Team Net Expected Pts 2.60 Kicking Team Expected Pts (Normal) 0 Receiving Team Position (Normal) 25 Receiving Team Probability (Normal) 100% Receiving Team Expected Pts From Own 25 1.90 Kicking Team Net Expected Pts (Onside) = .68-2.60 -1.93 Kicking Team Net Expected Pts (Normal) -1.90 Advantage of Normal .03

So, yeah.  That works a lot better in Excel, but hopefully you get the point.

A few other scenarios from Excel:

• If the kicking team has a 26% chance of recovery, as Brian cites in his post, there is no advantage to a deep kick (-1.90 expected points onside, -1.90 expected points normal).
• If the kicking team has a 25% chance of recovery, but the normal kick results in a drive starting at the receiving team's own 32 (maybe more likely with our kickers), there is a predicted .30 point advantage (-1.93 vs. -2.23) for an onside kick.

One more thing:  as per the borrowed data, this assumes an average offense and defense (I've employed a DENARD Constant in my spreadsheet, but it is difficult to represent here).

In conclusion, this is as much an appeal to The Mathlete (and others) as it is an effort at meaningful contribution.  I have no background in math or statistics, so if there are massive logical flaws in the above, please feel free to rip me in the comments.

For an onside kick, the kicking team's expected points would be:In response to the recent discussion of onside kicks, I wanted to look at some empirical data on expected yields.
The main source of the empirical data is from The Mathlete's most recent diary on 4th-down decision making.  In that post (I don't have the link, but if you're reading this, I'm sure you read it), The Mathlete provided a graph of expected offensive point yields for a given starting field position.  That graph showed an approximately linear equation with an (approximate) expected point value of .75 for drives beginning at the offensive team's own 1 yard line and an (approximate) expected point value of 5.0 for drives beginning at the opponent's 10.
Anyway, the resulting equation - and main assumption - is:
Expected Points = .75 + (Starting Position - 1) * .0477528.
Here, starting position is 1 - 99, with 99 being the opponent's 1 yard-line.
The other main assumption is that a successful recovery by the kicking team would result in a drive beginning at their own 42 yard-line, and recovery by the receiving team would result in a drive beginning at their opponent's 42 yard-line (58 yard-line in absolut terms).

For an onside kick, the kicking team's expected points would be:

One thing I have been wondering is if the team just completely stopped practicing regular kicks and spent all their kick-off practice working on on-side kicks.  That should increase the recovery rate, since other teams don't spend as much time on it.(they would for the week before MIchigan though)

I know it would decrease practice for the return team, but the returns have already been mediocre and it hasn't slowed down the offense.

The worse the kicker, the worse the starting field position on a regular kickoff, and presumably the worse the chance of onside recovery.  Unless we have idiot-savant kickers.

Not necessarily a worse chance of recovery.  Our kickers clearly lack the leg to put the ball past the 10 yard line consistantly.  That doesn't mean they can't accurately place it 15-20 yards away, with a good bounce.

You should note that there is a major difference in the success rate of onside kicks when they are not expected compared to when they are.  Expected onside kick are recovered at about a 25% rate while surprise onside kicks are recovered more than 50% of the time.  You seem to be using the former for your calculations, but it's the latter that are up for debate.

I was presenting the argument for doing it all the time or very often, ergo no surprises.  If it were 3 out of 10 or something, it's hard to say if it would be a surprise or not.  Maybe adding the expectation would also improve the expected field position (defense) of a normal kick.  Too many permutations.

I think the key to onside kicks is to do them when they are unexpected.  I forget which team I was watching but the did one to open the second half, worked pretty well too because it caught the receiving team completely off guard.  If you do them all the time, the other team will expect them however, given the kicking game the field position might not be that much worse if the receiving team recovers.

Worked for Payton and the Saints in the Super Bowl.  I agree that timing is everything when it comes to a high success rate for onside kicks.

I wouldn't be surprised to see some teams try an onside kick to start with the ball in both halves, since lets face it, we're going to score whether we start from our 1 or the 50.

I mean if there is less than two minutes in the game, your team just scored and needs either a field goal or touchdown to win there is no surprise what is coming next.  I think a situtation like that is where an onside kick is expected and more likely to fail.  However, noone would expect an onside kick when a team is barely ahead and would like to pad on that number.

I think the same thing can be said for going for it on fourth down.  But then again, 4th down is one of my peeves because everytime a defense holds on third down the announcers will say, "Well they're gonna have to punt".  Nothing in the rules says that.

I would much rather see a coach go down in flames trying win rather than doing the safe thing by trying not to lose.

vs low variance.  The stronger team should want to minimize large swings like attempting an onside kick.  This strategy would work better to give an inferior team a chance for consecutive possessions and possibly points.  I won't try to argue our current status in the big ten.  But given that it works better when a surprise, lets save this for tOSU.  The other situation to use it would be the Oregon example where there is less to lose if you fail to recover.  On the other hand, we should prepare to defend the [incredibly surprising] onside kick, particularly when winning late-ish.

Question:  Are we witnessing a shift in coaching philosophy regarding fourth down attempts and onside kicks?  Will we?