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 4thdown 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 yardline.
The other main assumption is that a successful recovery by the kicking team would result in a drive beginning at their own 42 yardline, and recovery by the receiving team would result in a drive beginning at their opponent's 42 yardline (58 yardline in absolute terms).
Down to business:
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) = .682.60 
1.93 
Kicking Team Net Expected Pts (Normal) 
1.90 
Advantage of Normal 
.03 
(please allow for rounding adjustments)
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 4thdown 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 yardline.
The other main assumption is that a successful recovery by the kicking team would result in a drive beginning at their own 42 yardline, and recovery by the receiving team would result in a drive beginning at their opponent's 42 yardline (58 yardline in absolut terms).
Down to business:
For an onside kick, the kicking team's expected points would be:
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