You see this is all absolute rubbish, the reason being that you never have enough of a sample size to make an ev decision.
You cannot use previous seasons due to personnel changes on both teams, conditions of play on the day of a game. So you never have an adequate sample to make a decision like this mathematically.
Until you prove otherwise, all of the "risk/reward" plays in football are decided by STATS and MATH. What else would you base them on? I agree that there are a TON of factors, but you still can account for a good amount of them, and a good amount really aren't of much concern.
I disagree with you regarding the application of equity from a poker standpoint compared to football. It is completely applicable. If you consider making tournament equity calculations of specific plays and their effect on the outcome of the tournament, it is actually very similar to football. The "factors you can't control" also exist in poker too. I mean, there is one very obvious factor you can't control in poker... the cards!
Let's just take a look at all of the factors that are necessary to take account of in the a 4th and inches situation:
The field position: we had it at our own 25
The game time: middle of the 3rd quarter
The game score: 16-10, 6 point lead
The opponent: Atlanta
That is the VERY basic. Compared to a poker decision, this would be like outlining a tournament situation where we are deciding whether to make a blind steal with a speculative holding. There are 6 players remaining, we are in the Cutoff position with 9T suited, we have 10 big blinds and the blinds are roughly 12 big blinds, and all fold to us.
The next step would be to estimate all of the outcomes.
In our football situation, the immediate outcomes are as such:
we punt and get (virtually) no chance at scoring points (on that drive)
we go for it and get the first
we go for it and turn the ball over
In poker, the outcomes are:
We fold and make a 0 EV play
We blind steal Allin and both blinds fold
We blind steal Allin and 1 blind calls
We blind steal Allin and both blinds call
Now you have to take a look at what the rewards/loss are for each outcome:
In football:
We Punt - no opportunity to score more points, likely gives ATL worse field position than going for it and losing.
When we convert - we have the opportunity to score more points, building a bigger lead, while we also kill more clock so that Atlanta has less time to make a comeback
when we fail - we lose the ball and give Atlanta great field position to score an almost automatic 3 and possibly 7
In poker:
We fold, and while we don't win or lose anything, we are going to have to make a move soon before blinding out and we just passed on one such opportunity.
We raise allin and both blinds fold, adding 1.5 big blinds to our stack
We raise allin and 1 blind calls. We either lose our entire stack, thus tournament, or we double up to 20 big blinds
We raise allin and both blinds call. We either lose our stack, or triple up to 30 big blinds.
Now, none of that yet includes any likelyhoods of such events happening. Thus, we need to include that, and figure out how to estimate such chances.
In football:
We need to first figure out how often we can expect to convert such a 4th down. You do that by looking at all the factors and making an educated guess. First, how has this team fared in the past on forth and short situations? In our case, this offense has been pretty similar since the 2007 season, so it would make sense to look at 4th and 1 stats since then. After you get that number, (say, 65%), you have to then adjust it to your opponent and situation.
We are having a ton of success running and passing the ball and Atlanta's interior defense isn't very good and hasn't been able to stop us yet. That would increase the odds of use making the first down, say from 65% to 75%. It's not an exact since, but it's the best method to go by.
So, we would calculate we have a 75% chance of converting and a 25% chance of failing to convert.
We might also want to look at what Atlanta averages on punt returns and the likely hood of them returning a punt for a TD. We could possibly get that statistic by looking at the how often a team, on average, in the NFL returns a punt for a TD and then adjust it to account for the ability of Atlanta specifically.
In poker:
We raise allin and both blinds fold: You estimate this based on how your opponent plays. If you, by observation, calculate that they are tight and will only call with the top 20% of their range (hands they could have), you calculate that they will fold 80% of the time. Together, that means that that both will fold 64% of the time.
We blind steal allin and 1 blind calls: 1 blind will call 16% of the time
We blind steal allin and both blinds call: Both blinds will call 4% of the time
Now we have to add in the reward/loss of each scenario and figure out how to calculate that.
In Football:
We convert: Given the 75% success rate, we need to figure out how often they will score points. The best way I can figure this is to look at the offense from 2007-present. I don't have the numbers on me, but lets say they averaged just over 3.5 points per drive in 2007 and 2.5 points per drive in 2008. By averages, you would think that 3 points per drive would make at least a good educated estimate, but given the game conditions (8 drives, 6 successful for 26 points, or 3.25 points per drive, while only 1 for 4 RZ efficiency) adjusting it to 3.25 points per drive would be reasonable.
We fail to convert: Atlanta was 1 for 2 (efficiency) in the RZ for 10 points, thus 5 points seems reasonable. The next (or previous) step would, again, be too look at their offense for the last couple years (or compare it to the league average, etc) and get a good estimate for RZ production and adjust it.
The final step would be to factor the reward/loss with the likelyhood of the events happening
In Football:
75% of the time we convert the 4th down and average 3.25 points on the drive or .75*3.25 = 2.44
25% of the time we fail and the Falcons average 5 points in the RZ or .25*5 = 1.25.
Subtract that from the success scenario and you get +1.19. That would be the expect value of making such decision. After this, then you have to compare that to the effects making/not making this play has on the game.
For instance, if we punt, what is the likely hood that they return the punt to essentially where it was punt from? What is the likely hood that they return the punt for a TD? What is the likely hood that they score on a drive with worse field position vs good field position (RZ)?
If we get the first down, what does scoring and/or killing more clock time mean for the game?
In poker:
64% of the time both blinds fold, we win 1.5 big blinds, or .64*1.5 = 0.96 big blinds
16% of the time the small blind will call. We will win 33% of the time they call and lose 67% of the time. So, (.16*((.33*10BB) - (.67*10BB)) = -.54
16% of the time the big blind will call it will cost us -.54 big blinds
4% of the time both blinds call it will cost us (.04*(.26*20BB)-(.74*10BB)) = -.09
Your equity is .96 -.54 -.09, or .33, thus, this play will net +.33 Big blinds.
The next step in poker is looking at the tournament equity. That is, your chips aren't money, and chips decline in value the more you have. You calculate your tournament equity using another equation using your chip equity and your stack sizes. Like in football, just calculation your equity or tournament equity doesn't account for everything. You might decide to pass up slight +EV situations if you think you don't need to take a big gamble if your opponents are really weak. Table dynamics also play a factor and so forth.
However, equity calculations are the most important factor in making your decision and can account for many factors. Football isn't any different.
