# Down 14 And Going for 2

Submitted by ikestoys on October 4th, 2009 at 10:11 PM
Disclaimer: This is not an attack on RichRod or any specific coach. This is more of a criticism of the 'common knowledge' of upper level football.
The situation: You are down 14 and probably only have 2 possessions left. Obviously, it will take two touchdowns to get back into the game. My question for you is, what combination of 2 point and 1 point conversions should you take to maximize your chance of winning the game?

Let's start off with a few assumptions. According to this rivals article, the average 2pt conversion rate in the NFL is 44%. I'll assume that it's about the same for CFB and that our team's conversion rate will be about the same in whatever specific situation we're in. We'll assume that we can estimate a PA kick as a sure thing. We'll also assume that we have a 50-50 chance of winning in OT.

So working with these assumptions, what is the optimal combination of 1pt/2pt tries?

Kicking 1pt tries only
This one is easy. Assuming we get 2 TDs to come back, taking 1pt each time will give us a 50-50 chance to win

Going FTW!
In this situation, we get the first TD and take the 1pt. On the second TD, we 'man up' and go FTW BABY! Our chances of winning are equal to the chance of converting obviously, so 44%.

Best Answer
In this situation, we'll go for 2 after the first TD. If we convert, then we'll kick a 1pt try. If we do not convert, then we'll go for 2 again.

This is a slightly more complicated calculation, but here we go:

1.) 44% of the time we make the first 2pt conversion and go on to win the game.
2.) (.56)*(.56) =  31% of the time we miss both 2pt tries and lose despite making two TDs
3.) (.56)*(.44) = 25% of the time we miss the first but make the second 2pt. This ties the game and we go to overtime.

So what is our final equity? It is:

.44*1 + .31*0 + .25*(.5) = .57 or 57%

A quick explanation of this equation. We basically multiply the probability of an event by the outcome of the event. So 44% of the time we win (1), 31% of the time we lose (0) and 25% of the time we go to OT with a 50-50 shot (.5).

Now why isn't this done in the real world? Well part of it is that some of our assumptions aren't known. However, mostly it is coaches covering their ass. No one gets criticized for taking the safe route to force OT, only to lose. If you go for 2 twice and don't make it, you'll be torn apart in the press. Not to mention that football coaches don't focus much of their time on equity calculations.

The common belief of kicking 1pt to tie or going FTW! at the end with a 2pt conversion is clearly wrong, even if it is most commonly done.

# Comments

Oh and I hope I didn't make any stupid math errors for once :)

I am sure about the result however.

... if things are statistically independent. That means that if you miss the first 2-pointer, the odds don't change (i.e., they don't get worse, due to a more desperate situation) for the second one.

The prior statistical outcomes are outweighed by the significance of the game's actual situational factors.

It isn't done more because the odds are against you when you are attempting it. To keep the team as motivated as possible, one doesn't push the odds until one has to. There is also momentum to consider, and when Michigan made up the 14 points deficit, all the momentum was on their side. Maybe you go for two after the second touchdown in regulation, and play the odds. But, again, with momentum on your side maybe you take it to overtime with the belief that your offense is going to score a touchdown.

I looked for evidence who won OT more, the tier or the team tied, but found nothing about it. Do you have some you can put up?

I am sure however that the momentum loss after missing a 2pt conversion explanation is not based evidence. I don't think a team will be much less motivated to score a TD down 8 compared to 7, and I'm sure you won't be able to prove it.

This is really interesting, and what I think would probably be how Tony LaRussa would coach football.

What would be most interesting about this is the fact that the 2 pt percentage would likely change in some statistically significant way if coaches employed this philosophy. Seems to me that more 2 pt conversions would be attempted, because teams trying to come back score that first touchdown, only to fall short on the second one fairly often. Wonder what that would do to the percentages and how it would change the way people coach.

My guess is most coaches will still go for overtime, though.

I think that's a more common mistake. We think in terms of the simple scenario, and don't give enough weight to the multiple-step possibilities.

In regards to the conversion likelihood, I heard many years ago in the upper 30s and a few years ago about 40% for CFB.

It would take quite a complex formula to model all the possible situations here. As the game becomes more and more complex, the formula for solving the game also becomes more complex. This is why tic tac toe is simple to solve and connect four is more difficult.

The point is that we can draw conclusions about more complex games from studying simpler ones. Here, in the simplifyed football game, we have a huge (7% is huge) edge by going for it twice rather than kicking twice. Does this translate to the more complex game? I'm not sure. My gut says yes though fwiw.

Oh, and I don't really blame coaches for not doing this as it's both counter intuitive and seccond guessable.

We're talking about late game situations here. You've just scored a TD and there is only enough time for one more possession if you can get the ball back.

This is valid at more than 2 possession btw, just much simpler

I think the 44% chance of conversion is contingent on having a threatening run game

Not that you were specifically applying this diary to the most recent game of ours, but the similarities are striking, and I'm just sayin' for sayin's sake

Road or home game? Who has the momentum? Did any key players get hurt and will not be around for OT? Are you a passing or running team and what is the weather? Do you feel lucky ... punk?

It depends on the specific circumstances.

I won't dispute that there are other variables at play.

I will submit that for the most part, coaches do not even consider doing this, and that other unknown variables will cancel out over time.

Hopefully not too tangential from this discussion, but why don't we have Denard holding kicks instead of Zoltan? Maybe it's in the works and he's just not reliable enough to use in games, but Denard's the perfect guy to have there if you ever want to run a trick play off a FG/PAT attempt. Only bringing this up here because the idea came to mind at the end of regulation, when I thought we might go for 2 instead of taking our chances in overtime.

"Hopefully not too tangential from this discussion, but why don't we have Denard holding kicks instead of Zoltan? Maybe it's in the works and he's just not reliable enough to use in games, but Denard's the perfect guy to have there if you ever want to run a trick play off a FG/PAT attempt. Only bringing this up here because the idea came to mind at the end of regulation, when I thought we might go for 2 instead of taking our chances in overtime."

Many teams use the punter as a holder, probably because he's assumed to have the best hands at handling a two-hand-snapped ball. He also gets lots of practice in with the snapper, which would take time away from a QB's practice day with the offense. This assumes the LS and short-snappers are the same person.

Actually, though, I don't think it really matters whether it's a punter or a QB athletically - whoever is non-flaky enough to call for the snap properly is your guy.

I'm not saying there's anything inherently wrong with using a punter. But holding the placekick doesn't seem like the kind of thing that would take away a significant amount of time from working with the offense (especially if you're a quarterback that mainly works out of the shotgun). Hell, you could even still use Zoltan if it's wet and you need sure hands, or if Denard has been playing on that drive. But the drastic change in risk/reward for a trick play between using your typical punter/backup QB and using Denard seems too enticing to ignore.

I mean, in a fake FG situation where your typical punter/backup QB just gets a first down, Denard is taking it to the house. In a fake PAT situation, Denard would beat the D to the corner or make a cut back in situations where your typical punter/backup QB gets tackled. Granted we'd probably only use this maybe once or twice a season, but if holding the placekick is as little work as I think it should be, then it might be worth the effort if it results in a momentum changing play against Penn State or OSU.

Statistics aside...in hindsight...it would have been fun to see them go for 2 after the last TD. MSU's defense was tired and reeling (as evident by their blown coverages....then last TO and subsequent blown coverage)

Tate was hot and playing out of control crazy good...Big Mo was on the Wolverines side... Sparty moved the ball vs. Michigan's D all game and they have a very good kicker....

Normally RR is a very aggressive coach...I wouldnt have faulted him for going for the win right there....

but he didnt, and Michigan lost....

and hindsight is still 20-20, last time I checked anyway.

Coaches follow this chart? It says down 8 with 3 minutes left, go for it if you get in 38% of the time, which sounds about right.

Well I guess some people think about it, but coaches don't have the balls to use it.

If your down eight with three minutes to go yo go for it no questions asked. If you kick the extra point you still need a FG to win same as if you don't make the two point try. Yet if you make the two pointer the game is tied.
There was no sense in going for it down 14 as two TDs with EP ties the game. Going for it on the first TD would be stupid as if you don't make it you have no option on the second. Kick the EP and make your decision after the second TD. Unfortunately, Tate was gassed at the end of the second drive. Which made the decision easy for RR. Now if we had a TO to use it may have been different.

You're wrong. You said something like this after my explanation in the other thread. I can't tell what you're saying exactly, but it sounds like you're confused. Somehow you're talking about field goals. Field goals don't even come into play in this scenario. We're talking about going for two after you have just scored a TD to go down 8.

You're down by 14 points. You score a TD which is worth six points. You are now down by eight points and have a decision to make. This is the decision we are talking about.

The correct decision is to go for two points.

I can see where ikes title may be confusing. It probably should be "Down 8 and Going for 2." Read the OP again, though. It's pretty thorough.

He was saying that 14=8(?), I think, and that to top 8 you really have to score twice (or roll the dice going for two).

If you don't make it after the first TD, you could tie it after the 2nd with a 2pt conversion. That's your option. The information here was that there was a better chance of going for it twice and making it once than going for it twice and missing it both times.

going for two after the second TD is the worst percentage play of all

(worse than going for two after first TD or kicking XP after both TDs)

The flaw within the generic math beyond what is noted previously would seem to be that it really should use specific numbers for the specific teams i.e. to get closer to the true "odds", Michigan's % of conversion against similar defensive teams, and the specific defensive teams % against similar offensive teams would be used.

It is a specific scenario after all: e.g. Delaware State does not have a 44% chance of converting 2 against Alabama.

The pure math you outline would play out if you think that on each given attempt that you have at least a 30 percent chance of converting in that situation.

I don't know if we can get enough real data to know if 30% would be likely/achievable for the specific scenario of last weekend. How many >3 yard runs did we have versus

In a purely mathematical world, this would work perfectly. Take the highest probable conclusion, and you're guaranteed over an infinite time period that you will always come out ahead.

However, in the human and risk averse atmosphere, this won't happen. The easiest example would be with money. If I asked for \$100,000, and told you there was a 57% chance that I'd give you \$200,000 tomorrow, Math says you should always do it. After all, \$100,000*.43+ \$200,000*.57 - \$100,000 = +\$14,000. You'd come out \$14,000 in the long term if you took every such investment. However, you're constrained by your resources. You don't have many \$100,000 bundles lying around to risk. If you don't come out ahead in the short term, you may not have another \$100,000 to risk. In the long run (>30 tries) it will even out, but only if the variables remain unchanged and the percentage was valid to begin with. That is, if this is available every single day at the exact same rate, and assuming I'm notsetting up a Ponzi Scheme.

You can apply this to coaching as well. Sure, in the long run doing this will cause you to come out ahead, but how many times is this applicable? 2, maybe 3 games at most in a season? If you're a coach with 3 such opportunities, and you fail 3 times, chances are that you aren't around long enough for the law of averages to come into play. You also need to find the true percentage of 2 point conversions, of a prepared O vs. a prepared D, how many aren't in garbage time, how many aren't against overmatched opponents, and so on.

After you do all of this, 99% of coaches will disregard this information and go with the chart. Why? Because there will be less fallout if they go into OT and lose (they came back from 14 down remember?). If they go for the win and lose, they'll be second guessed by everybody.

/math

The chart says go for it!

And your example is ridiculous. We don't have a finite number of games to play. We should be trying to maximize our chances of winning each one.

It's easy in hindsight to proclaim that we should have gone for the 2 point conversion. If he had gone for the 2 point conversion and failed, we'd all be screaming about that decision. Luck was just not on our side last Saturday. The one thing that is very satisfying about this season so far is the fact that I was extremely confident that Tate and the boys would make it a game at the end. That is a great feeling after the hopeless slump that I felt for most of the season last year. This season has been great fun, even with a loss tossed in.

There are 12 games in a season. That's a finite number of games to play. Of those 12 games, we will face 4 tomato cans, leaving 8 games where this could theoretically be applied.

If a coach risks it and loses, his chances of getting fired probably go up. If a coach is fired before the law of averages catches up, he's pretty much fucked isnt he?

Now, if he plays it safe and goes for the PAT, he can suffer equally bad OT luck and everybody will credit him for being a gamer and fighting back. He gets more chances to go into OT, and the law of averages will probably come back for him.

In the end, your strategy gives an incremental increase in winning percentages, but probably an unacceptable amount of risk in job security if it goes wrong. If you're interested in this subject, I'd recommend taking a class on how investment returns are calculated, its much of the same principle.

The vast majority of the attempts are going to be straight FGs and XPs, and if Robinson mishandles the snap even a few times over the course of a season, it completely eradicates the benefit of having him there. If (as I suspect) he has never done this in his football life in games that mattered, it's not the sort of thing one just picks up casually.

Let's let Denard try to master one position before giving him another.

2 teams 2 possible outcomes = 50/50 chance to win.

/sarcasm

I favor going FTW after 2nd TD. If at home, kick the PAT and go to overtime.

First, I have always had a problem with those who argue for going for two and/or going for it on fourth down for HS and/or college teams based on NFL statistics. "Let's start off with a few assumptions. According to this rivals article, the average 2pt conversion rate in the NFL is 44%." Followed later by: "44% of the time we make the first 2pt conversion and go on to win the game." Um, no. 44% of the time an *NFL team* makes it and goes on to with the game. You're dealing with different field dimensions (and by that I mean hash marks and goal-post width), different rules, and different maturity levels of players, both physically and mentally.

Second, what the math fails to take into account is the psychological impact of making/not making it. If you go for a 4th and 1 from your own 25 and don't make it in the NFL, professional football players are much more likely to block the missed attempt out of their minds and play ball. In high school, you do that and you are much more likely fucked. On the other hand, a QB sneak on 4th and inches is way more likely to be successful on the HS level than the NFL level, mostly b/c the DL guys aren't as quick off the ball and also b/c the QBs are more like regular ball players compared to the rest of the guys on the field.

I think what a successful coach does is to learn the mathematical probabilities using statistics gathered at the appropriate level of football (NFL stats for NFL coaches, college stats for college coaches, etc.), but also then assesses the psychological state of his team at the time and their likely psychological reaction to potential outcomes, and finally his instinct.

I, for one, would have kicked the first PAT and then gone for two at the end IN THIS PARTICULAR SITUATION. We had them reeling, totally on their heels, and I believe you take advantage of momentum as soon as possible. I think momentum goes out the door b/w the end of regulation and OT b/c of the time players and coaches have to regroup (officials regrouping, time b/w periods, coin flip, etc.). I don't think players are going, "We've got them reeling." I think they're going, "Okay, now we've got overtime." It's almost a true "reset" situation.

After the 2nd TD, I'd have gone for 2. Unfortunately, he was completely spent. That kid left everything on the field just getting those 92 yds down the field to score. DRob just wasn't an option (for obvious reasons).

If Tate had even a shred of energy at that point, and we went for 2, I wouldn't have just trusted it to his arm. MSU was reeling at that point, so I might have lined up in some kind of formation that could have gone either way to create confusion. Maybe put DRob in as one of the RBs, with Brown or Minor in to throw a block, or take a pitch on an option. Make Sparty beat DRob or Brown to the corner (lots o' luck). But, Tate would have to take the snap in either case. A confused Sparty would have to be looking for anything and everything at once.

Anyway, even if it were a high probability under normal circumstances, this particular situation was anything but. We took the "safer" option of playing for OT to give Tate a rest. It was the right move.

...I just said I would've gone for it.

In hindsight, we probably had a better chance of winning going for 2 at the end of regulation.

At the time, I wanted us to go for 2, but I wasn't disappointed that we didn't.

You're only saying that because we didn't win--not that you would have gone for two, but that we had a better chance going for two. No matter which option we take, we're going to lose somewhere bewteen 40 and 60 % of the time once with score the second TD. Unless we have a >50% chance of making the two point conversion, in the driving rain, with our backup center, and an exhausted freshman QB who has made some questionable decisions, we should go into overtime.

I'm not saying Tate's drive wasn't amazing. I'm just saying that going for two after the second TD is the worst option of the 3.

You can't compare this scenario with what happens in the NFL because it is not an apples to apples comparison. The NFL is sudden death, so going for 2 might make more sense because you control your own destiny (at 44% if the number cited above is right - I thought it was higher) vs. leaving it up to a 50/50 flip of the coin (since the majority of NFL OT games are won by the team that wins the toss).

It's a different equation altogether when each team gets the ball, and it weighs more heavily in favor of taking the tie since you will have an equal opportunity to win in OT.

Under the specific circumstances of this game, OT probably made rational sense - MSU was reeling and had to have felt the heavy weight of history slamming down on their little brotherly backs.

What I think the rational choice failed to take into account was that our defense was dragging - we'd have been better off keeping them off the field. And, win or lose, if you go for it, I think it sends a great message from the coaching staff that tells the players how confident they are in their ability to make the critical play when it matters most. I think players (and recruits) love to see it when a coach shows some nut.

You never truly control your own destiny - the other team has something to say about that. If you're evenly matched (and you wouldn't be in OT if you weren't) then both sides have an equal chance in OT, 50%. This is regardless of the format. Granted you might not be performing equally at the end of the game, but I think this is rather overblown except in really lopsided situations.

And going for 2 at 44% will never make sense vs taking a sudden death coin flip at 50%. At least if your objective is to win (as opposed to post-game PR or whatever.)

Anybody see the end of the Ball State/Toledo game? Ball scored a TD to get within one (about 40 seconds left). They went for two and made it. Up one, they gave up a touchdown and lost (Toledo went for and made a 2 pt. conversion).

If Michigan had come out on top in OT, I don't many of us would be questioning the decision to not go for two. It was amazing that we had come back at all in this game, I think Rich did the smart thing and gave the team their best chance to win.

Put yourself in RR's shoes at the time of his decision. The running game wasn't working for nearly 4 quarters and Tate appeared gassed to the point of collapse. No timeouts to give Tate a rest and very little time to choose a good play for a 2-pt conversion. The offense just rolled down the field twice in a row gaining 160(?) total yards, so, 25 yards shouldn't be a big deal in comparison. Kick the PAT, give Tate time to rest and feel *extremely* fortunate that we get to play an overtime. Running another play for 2 points was not the best choice, IME.

He was gassed most of the last drive, yet he still had to suck it up and make plays, which he did. Also, the last TD was on 3rd & 8. If that pass was incomplete, would he have been too gassed for the 4th down play? If RichRod had called for a 2 pt. convo, Tate wouldn't have thought or said, "Coach, I'm too tired."

I'll buy the statistical or strategic arguments, but not the conditioning one. If it's that much of an issue, take a delay penalty and then try it from 5 yards back, just like they did in the Indiana game.

If fatigue and momentum were an issue, then why did Dantonio elect to go on defense first for the OT? Because strategically it was the right move. Forget the last play, suck it up if you're tired, and get it done.