Going for 2 pt. 2

So, following up on my previous post, there's actually a good deal more you can do. Down by 5 points after a TD (11 before), you should go for 2 just like in the down 8 (14) case, or actually even a little more often. Making helps you out in the case where you score two field goals, and the only place it can hurt you, if they score a field goal more than you later on, devolves into the 8 (14) case as previously discussed. So other than the tie-the-game-right-now I'm-down-by-2 situation, this is actually just about the biggest no-brainer you can get. Aaaaaaaand... coaches go for one all the smegging time.

Indeed, things are more or less simpler than they seem. Sure, you have to account for safeties, too, in reality, but for the most part the biggest unknowns are the pace of the game, and the chances of your particular teams making 2 point conversions against the opposing defenses. The likelihood, given the teams and the time remaining in the game, of touchdowns getting scored vs. some multiple of field goals, is also helpful in some cases, if you're looking for precision.
But there is a principle, which I'm going to call the principle of cancelling scores, which nullifies most of the crazy complexity you have. Basically, the principle is this: all that matters is the difference in number of touchdowns which ou score, and which are necessary - i.e. if I score 5 more touchdowns and you score 4, this isn't really significantly different from me scoring one and you scoring 0 - there are a few little exception with ordering, but past the first or second, things aren't really going to make a diference; certainly the effect of the extra scores isn't going to be small, and it actually favors you, if many scores are likely, to pick the option which will maximize your expected points (in such a case, offense is pretty good, so it might actually be the 2 point conversion; but knowing the actual league numbers... it would probably be really close to a push, which swings the right now differential to being more important again). Combine this with the knowledge that an uneven number of total touchdowns per team is basically game, unless there are two FG for a TD and a missed conversion (or three FG for a TD of any kind, in which cae, again, going for one or two is irrelevant; I suppose you can get something like 5 FG for a coupe of TDs where conversions will make a difference, but this is going to be really rare - just like safeties, which also mess thing up).
So you can make a chart, but you know, the chart should be dynamic and change from week-to-week, and even somewhat within the coure of a game (i.e. at the beginning of a game, the chance of 2 FG vs one TD is a lot etter than at the end of the game, and on something like down 18, it becomes even more clear that you ought to be going for two the later in the game you get, etc. etc.).

So but okay, let's go with the easy things first. Down (after scoring the TD) 8, 5, or 2, go for 2. Down 14, 7, 3, tied, go for one. Down 6 or 9, most normally go for 2 (unless a bevy of field goal is way more likely than more TDs and it's early), down 4 you way most normally should go for 1. Down 10, you go for 1 if it's at all early, 2 if it's late (just how early or late has to do with your chances of having enough time to score more than one TD (that is, more than 1 TD more than the opponent)). Down 12 is a clear 2, and down 13 it's very unlikely to matter but there's very little reason to take 1. Down 1 is an interesting case, actually. Tie or take the lead? It's very very dependant on the amount of time left, and teams' relative abilitie to make drives in that amount of time. With no time left, you go for two iff your chance of making it is greater than your chance of kicking a PAT (say 99.5%) and then winning in overtime (almost certianly extremely close to 50%). With *slightly* more time left, you should go for 2 more often. This is counter-intuitive, but if you think about it a bit, it makes sense. If your opponent is able to drive the length needed to make a field goal, you are going to lose either way. But if you miss the 2PT conversion, then you are going to onside kick, and you have another chance to drive down to range and outright win yourself. So you lose the chance of them driving the field in EITHER case, but gain back the chance of recovering an onside kick they know is coming and getting down to score again in the 2 point case; for some amounts of time, and depending on the time out situations, the wind, your faith in yoru kickers, and the teams' relative skills, there's going to be some convergence there. Get to even MORE time out, and you should eventually revert back to going for 1, particularly in any situation where you'd be likely to get the ball back again once after they would score - if for no other reason than you want to be able to match a potential FG with one of your own. But then if you go to *early* in the game, it shifts back toward the go for 2 mode, because if they score once more, it gets you toward that classic 14 point deficit I mentioned last week, where you go WAY for 2. Is that enough to go for 2 most of the time here? It's really hard to tell, actually - this is one of those closest decisions, and expected value is likely going to be your friend, at least very early on.

If you already have a lead... there are no brainers at up 1, and 11, where you should go for 2, and up 2, 3, and 8, where you go for 1. There are a lot more close calls here, though. Up 4, going for one forces them to go for 2 on their touchdown, and lets you get a field goal to tie even if they make it. Going for 2 helps you if you get the chance to go for 2 again (and make both...), or if they end up scoring 2 field goals on you. Ultimately, that's normally fairly flimsy ground to walk on, so you should most certainly take the 1. Up 5, going for one matches two field goals, but going for 2 beats two FG and matches a TD, so go for 2. Up 6 is the sure-fire go-for-one scenario we looked at last time, where you need almost a 60% success rate for the 2PT attempt to be worth it even WITHOUT allowing the possibility of 2 FG... Up 7 is interesting. Taking one makes THEM go for 2 in reply, which they'll get mroe as the success rate goes up. Going for 2 means they need 2 scores off the bat. Basically this just boils down to whether the success rate is more than 50% or not in the simple case, and an interesting trade-off balance between your success rate and theirs in the more complicated, realistic case. Up 9 and 10 you more or less go for 1, at least until the percentage gets a bit north of 50%. Up 12, go for 1 early, where the field goals are much at all likely, go for 2 late, and know it doesn't matter much (making 2 gets them into their 14 point deficit sweet spot). You can keep going on and on (up 14, 15, and 16 are pretty clear go-for-one scenarios, etc.).