2 pt.conversion confusion

2 pt.conversion confusion Does anyone know why the falcons went for a 2 pt.conv. vs. the rams 2 weeks ago up 32-17 with under 2 min to go in the 4th qtr?

[QUOTE=vll BIGGZ llv;34238]Does anyone know why the falcons went for a 2 pt.conv. vs. the rams 2 weeks ago up 32-17 with under 2 min to go in the 4th qtr?[/QUOTE] If they kick the extra point, they go up 16. If they go for 2 and get it, they're up 17 (two TDs and a FG) and if they don't get the 2, then they're up 15. There's no competitive disadvantage with only 2 minutes left in the game to only being up 15 vs. being up 16, but there is something to gain in being up 17.

That is so wrong.

Also, why did PSU go for 2 down 6 with one minute left. Cost me the over. Also stupid.

Disagree [QUOTE=IrishTim;34239]If they kick the extra point, they go up 16. If they go for 2 and get it, they're up 17 (two TDs and a FG) and if they don't get the 2, then they're up 15. There's no competitive disadvantage with only 2 minutes left in the game to only being up 15 vs. being up 16, but there is something to gain in being up 17.[/QUOTE]They would have to make two 2-pt conversions instead of 1. While the chart that was developed by Dick Vermeil in the early 70's and used by most coaches would agree with you, most modern computer generated charts do not.

[QUOTE=bkeiller;34247]They would have to make two 2-pt conversions instead of 1. While the chart that was developed by Dick Vermeil in the early 70's and used by most coaches would agree with you, most modern computer generated charts do not.[/QUOTE] This is correct. The charts developed by Vermeil and others were way too crude to give accurate strategies (AFAIK, they left out time remaining as a parameter). In this case, it is possible to give some very close approximations to the estimated win % in both cases. I won't bore everyone with the math, but if you assume a two pt successful conversion rate of 44%, late in the game, kicking the extra point when up 15 is better than going for two. This is also confirmed by computer generated solutions using dynamic programming models. Actually, going for two later in the game when up 15 gets to be a worse choice (i.e requires a higher conv rate to be optimal) than say in the 3rd quarter.

I'll defer to ComptrBob who is one of the smartest guys around. I haven't looked at the data (I hardly bet the NFL at all) so am in no position to discuss the validity, but was simply trying to at least explain the square logic of going for 2 there. I wouldn't even know the 2-pt conv. % without looking it up, but I assume the coaches were thinking "let's make this a 3 score game". And CB, if you're ever bored on a rainy day, feel free to "bore" us with the math. :)

[QUOTE=IrishTim;34252] And CB, if you're ever bored on a rainy day, feel free to "bore" us with the math. :)[/QUOTE] Ok, remember you asked for it ... I'm sure with some thought, it is something that you should have no problem deriving ... Anyone, please feel free to check the logic and math. I did this hurriedly on the back of an envelope. Goal: maximize Team A's win probability where Team A is up by 15 pending the XP. Assumptions: Let P2xA be the two pt successful conversion rate for Team A. Let P2xB be the 2 pt rate for Team B (opponent). Assume the 1 pt successful conversion rate for both teams is 98%. Prob Matrix for Team A [B]Result after XP .... 1ptXP ..... 2ptXP[/B] Up 15 ... 2% ....1-P2xA Up 16 ... 98% ...0% Up 17 ... 0% ....P2xA Now Team B will [B]try to tie [/B]Team A in the following manners (not very likely or optimal at all to try to win outright), better to tie and go to overtime.: Prob Matrix after Team A XP for Team B [B]Result after XP .... options[/B] Down 15 ... 1TD + Onside kick(Succ) + 2ptXP + 2ndTD + 1ptXP to tie Down 16 ... 1TD + Onside kick(Succ) + 2ptXP + 2ndTD + 2ptXP to tie Down 17 ... 1TD + Onside kick(Succ) + 1ptXP + 2ndTD + 1ptXP + 2nd Onside(Succ) + FG to tie Now let's make the assumption that the common probabiity term for "1TD + Onside kick(Succ) + 2ndTD" (defined as PBc) is indeed almost the same for all 3 cases. Probably a very good assumption since this is central to being able to tie the game with little time left. Any failure will almost certainly result in Team B losing the game outright. Let P15B be the probability of Team B, down 15, tying, P16B and P17B similar definitions. Similarly, let P1A be the win % for Team A trying the 1ptXP and P2A be the win % for trying a 2ptXP. Further let's assume that once the game is tied, the win % for each team is 50%. So: P15B = PBc * P2xB * 98% P16B = PBc * P2xB * P2xB P17B = PBc * 98% * 98% * PB2nd_onside * PBFG Now let's put this stuff together: P1A = 2% *(1 - 50%*P15B) + 98% *(1-50%*P16B) and P2A = (1-P2xA) *(1 - 50%*P15B) + P2xA *(1-50%*P17B) Simpifying, we get: P1A = 1 - 0.01*P15B - 0.49*P16B but P16B is only a factor of P2xB smaller (roughly 44% say) than P15B so the dominant term in the equation above is 0.49%*P16B also P2A = 1 - (1-P2xA)*50%*P15B - P2xA*50%*P17B Now P17B is extremely small compared to P15B because a 2nd onside kick might be a 30% prob and a third score of a FG is maybe a 1% prob since almost all time would be gone. (This is common sense, a 3 score cushion is virtually insurmountable) Thus P2A approx = 1 - 0.5*(1-P2xA)*P15B and P1A approx = 1 - 0.49*P16B so to get the best win % we want to identify the smaller (case 2 vs case 1) of 0.5*(1-P2xA)*P15B vs 0.49*P16B Divide each by P15B to get: 0.5*(1-P2xA) vs 0.49*P16B/P15B or 0.5*(1-P2xA) vs 0.49*(P2xB/0.98) Assume P2xA = P2xB = 44% and we have 0.5*0.56 vs 0.49*(0.44/0.98) or 0.28 vs 0.22 Ergo, to a first approximation, Case 1 (kicking the XP) gives a smaller Team B win% and greater Team A win%.

Thanks Bob. This is pretty amazing stuff. I would imagine that most coaches though are not sharp enough to get this and just say "3 scores is insurmountable". One I would very much like to see the math for is when a team is up early in the 4th by 4 and they go for two. It sure seems like they should kick and that way if the other team gets a TD then they have to go for two or the first teams next FG wins instead of ties. If you make the 2 you are still down 6 and the chances of a missed XP by the other side is very remote.

Brilliant, thanks ComptrBob. I've been to Tahoe a few times (Heavenly and Squaw) and if/when I go back out, I'd love to meet up and chat about various and sundry topics such as this. I'm not nearly the mathematician you are, but after I asked the question, I kind of scribbled out some matrices the same way you did. I was most curious in what assumptions you made and what kind of approximate probabilities you would assign to each event. Thanks again. That post alone should be enough to satisfy the ones bitching about the value of their $25/mo subscription fee for a little while. Bkeiller, of course most/all NFL coaches wouldn't know where to start with this type of thing and frankly, most are more concerned with doing the conventional thing and preserving their image in the media than giving their team the highest probability of winning. You see stuff all the time where they'll kick a FG late in the game instead of going for a 4th and 6 that makes the score look a bit better, but effectively drives his team's chance of winning to 0%. Ernie Adams is one rather high profile example of a "quant" who applies his skills to football. He grew up with and was good friends with Belichek; he's actually one of the few guys in his headset during games. Ernie is a veritable genius, and likely the guy behind that 'controversial' 4th down call against Indianapolis last year that was obviously the right move statistically, but didn't work out over the 1-data point sample.