Have I Discovered Another Mathematical Football Coaching Error?

[David Sklansky]

First assume that after scoring to go down by four you stop them. (This assumption hurts my position because if you go for one and they come back to score a field goal, a rare last second comeback touchdown by you is a win rather than a tie [if you missed the two pointer]. But since this scenario is so rare, I will ignore it.)

Assume also that overtime is even money.

Now to throw out some reasonable numbers, we will say that after scoring and stopping them you have a twenty percent chance of scoring a touchdown if you need it (because you missed the two pointer). And if you don't need it you will come back and score a field goal 40% and a touchdown another 3%.

If a two conversion is 40% and a one pointer is 100% (the real numbers help my case a bit) then:

If you go for one you will win 23%. The touchdown plus half your chances of making a tying field goal.

If you go for two your chances of wining is 40%x43% = 17.2% when you succeed and score PLUS 60%x20% = 12% when you fail on your two pointer but come back with a touchdown. That adds up to 29.2%. Quite a bit better than 23%.

Drop the needed touchdown percent to 15% and we still have a clear edge for the two point attempt.

Again remember that these numbers assume the opponent is stopped. The real numbers are smaller.

It is important to realize that plays like this come up not only because of disadvantages of going for ties but also because of poker like advantages of going last. It is sometimes worth giving up a little bit of instant EV if it will make a later decision more clear cut. For instance suppose you dealt five cards to an opponent who drew to them and showed you his hand. You win if your five cards, after drawing, beat him. Knowing what you have to beat is enough of an advantage that you could lay a small price every hand. This football situation may be analogous.

[Austiger]

[ QUOTE ]
If you go for one you will win 23%. The touchdown plus half your chances of making a tying field goal.


[/ QUOTE ]

Where did this number come from? I'm assuming you used someone's estimate from this thread to get the 23%?

Wait- I just realized, you're using the 3% TD + 1/2*40% FG? That's not going to be correct. The 3% TD is for when you are down 2 and don't need the TD to win. If you are down 3, you are obviously going to go for the TD much more often than if you're down 2 (see the Oregon St/Cal finish.)

[David Sklansky]

[ QUOTE ]
[ QUOTE ]
If you go for one you will win 23%. The touchdown plus half your chances of making a tying field goal.


[/ QUOTE ]

Where did this number come from? I'm assuming you used someone's estimate from this thread to get the 23%?

Wait- I just realized, you're using the 3% TD + 1/2*40% FG? That's not going to be correct. The 3% TD is for when you are down 2 and don't need the TD to win. If you are down 3, you are obviously going to go for the TD much more often than if you're down 2 (see the Oregon St/Cal finish.)

[/ QUOTE ]

My 3% figure(for a touchdown, while playing for a field goal), unlike the last preliminary question I asked originally, did in fact assume that a field goal will only come back and tie. So it might be too low. And if it is high enough, it makes me wrong. That is one reason that there has to be a fairly small window of time left for the play to be considered. Enough time to get that touchdown if it is really needed, but not enough time to make a concerted effort for it if it is not.

Still the figures I postulated were so far in favor of the two pointer, that it would surprise me if the actual figures were enough off to always change the decision back to a one pointer.

[Austiger]

[ QUOTE ]
First assume that after scoring to go down by four you stop them. (This assumption helps my position because if you go for one and they come back to score a field goal, a rare last second comeback touchdown by you is a win rather than a tie [if you missed the two pointer]. But since this scenario is so rare, I will ignore it.)


[/ QUOTE ]

Also, I don't see how this assumption helps your case. It seems like it hurts it. If you don't stop them and they kick a FG, then obviously you would hope that you had kicked the XP to be down by only 6.

[David Sklansky]

[ QUOTE ]
[ QUOTE ]
First assume that after scoring to go down by four you stop them. (This assumption helps my position because if you go for one and they come back to score a field goal, a rare last second comeback touchdown by you is a win rather than a tie [if you missed the two pointer]. But since this scenario is so rare, I will ignore it.)


[/ QUOTE ]

Also, I don't see how this assumption helps your case. It seems like it hurts it. If you don't stop them and they kick a FG, then obviously you would hope that you had kicked the XP to be down by only 6.

[/ QUOTE ]

My misprint. Changed it.

[T-God]

[Pudge714]

MT2R,
Two point conversions aren't rare a spot as they are very similar to most redzone plays. The dynamic system can improve chances as well.