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BGonline.org Forums
Simple Model w/BG analogy
Posted By: Chuck Bower In Response To: Situation 2: hate to disappoint (Matt Cohn-Geier)
Date: Saturday, 11 December 2010, at 1:56 p.m.
Most know this, but just to make it clear, TN needs two scores -- a touchdown (+extrapoint) and a field goal -- with a successful onside kick in between. From a score standpoint it doesn't matter if they get the FG first or the TD first.
Suppose there is a yardline threshold for the FG. Say longer than x-yardline and the kick success has 0%, and shorter than this threshold the kick has 100% ("step function"). For the FG part of this problem, the goal of the offensive should be to just get past the threshold yardline.
If the team decides to try for the TD first, they don't know how much time to allot for the TD in order to give themselves enough time to later get to the proper field location and execute the field goal. But if they go for the FG first, they know exactly how much time they have for the TD part -- all the remaining time in the game.
Of course the FG success curve is not a step function. Do you (armchair or professional) mathematicians know the proper place on the curve to shoot for? Does it occur at the local maximum of the second derivative? (WAG :)
There are a couple loose analogies here that have been discussed before, one of them is a BG analogy:
1) the theoretical optimal place to double is when you arrive at the point of the game where your opponent can neither gain nor lose by dropping vs. taking. If you double before reaching that point or after passing over it, you haven't squeezed out the maximum (theoretical) amount of equity. (And again, here, this model is too simple since in most games you will never have the opportunity to land exactly on the drop/take line.)
2) A few weeks back during the lively OT football discussion of going for 1 or 2 when trailing by 15 and facing a PAT decision, it was pointed out that going for the 2-points first rendered your decision making simpler for the rest of the game, because if you fail now you KNOW you need two possessions to get at least 9 points whereas if you take the (almost sure thing) 1-point now you still don't know if you'll be able to convert the (~coin-toss) 2-pointer later. Thus you won't know if you need to allocate time for the second score until it's possibly too late.
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