Suppose the same situation of the Mich-Mich St. game on the nfl. The difference in the overtime rules changes your analysis?

In my opinion, in the NFL I would always go for two. It’s better than lose on the toss and watch the other team kick a 40-yard FG without never touching the ball…

In college I think you are right. The better team has to diminish variance.

Eduardo

Now, if I knew my team was physically exhausted or if I knew that I had three key guys sidelined by injury, then I would bet the house and go for it on 4/23. I would have no choice. But that’s obvious, and those conditions were not included in the problem.

I know this is all in fun, but if we’re going to analogize via quantitative finance, I think we need to be careful. By labeling a football game loss as a black swan event, which it is not, we eliminate discussion. Someone always loses in every game; therefore a loss is not an unknowable externality, which is what a black swan event is.

So:

a) a game loss is not a ‘black swan’ event — it’s an expected outcome that is a *cliff event*. 9/11 was a black swan event — an event that, literally, could not be modeled. Russia defaulting on its national debt: black swan event (cf. Long Term Capital). The electricity going off in the stadium before Wisconsin can finish beating Nevada — black swan event. Somebody must lose every game, however. It’s a tautology: a compound proposition. Team A will win and if so, Team B will lose. Just as there will always be individual mortgages that default. Therefore one models credit default (cliff event) — an expected event — differently than one *prices* (measures the probability of a price) the credit.

I think an interesting question to ask in looking at your puzzle is this: how is the FG attempt/TD attempt decision altered if the moment occurs at the end of the first half? Because this changes context while the cliff event (the end-of-time loss) remains distant.

If one returns to analogy, consider the following. A small-town bank has been in the family for 100 years. Some wiseguy from Lehman shows up with an offer to sell $5mm of deconstructed subprime mortgage paper that “can’t fail.” The banker must weigh the following choices, which are no different than your end-of-game

a) the opaque piece of engineered financial security, which on average cash flows, is not rendered worthless by the underlying, actual mortgages — and bank earnings climb. This will *probably* happen. Using a propensity modeling outlook, this is clearly the right decision.

b) the security fails, as does, actually, Lehman because of underlying default. Who cares if on average Lehman was selling profitable, cash flowing paper? In this specific instance, the small town bank has $5mm of capital wiped out, their capital ratios fall below required thresholds, the regulators move in and seize the place, and the family bank is … dead. Note, that the defaulting security is not itself a black swan event. Mortgages and banks fail all the time.

The actual mathematical technology used to model price (probability) and default (cliff event), in practice, is profoundly different. That’s because the problems being solved are distinct. I think end-of-game decisioning more closely reflects default, rather than pricing, analysis. It is a stochastic optimization problem, not a probability optimization. Different math, different methods.

If anything in this scenario is a black swan event, it’s the hiring of a 33 year-old with no coordinator or head coaching experience to run an NFL team. (But really not: sports ownership has proven itself feckless some major percentage of the time.)

I definitely buy that many of the popular 4th down analyses overlook the sort of “instant death” risk — i.e. that going for it on 4th might on average be better in terms of points, but if you go for it and fail the game is likely over, whereas punting, to use the poker term, gives you at least some “outs,” and thus is actually desirable.

Anyway I’m glad we can all agree that Raheem Morris is insane.

I believe your stochastic analogy is flawed in that catastrophe avoidance is only advantageous if there is value to be gained in the time between avoiding the potential catastrophe and the end result. All college football games result in a win or loss. Unless you have reason to predict your odds will improve in the future (eg., you believe your athletes are less susceptible to fatigue) I don’t see the value to delaying the decision.

OU field goal good, OU needs the ball back for another FG
OU field goal no good, Ou needs ball back for a TD
OU go for it make it, OU up 3, need a stop to win the game
OU go for it miss it, OU down 4 still, need a stop to for a TD

why not try going for it, its the best probablity. You got to concider not getting the ball back anymore;

“Well, kinda tough deal. Tough deal. Have to make the call, no one else is there to hold your hand. Gotta take the points and move on. Liked our chances once the field was level. Something like that. Very tough deal, do it again. Take the points, everybody gets the same shot in OT. Sure, half of you would have a better idea, but I’m from Pittsburgh, live in Iowa. Our state: put hay in the barn. Can’t remember when I was unhappy with points and still breathing.”