look, there are 3 relevant #'s you need to try to predict:
% chance the Pats make that 4th down
% chance the Colts score from the 30
% chance the Colts score if you punt
what do you think these are?
But, you're not arguing that this is a matter of what "I think," but rather of established probabilities. I can think anything I want, but it's quite meaningless, as is the model you cite without more detail. I am holding that those probabilities are in themselves useless for decision making at this point because they are not robust enough [thus my original (unanswered) question to you of what you think BB should have done if the QB on the other side of the ball were Trent Edwards and the Bills, when the model as currently designed would suggest the same result for both Edwards with the Bills and Manning with the Colts].
I can cite probabilities until I'm blue in the face and I might actually get lucky and end up being right, but I will have been lucky and not data-driven, so why bother other than as an academic exercise?
In addition, the"Probabilities" that you are asking all of us to produce are, in reality, means, around which there are distributions. Decision making requires understanding the distributions and their impact on the decision.
I agree that their generic #'s are wrong, and thats why I changed them in my example in the OP. but they would have to be REALLY, REALLY wrong in this situation for punting to be right. like, "unreasonably, don't pass the smell test wrong". see above, give me what you think the actual #'s are in the 3 relevant situations
But that's the whole point.
Statistical analysis has a way of describing the chance of what in layman's terms is the chance of "being 'REALLY, REALLY wrong,'" it's called a Standard Deviation around a mean.
The decision to go for it under any of the inferred "Probabilities" is a function of the Standard Deviation as much as it is of the Mean Probability. That's why people do Monte Carlo simulations and look at the curve that results before they use "Probabilities" to make decisions.
In this case, the model to which you link us is so naive as to be practically useless. You and I can tweak it all we want, but in the end, if we're right, we're lucky, just like the bettors in Vegas when they play the Spreads every week.
Each of the Probabilities for which you are seeking a single magic number is actually the product of a highly nuanced set of variables.
The Probability of making "that 4th down" also carries with it the chance of a fumble or a pick-Six. It carries the chance of a holding or motion penalty that push the ball farther back in the field. So, you're asking for the wrong thing. You should be asking for the "Expected Outcome" of going for it on 4th down, which is a lot broader than "making it."
Same with the Probability of the Colts scoring from the 30. How long will it take them to score? What is the P of the Pats making a play on D that results in a score for them? Once again, instead of asking for the "Probability" of "scoring from the 30," you should be asking for the "Expected Outcome," which carries with it a range of possible outcomes.
The P that the Colts score if we punt has to take into account where they get the ball and then the whole range of possible outcomes, yielding a mean that we call the "Expected Outcome."
My point is simple: the way you are trying the model this is far too simplistic to be useful.
I personally believe that we are probably five to ten years away from being able to do this in a useful fashion, once Quantum Computers are readily available (they will effectively put a Supercomputer on something no larger than an IPOD).
Until then, this is just a game at which we might or might not get lucky once in a while, just as these guys get lucky and call a few games right and a few games very wrong.
