Quote:
Originally Posted by GuyIncognito
I understand completely what you said. The advantage of going for it on 4th down was computed to be +9%, but it might be as high as +20% or as low as -10% (I kind of doubt the 95% confidence interval would be this wide after playing around with the numbers a bit, but I could be wrong). Why exactly should punting be the null hypothesis? Whether you go for it or punt, you're still taking an action based on some estimated probability of success.
The null should always be the status quo, which is likely punt, since almost every other coach would punt here (whether right or wrong). Also, we can never prove the null hypothesis correct, we can only disprove it to a certain confidence.
I just think trying to prove this by mathematics is going to turn out to end up leaving many holes in our logic and assumptions.
I'm not trying to argue one way or the other. But, I think the way people have been proving this mathematically is somewhat illogical by not including variance.