Re: Why going for it was right
facing 4th and 2, the Pats had about a
60% of getting the first down. This of course would have ended the game. 60% is a historical league average, you can quibble with this figure up or down if you want, but thats around the ballpark % chance the Pats make it.
so if they will convert 60% of the time, then going for it gives them a
Win Probability of at least 60%. I say "at least" b/c even if the fail to convert, the Pats still have a chance of stopping the Colts from the 30. what % is that? the league average in this situation is around 53%, though I think we would agree that the Colts vs our defensive had a much higher % chance of scoring. call it...75% ? that means 25% of the time, even when we don't get the first down, we win by stopping the Colts.
so,
(0.60 * 1) + (0.40 * (1-0.75)) = 70% Win Percentage for Pats
the alternative move of course is to Punt, which on average will put the Colts right around their 34. (again, these #'s are taken from the above link).
what are the odds the Colts drive down and score now? We used 75% chance from the Pats 30, so it's obviously going to be much less from their own 34. The historical league average is 30% in this situation, but again I think it's higher than that. Call it 45%. that means the Pats have a 55% Win Probability from punting.
given those assumptions above, going for it leads to pats victories 70% of the time while punting leads to victories 55% of the time. you can play around with those #'s yourself and change the assumptions, but you would need to plug in some weird #'s to come to a conclusion that says punting is the right move.
2nd point:
in terms of the decision making process, the results don't matter. the decision to punt or not punt is not made correct or incorrect by what happens afterwards. to call decisions "right" or "wrong" based solely on the results is horribly incorrect "analysis". sometimes Faulk gets to the 30, sometimes he doesn't, but either way going for it was right. sometimes the result is going to look bad, sometimes it won't. you need to divorce yourself from the results if you want to learn how to make the best decision.
I think that analysis is far too simplistic and dumbs down the decision that Belichick actually made, which, BTW, I think was the right decision. He made a SITUATION SPECIFIC decision to the effect that his Defense couldn't stop Peyton Manning at that time in that game under those specific circumstances. It had nothing to do with a flawed, generic model.
As you read what I write below and if you doubt what I'm saying, ask yourself this question: if the score of the game and the position on the field and the time on the clock and the timeouts remaining were all exactly the same but the QB and Team on the other side of the ball were Trent Edwards and the Bills, would Belichick have gone for it or punted? The model to which you link us suggests that he should have gone for it. Do you really think that would have been the right decision? Be honest. This was a situation-specific decision. The model you cite is not robust enough to be used to make that decision, one way or the other.
I followed your link. It's pretty amateurish stuff. The statistical error is called the "flaw of averages." It's based on a generic model of any NFL team and doesn't take into account the game circumstances (other than the yard line and score) and certainly doesn't take into account the players on the field. In other words, the model is basically useless unless you're programming a video game. The fact that it suggests that Belichick made the right decision is blind luck and has nothing to do with the circumstances BB was facing last night.
Just because a few guys have turned it into a web page and call it "Advanced NFL Stats" doesn't make it right. What you end up with is a mean/average with no indication of the distribution around it. That's the only way even a well-designed model can guide this kind of decision.
In the case of this "model," there is presumably a .60P of gaining 1.5 yards. Fine, but that really tells us nothing and if the SD is anything more than .1 yards, it really doesn't help you decide at all, and I'm pretty sure the SD is in the range of .50--.75 yards. What the model doesn't try to consider is what happens when the Colts get the ball. How long will it take them to score from the 30, if indeed they score.
The model then says that there is a .30P that the Colts score from their 38 after a punt. That part of the model muddles two different sets of uncertainties; one, where the Colts actually get the Ball. The Average is the 38. Once again, what is the SD? Then, from the 38, there's a .30P that they score. Once again, what is the SD? What does a distribution of likely outcomes look like, based on real data from THESE TWO TEAMS.
Finally, even if you Monte Carlo a few hundred thousand scenarios and it shows the Pats better off within reason, the only way that model could possible be useful is if it's robust enough to account for the propensities of those players on that field at that point in the game.
All of that said, I think that the Computer in Belichick's head decided that the risks of going for it outweighed the risks of punting, but for entirely different reasons.
BTW, their models yesterday predicted the following:
.72 likely that the Jets would win.
.74 that the Steelers would win
.83 that the Broncos would win
.65 that Oakland would win
.54 that Dallas would win.
They also called some games right, but really did no better than Vegas bettors.
