This blog previously considered the question whether or not one should go for it on 4th and goal from the 2. I recall the analysis, among other advantages, showing that, from NFL stats, the chance of making a touchdown (7pts) was about .6, yielding .6*7=4.2 pts on average, which exceeds the score from a made field goal.
Now Bill Belichick is being fried by the talking heads in New England for making a similar decision to go for...but to go for it not on the goal line but in his own territory (30 yd line) on 4th and 2 with 2 minutes left in the game vs IND, who is down by 6pts. Brady's pass was complete but marked inches short when it was bobbled, enabling IND to have a short field (30 yards) to score the winning TD. I know that Belichick's decision to go for it violates intuition and almost universal coaching practice. But was the decision really a mistake, as so many claim?
According to my VERY ROUGH and QUICK calculations and the graphical link below, the chance of NE winning was .68 with the decision to go for it vs. .5 if he decided to punt. So, I think Bill made the right choice. I'd be interested to know if anyone has different opinions about the chances of winning based on the assumptions, I have made below.
Note: Remember that, if NE succeeds on 4th and 2, the game is virtually over as they can run out the clock. I've assumed a 40 yard punt and no unforeseen turnovers. I considered that Peyton Manning had a hot hand, the NE defense was tired, and that IND had a higher than usual chance of making a TD, whether it was from 30 yards out (after NE fails on 4th and 2)(Pr=.8) or 70 yards out (ie after a punt)(Pr=.5).
Summary: NE had a greater chance winning by going for it on 4th and 2 (.68 vs. .5)
Analysis of the 2 possible decisions:
1. NE goes for it P(make 4th and two )=.6 =Chance PATS win immediately
Pr(don’t make 4th and two) = .4
p(Ind TD with 30 yard drive)=.8, Pr(IND does not make TD with 30 yard drive)=.2
Pr(IND fails to make TD on 30 yard drive and Pats fail on 4th and 2)=.2*.4=0.08
TOTAL CHANCE PATS WIN=.6+.08=.68
2. NE punts
Pr(IND TD with 70 yard drive)=.5* Pr(IND fails to score on 70 yard drive)=.5
TOTAL CHANCE PATS WIN=.5
Here's an article on the game decision.http://www.nj.com/sports/ledger/politi/index.ssf/2009/11/new_england_patriots_coach_bil.html