Further Thoughts on Fourth-and-2

by Bill Barnwell

(Ed. Note: This was the introduction to yesterday's Quick Reads on ESPN.com. We're running it as separate commentary on FO in order to prevent the fourth-and-2 discussion from blocking out discussion of the other 14 games in the Quick Reads discussion thread. The rest of Quick Reads for Week 10 can be found here [1].)

Too close to call.

It's not the satisfying answer to the Great Belichick Debate, which has seen him declared to be either an infallible genius or an overzealous tinkerer by most observers, but it's the most accurate one.

No matter how we tinker with or adjust the probabilities to account for the game situation and the quality of the two offenses and defenses, it's difficult to find a dramatic difference between the choices of going for it or punting.

Take the first option, the one Bill Belichick chose. Teams attempting to convert a fourth-and-2 have successfully done so at a 48.6 percent rate this year, well down from 62.3 percent the year before. The "true" likelihood of such a play being converted by an average team in an average situation is closer to that latter figure, based on historical data.

Of course, the phrase "…average team in an average situation" simply does not apply. The Patriots don't have an average offense, they have the league's best by DVOA [2]; the Colts' defense ranks sixth. Although the Patriots had failed to convert in two of their three previous third-and-2 situations (including the one directly preceding the decision to go for it), their chances of making it in this situation are greater than the average team's.

On the other hand, the probability has to be adjusted for the situation. Robert Mathis had been abusing right tackle Nick Kaczur all night, meaning that Brady wouldn't have time for the combination of Randy Moss and Wes Welker to run anything resembling an intricate route pattern. Dwight Freeney lurked on the other side. Furthermore, the probability of a team going for it on fourth down might very well be artificially high because of selection bias -- teams are far more inclined to go for it on fourth down against the Lions or the Rams than they are against the Vikings or Ravens.

Throw all these numbers into a big soup, spin them however you'd like, and you'll end up with an expected conversion rate of about 60 percent. It might be 63, it might be 57; truthfully, it's not going to be enough to change our analysis.

The Colts aren't going to score every time they get the ball on the opposition's 29-yard line, but they will score most of the time. Toss in momentum and the quality of the Colts' offense versus the Patriots' secondary, and you can estimate, say, an 85 percent chance of the Colts scoring in that situation. That makes Belichick's decision to go for it a little stronger, upping the Patriots' chances of winning by going for it to 66 percent.

Then, it comes down to punting and where Manning gets the ball, which requires even more theoretical assumptions. Chris Hanson has a 39.6-yard net average, but it was in a dome, and the Colts don't have great return units. If we just assume 40 yards, the Colts get the ball on their own 32-yard line with two minutes to go and one timeout. If you believe that the Colts had a 34 percent chance or better of scoring a touchdown in that situation (100 percent minus the 66 percent chance we mentioned a moment ago), Belichick was right. If you think the odds are below 34 percent, Belichick was wrong.

If you disagree with the expected percentages of conversion above, Mike Harris (creator of the playoff odds simulator [3]) has developed a nifty calculator that lets you plug in your own averages and figure out whether Belichick made the right call by those figures. You can find that calculator here [4].

Of course, we haven't even considered the possibility of running the ball as opposed to passing it on fourth down, turnovers, onside kicks, or the Patriots scoring on a game-winning drive. The bottom line is that a mathematical analysis of the decision boils down into too many assumptions and inapplicable historical expectations to say very much about one decision on one drive in a very unique situation, and when we make the broadest assumptions possible about the decision, the decision isn't close to clear-cut.

The important factor that the cacophony of responses seems to be missing is that you can't judge Belichick's decision by the fact that it didn't work. As we've mentioned more than once in these pages, you cannot judge decisions by their outcome. You have to consider the process that goes into them, and then decide whether they're right or wrong at the moment they're made.

Think back to another controversial Belichick decision made in the heat of a prime-time game, his decision to take a safety on purpose [5] down one point during the fourth quarter of a Monday night game against the Broncos. Of course, the Patriots ended up getting the ball back and won the game. Belichick took virtually no flak after the game for his unconventional choice, and was instead hailed as an aggressive, brilliant game manager.

If Kevin Faulk stumbles two feet forward, Belichick is being spoken about in those glowing tones today by virtually everyone lining up to criticize him. That doesn't make his decision correct or incorrect, any more so than Faulk coming up short does. If Belichick's decision was wrong, it was wrong from the moment the playcall went to Tom Brady. And with everything we know about the situation, it's impossible to say whether that was truly the case.

(Another Ed. Note: If you would like to read a similar analysis of a completely different coaching decision, find a copy of the 1986 Bill James Baseball Abstract and read his commentary on Tommy Lasorda's decision to pitch to Jack Clark with a base open late in Game 6 of the 1985 NLCS. Some truths are universal.)