Numbers Were in Favor of Bill Belichick and Tom Brady on Fourth-Down Attempt

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Numbers Were in Favor of Bill Belichick and Tom Brady on Fourth-Down Attempt Bill Belichick made an intelligent gamble to go for it on fourth-and-2 against the Indianapolis Colts on Sunday night. He pulled out his slide rule, did some basic high school statistical analysis, and determined that Tom Brady has a better-than-average chance to keep the ball out of Peyton Manning‘s hands and win the game, right then, right there. If he had been successful, all the talking heads in Boston and Bristol would have praised him as “assertive” and “courageous.”

Belichick’s aggressive game strategy has made him a winner, from Super Bowl XXXVI (going for the win and not playing for overtime) to this season (going for it on fourth down against the Falcons). His assertiveness transformed the Patriots from also-rans into aggressive champions and leaders in the NFL, and his decision Sunday night showed the same winners’ edge.

Arguments are cheap, though. Let’s open up our high school stats textbook and look at the numbers.
In the entire game, the Patriots averaged 6.84 yards per play on actual plays (no kneel-downs, no field goals) with a standard deviation of 11.45 yards per play. Using these numbers, the Pats had a 66.27 percent chance of gaining two yards on the fourth-and-2.

Of course, the Patriots’ offensive performance suffered in the fourth quarter. Did that decline make Belichick’s bet a loser? Not really. In the fourth quarter, the Patriots averaged 2.94 yards per play with a standard deviation of 3.85 yards per play. Using these numbers, the Pats had a 59.48 percent chance of gaining two yards on the fourth-and-2.

One question remains: what if the Patriots had punted? As Brian Burke of The New York Times notes, the league-wide average touchdown odds for the Colts’ starting position (their own 34-yard line) are about 30 percent, whereas a start from the opponent’s 28-yard line results in a touchdown 53 percent of the time. The Pats’ winning percentage when going for the fourth-and-2 was approximately:

0.6 + (0.4 * (1 – Peyton’s odds from the New England 28))

and their winning percentage by punting was:

(1 – Peyton’s odds from the Indianapolis 34)

If we assume the league’s averages hold for Peyton, the Patriots’ winning odds are 78.8 percent when going for it and 70 percent when punting. For Belichick’s decision to be a coin-flip, we’d need to increase Peyton’s odds from the New England 28 to 2.5 times his odds from the Indianapolis 34. Anything less than that makes Belichick’s decision the right one, and while Peyton’s good, he’s not proportionately that much better than the rest of the league.

Belichick’s bottom line is the Patriots’ bottom line: cold logic over hot emotion. Lady Luck wasn’t with him on Sunday, but over the long run, he’ll beat conservative coaches.

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