Math shows Bill Belichick made bad choice

October, 25, 2010
10/25/10
9:48
AM ET
All right, people. Take a deep breath before you read this. Feel free to grab a cup of coffee. You might need to invest a few minutes here.

ESPN Stats & Information researcher Alok Pattani endeavored to explore what New England Patriots coach Bill Belichick had to gain by going for it on fourth-and-1 late in Sunday's victory over the San Diego Chargers.

The Patriots failed to get the first down. BenJarvus Green-Ellis was dropped for a 1-yard loss. But the Chargers missed a 50-yard field goal that would have sent the game into overtime.

Belichick's decision to run an offensive play on fourth-and-short with a late lead was reminiscent of his controversial call last year in Indianapolis. Belichick chose to go for it on fourth-and-2. The Patriots failed to get the first down then, too, and Peyton Manning made it hurt.

Let's mince the statistical data on Sunday's decision in San Diego.

With help from Brian Burke's win probability calculator at AdvancedNFLStats.com, we can calculate the following with a three-point lead and 1:55 to play:
  • Patriots' chance of winning if they converted the fourth down and had first-and-10 at midfield: 91 percent.
  • Patriots' chance of winning if they don't convert the fourth down and Chargers take over on Patriots' 49-yard line: 64 percent.
  • Patriots' chance of winning if they punt on fourth down, with assumption Chargers take over on their own 13-yard line (using Zoltan Mesko's net average of 38.2 yards): 87 percent.

We then need to factor in the likelihood New England converts the fourth down. There are many methods to hash this out.
  • NFL average on fourth-and-1, entering Sunday's games: 67.1 percent.
  • NFL average on fourth-and-1 the past 10 seasons: 66.3 percent.
  • Patriots' average on fourth-and-1 this season before the game: 66.7 percent.
  • Patriots' average on fourth-and-1 the past 10 seasons: 78.1 percent.
  • Chargers' opponents' average on fourth-and-1 this season before the game: 100 percent.
  • Chargers' opponents' average on fourth-and-1 the past 10 seasons: 69.7 percent.

For the sake of computation, Pattani reasonably selected 66.7 percent as the value to determine the Patriots likelihood of converting because all the numbers are close.

Then we come to an equation that adds up the Patriots' victory probability if they go for it:
  • Expected win probability when going for it, which is (likelihood of converting multiplied by win probability if successful converting) plus (probability of not converting multiplied by win probability if unsuccessful converting): 82 percent.
  • Expected win probability when punting: 87 percent.

Belichick couldn't have crunched these numbers quickly enough to analyze them, but the math shows he gave the Patriots a worse chance to win by not punting.

And if you drag your mouse over to your computer's calendar, you'll notice it became November while you were reading this.

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