Math shows Belichick barely made right call

November, 16, 2009
11/16/09
5:12
PM ET
ESPN Stats & Information, using the Win Probability Calculator from wp.AdvancedNFLStats.com, computed whether Bill Belichick made the right statistical call in deciding to go for it on fourth down Sunday night against the Indianapolis Colts.

ESPN Stats & Information aimed to break it down four ways:
  1. Chance of winning the game if the Patriots converted the fourth down.
  2. Chance of winning the game if the Patriots missed the fourth down.
  3. Chance of winning the game if the Patriots punted the ball.
  4. Chance of converting the fourth down.

The Win Probability Calculator factors the score, time remaining, field position, down and distance.

Predicted outcomes to the above scenarios came back thusly:
  1. If the Patriots converted, they would have had a first down roughly on their own 30-yard line with two minutes to go. Their average win probability in this situation would be 92 percent.
  2. If they missed the fourth down, the Colts would take possession on roughly the Patriots' 29-yard line with two minutes to go. The Patriots win probability in this situation would be 66 percent.
  3. If they punted the ball, using Chris Hanson’s average of 44 net yards in the game, the Colts would have gotten the ball at about their own 28-yard line. The Patriots' win probability in this situation would be 79 percent.
  4. The answer to this one has many variables. The NFL average when going for it on fourth-and-2 over the past two seasons was 55.7 percent. The Patriots had converted three of four attempts in that situation over the past two years prior to Sunday night. The Colts' defense allowed opponents two conversions on three fourth-and-2 attempts over the past two seasons. Even though this indicates that the Patriots were more likely to convert than the league average, ESPN Stats & Information placed their chances of converting at the league-average rate of 55.7 percent.

Next is some hardcore math that produces the following:
  • The Patriots' win probability when going for it (factoring expectation of winning with the probability of a successful conversion versus the expectation of winning with the probability of a failed conversion) was 80.5 percent.
  • The Patriots expected win probability when punting, as stated above was 79.0 percent.

Here is ESPN Stats & Information's final synopsis:

Using these estimates, the decision is very close. The Patriots’ expected win probability when going for it is actually greater than the expected win probability when punting, but just by 1.5 percent. If you say the Colts and Peyton Manning had a greater chance of coming back after the missed fourth down conversion than the 34 percent given to them by the NFL average ... then you’d probably also give them better than the 21 percent chance to come back if the Patriots had punted. So you’d have to decrease the win probability when punting from 79 percent. Most likely, you end up with a close decision either way.

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