Kurt Bullard is a freshman at Harvard and a first year member of the Harvard Sports Analysis Collective. He intends to major in either Economics or Statistics. Go 'Cuse.
This Sunday, the Patriots found themselves down six points to the Saints with only 1:13 left in the game. In that span, Tom Brady was able to lead a drive down the field, connecting on a 17-yard pass to Kenbrell Thompkins in the left corner of the end zone to complete one of Boston’s two major come-from-behind wins of the day.
Hidden by the final drive were two controversial fourth down calls in the fourth quarter that happened at key moments in the game. The first came with 8:34 remaining in the game when the Patriots held a 20-17 lead over the Saints. Faced with a 4th-and-goal at the five yard line, New England opted to kick a field goal rather than try to score a touchdown to go up two scores.
The win probability and expected point value each suggest different optimal decisions. The expected point formula suggests that the Patriots ought to have gone for it, while the win probability calculator says otherwise, albeit by a slight margin.
The second decision came later in the game. Down, 24-23, with 2:46 left in the contest and all three timeouts remaining, Belichick decided to go for it on 4th-and-6 on his team’s own 24-yard line. This time, Belichick adopted the more aggressive strategy, going for the first down deep in his own territory. The Patriots attempt was unsuccessful, as Brady’s pass fell incomplete to Aaron Dobson.
This model also suggests two different courses based on the two statistical methods employed here. Going for it would have increased the win probability, but it also would have led to fewer expected points.
Such a difference in win probabilities may be attributed to situational defense. When the Saints had forced a turnover on downs, they got the ball at the NE 24. The chances that they would be able to kick a field goal here are relatively high, at 74 percent for a 41-yard field goal. However, it was on the edge of field goal range. A six-yard sack could have pushed New Orleans to the NE 30 for a 47-yard field goal, which would have reduced the probability of success to 62 percent. This may be an overestimate for Hartley too, whose career long is only 53 yards. With that being said, the Saints were more likely to play conservatively in this situation, since any negative play would have a significant effect on the probability of a made field goal from Hartley. Belichick trusted that, if they failed to convert on fourth down, his defense could force a three-and-out, with the Saints most likely being very careful with the ball. This outcome would give Brady a chance to lead a two-minute touchdown drive to victory -- odds that Belichick probably thought were in his favor.
From this conversation stems another one: Should teams follow the expected points values of a decision or the win probabilities. As was demonstrated in both situations above, the two do not always coincide with each other. A team should not necessarily be looking to always maximize its score – doing so depends on the situation of the game. For example, when faced with a fourth-and-goal at the five yard line up 14 points in the fourth quarter, it would make sense to kick a field goal and go up by three scores, instead of taking the risk of going for it despite the expected points value being higher. Conversely, if a team were instead down 14 points, it would make more sense to go for it, since a team would still be down two scores after a successful field goal. Expected points only account for an isolated situation; win probabilities, on the other hand, account for the context of the situation.
So, while going for the fourth-and-goal and punting in the Patriots’ two respective situations would have maximized expected points, win probabilities said otherwise. The extra four points from scoring a touchdown instead of kicking a field goal were not valuable enough to risk going for it. In contrast, risking turning the ball over on downs, even though punting would have led to more expected points, was a good decision because those points were valuable enough given the time crunch.
Belichick’s change of mind from conservative to aggressive is, by the statistics, justified. While either choice in the first situation was defensible, it was clear that the right choice on the last fourth down call was to entrust the game to Brady and company.