A model-based approach to football strategy.
|January 4, 2005|
In this article we discuss some notable coaching decisions from selected games. Many of the analyses use the footballcommentary.com Dynamic Programming Model .
With 1:18 left in the 3rd quarter, the Jets' Jonathan Vilma intercepted a tipped Marc Bulger pass and ran it back for a touchdown, giving the Jets a 26-21 lead before the try. Jets' coach Herman Edwards elected to attempt a two-point conversion. This was the right choice, even if we assume (and we see no reason why we should) that the Jets' probability of success on the try was considerably below the league average.
According to the
if the Jets kick the extra point, their probability of winning the game is 0.731. If they go for two, their probability of winning is 0.797 if they make it but 0.709 if they fail. If we assume that their success probability is 0.4, which is near the low end of reasonable estimates, then going for two gives the Jets a win probability of
With 0:05 left in regulation, Washington trailed 13-10 and had the ball, 1st and 10 at the Dallas 39 yard line. Washington decided to try a field goal, but Jeff Chandler's 57-yard attempt was well short, and Dallas won the game.
Since the Redskins still had a timeout, they missed a good opportunity. As the Jets demonstrated at the end of the first half of their Week-8 game versus Miami, five seconds is enough time to run another play. In that game, as we described previously , the Jets were just out of decent field goal range with 0:05 left in the first half. Rather than try a Hail Mary, the Jets called a short pass play. The receiver downed himself for a 6-yard gain and immediately called timeout, stopping the game clock at 0:01. (The success of that play was not the result of sloppy work by the clock operator; only 3.2 seconds elapsed from the snap to when the receiver downed himself.)
Had Washington employed this tactic, they might have gotten in position for a more makeable field goal attempt. And of course, if the pass is incomplete, they can still try the 57-yard field goal.
With 2:04 remaining in the 3rd quarter, Buffalo led 17-16, and faced 4th and 1 at the Pittsburgh 11-yard line. Buffalo decided to attempt a field goal.
According to the
Buffalo's probability of winning the game is 0.68 if the field goal is good, but 0.56 if it misses and Pittsburgh takes over at their own 20-yard line. NFL place-kickers make about 92% of their kicks from 28 yards, and if we use that value, we find that Buffalo's probability of winning the game if they attempt the field goal is
If instead the Bills go for the first down, their probability of winning the game is either 0.775 or 0.585, depending on whether or not they make it. Using 0.6 for the probability of success, we find that Buffalo's probability of winning the game if they go for it is
With 10:28 left in the 1st quarter, on the game's opening possession, Green Bay had the ball on 3rd and 5 at the Minnesota 44-yard line. Brett Favre dropped back to pass, but the ball was knocked from his hand, ultimately going out of bounds at the Green Bay 30-yard line. Green Bay challenged the ruling on the field that Favre fumbled, claiming that it was an incomplete pass.
Even if the ruling on the field were reversed, Green Bay would presumably punt. In that case, Minnesota's expected starting field position would be around their own 10-yard line. With the play ruled a fumble, and Green Bay punting from their 30-yard line, Minnesota's expected starting field position is around their own 30-yard line. So 20 yards were at stake. The value of those 20 yards is not trivial.
According to the
those 20 yards at that point in the game were worth an increment of 0.025 to Green Bay's probability of winning. The problem is, the sole replay that had been shown prior to Green Bay's decision to challenge seemed to show clearly that it was a fumble. It would be optimistic to suppose that there was even a 10% chance of a reversal after review. The value to Green Bay of a 10% chance of gaining those 20 yards is just
Later in the game there was a ruling that did merit a challenge. When Minnesota punted from the Green Bay 45-yard line with 9:50 remaining in the 4th quarter, and the score 24-24, the officials ruled that Minnesota successfully downed the ball at the Green Bay 1-yard line. Replays suggested that there would have been a substantial probability, perhaps 50%, that the play would have been judged a touchback after review. The difference between the 1-yard line and the 20-yard line is worth an impressive 0.067 to Green Bay's probability of winning at that point in the game; even 50% of that is worth 0.033. Unfortunately for the Packers, they were out of challenges.
With 6:19 left in the 1st quarter, after scoring a touchdown to take a 7-0 lead, Atlanta attempted an onside kick.
According to the
if the Falcons kick deep, their probability of winning the game is 0.699. With the onside kick, their probability of winning is 0.749 if they recover the kick, but 0.67 if the Seahawks gain possession. Using these numbers, it's easy to verify that the onside kick is preferred in this situation only if the probability of success exceeds 0.37. That's a pretty high hurdle. However, even if the true success probability is only 0.3, Atlanta's probability of winning the game if they kick onside is
For this reason, we think it's beneficial for teams to attempt occasional surprise onside kicks. However, the particular approach to the onside kick that Atlanta selected removed some of the element of surprise. After teeing the ball up, Atlanta kicker Jay Feely walked only three yards back toward his own goal line before turning around to kick the ball. Undoubtedly Atlanta was hoping to catch Seattle off guard. However, as soon as Feely turned around, the Seattle players knew an onside kick was coming.
With 2:18 remaining in the 4th quarter, Seattle led 24-21 and had the ball, 3rd and 6 at their own 24-yard line. Arizona had just used its final timeout. On the next play Seattle quarterback Trent Dilfer scrambled for 7 yards and a 1st down, and the clock ran down to the two-minute warning. The Seahawks then took a knee three times to end the game.
As we described in a previous article , the Cardinals actually still have a slim chance to win after Dilfer's run. They simply need to commit a penalty before the clock reaches 2:00. This stops the clock, forcing Seattle to run another play before the two-minute warning. The Seahawks are then unable to run out the clock by taking a knee, and if they fail to make another first down, Arizona gets the ball back with about a half minute remaining, needing only a field goal to tie.
There were at least two coaching decisions in this game that received attention. The first came with just 0:20 left before halftime, when Indianapolis faced 4th and 1 at the San Diego 5-yard line, trailing 17-6. The Colts decided to kick a field goal.
According to the Model , When San Diego kicks off to start the second half, Indianapolis's probability of winning the game will be either 0.158, 0.237, or 0.367, according to whether they trail by 11, 8, or 4 points. So, if the Colts settle for the field goal, their probability of winning is 0.237.
If the Colts decide to go for it, there are three possible outcomes for the play: The Colts can fail to pick up the first down, they can score a touchdown, or they can pick up a first down without scoring. In the latter case, they can use their final timeout to stop the clock, leaving time for an attempted pass into the end zone. If that pass is incomplete, the Colts can kick a field goal, but of course a sack would end the half.
We will suppose that if the Colts go for it, there is a 0.45 probability that they get no points before halftime, a 0.25 probability that they score a field goal, and a 0.3 probability that they score a touchdown. With these assumptions we find that Indianapolis's probability of winning if they go for it is
0.45 × 0.158 + 0.25 × 0.237 + 0.3 × 0.367 = 0.24.
This is essentially the same as kicking the field goal, so in this case the decision to kick was unobjectionable. One of the reasons is that it's so close to halftime: The usual field-position benefit from going for it doesn't apply.
The second decision came with 9:35 remaining in regulation. San Diego, leading 31-23, faced 4th and 18 at the Indianapolis 34 yard line. The Chargers decided to punt rather than attempt a 52-yard field goal.
We will suppose that following a punt, the Colts' expected starting field position is their own 10-yard line. Then according to the Model , San Diego's probability of winning the game if they punt is 0.922.
If the Chargers attempt the field goal, their probability of winning is 0.957 if it's good, but 0.88 if it misses and the Colts take over at the 42-yard line. It's easy to check that in order for attempting a field goal to be better than punting, the probability of making the field goal has to exceed 0.55. Since 0.55 is close to the actual probability, San Diego's decision to punt appears justified. Of course, their probability of winning in this case is about the same with either choice.
With 0:04 left in regulation, Carolina trailed 21-18 and had the ball, 2nd and 10 at the New Orleans 42-yard line. Carolina elected to try a 60-yard field goal, but John Kasay's attempt was blocked, and New Orleans won the game.
This situation is reminiscent of the one we discussed above for the Week-16 Washington-Dallas game, but there are important differences. First, a 60-yard field goal isn't a realistic possibility, particularly outdoors on grass. And keep in mind that the probability of making the field goal has to be twice as large as the probability of scoring a touchdown on a Hail Mary, because the field goal only gets Carolina to overtime.
In addition, the clock reads 0:04 rather than 0:05, and Carolina has no timeouts. Carolina would have to pass to the sideline so that the receiver could get out of bounds. We will examine whether it makes sense to try to do so. Let q denote the probability that Carolina completes a pass and is able to stop the clock before time expires, and let pFG denote the probability of success on the subsequent field goal attempt. Let pI denote the probability that the pass is incomplete, and let pHM denote the probability of scoring a touchdown on a Hail Mary. Then trying a pass play of about 6 yards (followed by a Hail Mary if the pass is incomplete) is better than an immediate Hail Mary if
q pFG 0.5 + pI pHM > pHM.
Since pI is roughly 0.5, this inequality simplifies to
q pFG > pHM.
Now, pFG is around 0.45, but there is enough uncertainty about the other two probabilities in this inequality that the correct strategy isn't clear. In any case, Carolina's chances are slim.
Copyright © 2005 by William S. Krasker