A model-based approach to football strategy.
|November 16, 2004|
In this article we discuss some notable coaching decisions from selected games. Many of the analyses use the footballcommentary.com Dynamic Programming Model .
With 10:44 left in the 4th quarter, Tampa Bay trailed 17-14, and faced 4th and 1 at the Atlanta 28 yard line. In a controversial decision , Tampa Bay coach Jon Gruden decided to go for the first down rather than kick a field goal. However, Michael Pittman was stopped, and Atlanta took over on downs.
According to the
if the Bucs attempt a field goal, their probability of winning the game is 0.458 if it's good but 0.258 if it misses. The average NFL place-kicker makes about 68% from 46 yards, and if we use that value, we find that Tampa Bay's probability of winning if they kick is
If the Bucs go for it, their probability of winning is 0.501 if they make it but 0.273 if they are stopped. If the probability of gaining the yard is 0.7, then Tampa Bay's probability of winning if they go for it is
Trailing Baltimore 17-14 in the final minute of regulation, the Jets had the ball deep in Baltimore's end. The Jets obviously needed to score, and since Baltimore still had two timeouts, they also wanted to run time off the clock.
The critical moment came with the clock stopped at 0:08, on 3rd and goal at the 3 yard line. At that point the Jets are in excellent position, and we have no complaints about their clock management up to that juncture. They still have a timeout, and so have the option of running or passing. If they score a touchdown on 3rd down, they win unless the Ravens can run back the ensuing kickoff. Otherwise, on 4th down the Jets can kick a chip-shot field goal to send the game into overtime, or else go for it. Notice that if they end up inside the 1 yard line after their 3rd-down play, the correct play is to go for it on 4th down.
Poor execution then derailed the plan. With the play clock winding down, Jets' coach Herman Edwards concluded that the Jets were not going to get the play off in time, and used the Jets' final timeout to prevent delay of game. Edwards then elected to kick a field goal on 3rd down.
Even after burning their final timeout, the Jets should try to pass into the end zone instead of kicking on 3rd down. If they do so, they win if they score, and lose if there is a sack or an interception. If the pass is incomplete, they kick a field goal on 4th down, and go to overtime where their probability of winning is about 0.5. So the situation is completely symmetric, and it makes sense to try another play as long as the probability of scoring exceeds the combined probability of a sack or an interception. This is surely the case from the 3 yard line, from which the probability of scoring is around 0.3.
Finally, there is the question of whether Edwards would have been better off taking a delay-of-game penalty instead of using the Jets' last timeout. For one thing, when Edwards signaled for a timeout, it wasn't certain that the play clock would expire before the snap. A review of the video tape suggests it would have been close. But leave that aside. If the Jets take the penalty, it's 3rd and goal at the 8 yard line rather than the 3, but they still have a timeout. Their probability of scoring a touchdown is smaller (though not by as much as usual in this case, because with a timeout the Jets have more flexibility in their choice of play). On the other hand, in case of a sack they can call timeout and attempt what would be about a 31-yard field goal, whose probability of success is about 0.91. If the attempt is good, it gets them to overtime, where their probability of winning is 0.5. Compared to calling timeout, then, letting the play clock expire lowers their probability of winning by the difference in the probability of scoring a touchdown, and raises it by 91% of 50% of the probability of a sack. Because the probability of a sack is small, on balance we think it's better to call timeout.
With 9:50 left in the 1st quarter, and no score, Tennessee had the ball at the Chicago 45 yard line, 4th down and 1 yard to go. The Titans decided to go for the first down. Unfortunately for them, running back Chris Brown was stopped for no gain.
We will assume that if Tennessee punts, Chicago's expected starting field position is their own 10 yard line. In that case, according to the Model , if the Titans punt their probability of winning the game is 0.485.
If instead the Titans go for it, their probability of winning is 0.534 if they make the first down but 0.443 if they are stopped. If we assume they have a 0.7 probability of success, then their probability of winning if they go for it is
The game ended in overtime when Tennessee quarterback Billy Volek fumbled into his own end zone, and Tennessee lineman Fred Miller fell on the ball for a safety. What Miller thought he was accomplishing by falling on the ball is unclear.
Perhaps they had already given up. Otherwise, why didn't Dallas use any of its timeouts near the end of the first half?
With 1:16 left in the half, and Philadelphia leading 28-14, the Eagles had 3rd and 1 at the Dallas 6 yard line. Philadelphia then ran for 5 yards, making it 1st and goal at the 1 yard line. Philadelphia still had two timeouts, so there was no way that time limitations would prevent them from getting a touchdown. On the contrary, it was in Philadelphia's interest to take time off the clock. Their next play, on which they scored a touchdown, came at 0:34.
You can make a case that Dallas should have begun using its three remaining timeouts much earlier in Philadelphia's drive, but they certainly should have done so at 1:09 when the Eagles got to 1st and goal at the 1 yard line. If, as actually happened, Philadelphia scores on the next play, Dallas then gets the ball back with two timeouts and about 1:06 left, and a chance to get back into the game.
With 8:31 left before halftime, Houston trailed 14-0, and faced 4th and 2 at the Indianapolis 37 yard line. The Texans elected to attempt a 55-yard field goal rather than go for the first down.
According to the
Houston's probability of winning is 0.143 if the field goal is good, but 0.085 if it misses. We will optimistically suppose that place-kicker Kris Brown has a 45% chance of making the kick. In that case, Houston's probability of winning if they attempt the field goal is
If instead the Texans elect to go for the first down, their probability of winning is 0.147 if they make it and 0.089 if they are stopped. If the probability of picking up the required two yards is 0.54, then Houston's probability of winning if they go for it is
With 6:54 remaining in the 4th quarter, Detroit trailed Jacksonville 17-7, and faced 4th and goal at the Jacksonville 3 yard line. The Lions decided to settle for the field goal rather than try for the touchdown.
For simplicity we will assume that the field goal is a sure thing. According to the Model , if the Lions kick the field goal, their probability of winning the game is 0.079.
If instead the Lions try for the touchdown, their probability of winning is 0.195 if they score but 0.02 if they fail. If we assume that the probability of scoring is 0.35, then Detroit's probability of winning if they go for it is
Carolina place-kicker John Kasay was injured in the 3rd quarter, forcing the Panthers to turn to punter Todd Sauerbrun for field goals and extra points. When the Panthers scored a touchdown with 9:24 left in the 3rd quarter to close the deficit to 17-12 before the try, Carolina considered going for two rather than have Sauerbrun kick. Ultimately they decided to kick, but in fact they should have gone for two even in the absence of whatever concerns they might have had about Sauerbrun. As can be seen from the Chart , the Panthers need only a 0.33 probability of success on the two-point conversion in order to justify going for it.
Minnesota trailed 31-24 late in the game, but had possession deep in Green Bay's end. On 1st and 10 at the Green Bay 17 yard line with 1:29 left, Daunte Culpepper completed a pass to Moe Williams, who powered through a would-be tackler to score the tying touchdown with 1:20 on the clock.
Were we the only ones who had a feeling that Minnesota had scored too soon?
Now, even we would not suggest that Williams should have been instructed to down himself at the 1 yard line, rather than score, if the opportunity arose. But suppose he just happened to be tackled at the 1 yard line. Minnesota can get three plays off in the remaining time, even if they're all running plays. If one of the plays is a pass, they might have time for four plays. With even three shots from the 1 yard line, the probability that Minnesota fails to score must be under 0.2. This is less than the probability that Green Bay, with two timeouts, scores in the final 1:20. So we actually do think that Minnesota has a higher probability of winning the game if Williams is tackled at the 1 yard line than if he scores.
With 2:33 left in the 3rd quarter, having just returned a punt for a touchdown to close the deficit to 23-6, Buffalo decided to try a two-point conversion. As can be seen from the Chart , it really doesn't make sense to go for two in that situation. To justify a two-point conversion, Buffalo needs a 0.46 probability of success, but the actual probability of success is around 0.4.
The try failed, but New England was called for roughing the passer, giving Buffalo a second chance, this time from the 1 yard line. Buffalo went for two again, and this time they were correct to do so. From the 1 yard line, their probability of success is about 0.57.
Buffalo didn't make it the second time, either.
Playing as a substitute in New England's injury-depleted secondary, Troy Brown made a nice catch for an interception. We were reminded of the quip we sometimes hear when a defensive back drops the ball on that kind of opportunity: If he could catch, he'd be a wide receiver.
Copyright © 2004 by William S. Krasker