A model-based approach to football strategy.
|November 30, 2004|
In this article we discuss some notable coaching decisions from selected games. Many of the analyses use the footballcommentary.com Dynamic Programming Model .
Trailing 21-10 with 3:50 left in the 3rd quarter, and facing 4th and 7 at the Green Bay 24 yard line, St. Louis lined up for an apparent field goal attempt. However, St. Louis coach Mike Martz had called for a fake. Holder Dane Looker passed the ball to kicker Jeff Wilkins, but Wilkins was stopped immediately for a loss, and the Packers took over on downs.
Commentator Al Michaels remarked after the play that a field goal would have made it a one-possession game. We think it was a bit early to reduce the score differential to a "number of possessions." (Even near the end of the game, one shouldn't overestimate a team's prospects when they pull to within 8 points: In addition to scoring a touchdown, they still have to make a two-point conversion and then win in overtime. Down 8 is much worse than down 7, which is much worse than down 6; yet all are one-possession games.)
According to the
if the Rams attempt a field goal, their probability of winning the game is 0.143 if it's good but 0.076 if it misses. NFL place-kickers make about 76% from 42 yards. If we use that percentage, it follows that the Rams' probability of winning the game if they kick is
To analyze the fake field goal, we need some assumptions. We will suppose that conditional on the play not gaining the first down, its average outcome is a 2-yard loss, in which case the Rams' probability of winning is 0.08. Conditional on gaining a first down but not scoring, we'll suppose the average outcome is the 12 yard line, at which point the Rams' probability of winning is 0.212. Finally, if the Rams score a touchdown on the play, their probability of winning is 0.284. (This value incorporates the fact that it's optimal to attempt a two-point conversion.)
The final step is to come up with probabilities for these events. Note that St. Louis had the option of going for the first down openly, instead of from field-goal formation. It follows logically that Mike Martz, at least, thought the fake field goal gave the Rams a better chance of success. We don't have a strong opinion on that, so we'll use probabilities that would be reasonable if the Rams went for the first down openly.
We will suppose that there is a 0.67 probability that St. Louis fails to make the first down, a 0.28 probability that the play results in a first down but not a touchdown, and a 0.05 probability that the play results in a touchdown. With these assumptions, if the Rams fake the field goal their probability of winning is
0.67 × 0.08 + 0.28 × 0.212 + 0.05 × 0.284 = 0.127,
which (coincidentally) is the same as for an actual field-goal attempt. Changing the probabilities, either for the actual field goal or the fake, will change the result. But with reasonable probabilities, the decision is likely to remain a close call.
With 14:57 remaining in the 4th quarter, New England scored a touchdown to increase their lead to 15-3 prior to the try. The Patriots then elected to attempt a two-point conversion.
This is the right decision, although it increases New England's probability of winning by only a small amount. At that point in the game, the Patriots are highly likely to win regardless of their choice. According to the Model , New England's probability of winning the game is 0.944 if they go for two, versus 0.94 if they kick. Nevertheless, the decision to go for two is robust, in the sense that it remains the correct decision even if we assume a sub-par chance of success. In fact, going for two is preferred as long as New England's probability of success exceeds 0.24. (The same result can be found by consulting the Chart .)
Late in the first half, Arizona trailed 3-0, but had the ball deep in the Jets' end. Arizona had one timeout. On 3rd and goal with 0:38 left, the Cardinals ran a quarterback draw to the Jets' 3 yard line.
The camera showed Arizona coach Dennis Green on the sideline holding up three fingers, obviously indicating to his players that he wanted to call timeout with 0:03 remaining, to set up for a field goal. Although this is considered good practice, we have argued elsewhere that if it's fourth down, there is no point to leaving even 0:03. Depending on the clock operator, a short field goal will occasionally consume less time than that. Admittedly, the risk that the ensuing kickoff will be returned for a touchdown is very small, but it's completely unnecessary.
The events on the field provided still another reason to target 0:02: Notwithstanding the coach's instructions, the Arizona players called timeout at 0:04. (On the field goal, Arizona was helped by a slow clock operator, who clearly should have stopped the clock at 0:01, but instead let the half expire.)
By the way, we agree with the decision to kick the field goal. According to the Model , it makes sense to go for the touchdown in that situation only if the probability of success exceeds 0.42. That's not the case from the 3 yard line.
Late in the game, the Jets led 13-3, and had the ball on 2nd and 10 at their own 12 yard line. The Cardinals used their final timeout to stop the clock at 1:41. On the next two plays, the Jets had LaMont Jordan run up the middle.
We would have taken a knee on both plays. The most serious risk that the Jets face at that point is a fumble deep in their own end. (There is also a risk of a blocked punt, but that risk comes into play either way, and arises with very little time left.) If the Jets take a knee twice, and are careful to use the full play clock, Arizona will get the ball back with about 0:15 left. If they can figure out how to score twice in that period of time with no timeouts, good for them.
With 7:54 left in the 2nd quarter, Seattle had the ball on 4th and goal at the Buffalo 1 yard line. Seattle trailed 10-0. In one of the week's worst coaching decisions, measured by the effect on the probability of winning the game, Seattle decided to kick a field goal.
According to the Model , if the Seahawks kick the chip-shot field goal, their probability of winning is 0.27. If they go for the touchdown, their probability of winning is 0.4 if they score but 0.224 if they are stopped.
If we assume 0.57 for the probability of scoring, then Seattle's probability of winning if they go for it is
Late in the 2nd quarter, Indianapolis scored a touchdown to take a 27-6 lead. The ensuing kickoff was caught by Detroit's Eddie Drummond several yards deep in his own end zone. Rather than try to run the ball out, Drummond took a touchback, and the Lions took over at their own 20 yard line with 0:50 remaining in the half.
If it had been the opening kickoff, Drummond's decision would have been unobjectionable. On a kickoff return that starts several yards deep in the end zone, the average starting field position is probably inside the 20 yard line. But the point here is that this was not the opening kickoff. Trailing by 21 points, Detroit needs a score before halftime to get into the game, and in particular they need a touchdown. According to the Model , when Indianapolis kicks off to start the second half, Detroit's probability of winning the game will be 0.026 if they still trail by 21 points. If they trail by 18 their probability of winning will be 0.048, and if they score a touchdown before halftime to close to within 14, their probability of winning will jump to 0.1. Detroit's chances of a touchdown before halftime improve dramatically if they can get good starting field position.
The touchback gives Detroit the certainty of the 20 yard line. If instead Drummond tries for a runback, the outcome is random. However, since Detroit's chances are already pretty low, the amount by which they are hurt if the runback is short is much less than the amount by which they are helped if the runback is long. Because of this "convexity," we think Drummond should have run it back.
With 9:46 left to play in the 3rd quarter, leading 13-0, Pittsburgh lined up to punt at the Washington 33 yard line on 4th and 3. The Steelers were then penalized for delay of game, making it 4th and 8 at the 38. However, because they had decided to punt, the delay penalty wasn't harmful, and might even have been deliberate. Therefore, the decision to punt should be evaluated from the original line of scrimmage.
According to the Model , if the Steelers punt their probability of winning the game is 0.913.
If instead Pittsburgh goes for the first down, their probability of winning is 0.947 if they make it and 0.893 if they fail. (The former number was computed under the assumption that conditional on making it, the expected gain on the play is 5 yards.) If we use 0.5 for the probability of making the first down, then Pittsburgh's probability of winning if they go for it is
With 1:47 left in the game, and Dallas leading 21-7, Chicago quarterback Jonathan Quinn's pass was intercepted by Dat Nguyen. Chicago had no timeouts. There is nothing good that can happen for Dallas if Nguyen tries to run, and indeed, it had been only an hour since a defender intercepted a pass and then fumbled. Nevertheless, since Nguyen had some room to run, we expected him to try to be a hero and score. We were pleasantly surprised when he dropped to the turf immediately. Dallas took a knee three times and the game was over.
Copyright © 2004 by William S. Krasker