A model-based approach to football strategy.
|December 21, 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 6:08 remaining in the 2nd quarter, Dallas scored a touchdown to close the deficit to 14-12 before the try. The Cowboys then chose to attempt a two-point conversion.
This attempt is literally off the Chart: The two-point conversion Chart we prepared using the Model doesn't even cover the first half of the game. Although there are certain score differentials for which it is correct to go for two even with a significant amount of time left in the 2nd quarter — down by two being one of them — the gains from going for two are very small.
Direct calculations using the Model indicate that it's correct for Dallas to go for two as long as the probability of success exceeds 0.38. However, if the actual success probability is 0.4, going for two increases the Cowboys' probability of winning the game by only 0.001. Even if Dallas's success probability is 0.5 (and we have no reason to believe it's that high), going for two increases their probability of winning the game by only 0.008.
If this were the whole story, we would conclude that Dallas's decision was innocuous; it didn't help much, but it didn't hurt. The problem is that before the try, either to decide whether to go for two or to decide what play to run, Dallas called timeout. One thing is certain: The use of a timeout more than offset whatever miniscule benefits Dallas could have obtained by going for two.
If the game is still in the first half, and you have to call a timeout to think about whether to go for two, don't bother. Just kick the extra point.
Late in the game, New England had the ball, leading 35-28. With 2:10 remaining, on 1st and 10 at the New England 46-yard line, Corey Dillon ran for no gain, and Cincinnati elected to use its final timeout to stop the clock at 2:04. The question we wish to address is whether the Bengals should have preserved their timeout and let the clock run down to the two-minute warning.
Regardless of when the Bengals use their timeout, if the Patriots make a first down, the game is over. So this decision should be analyzed under the assumption that the Bengals stop the Patriots. With the clock stopped at 2:04, the next play takes the clock to about 1:59, where it stops for the two-minute warning. If New England's 3rd-down play keeps the clock running, they can take the clock down to about 1:15 before punting. If the 3rd-down play is an incomplete pass, the clock will stop at about 1:54.
Alternatively, if the Bengals preserve their timeout, the Patriots run their 2nd-down play at 2:00, and if that play keeps the clock running, Cincinnati calls timeout at about 1:54. If New England's 3rd-down play also keeps the clock running, the Patriots can take the clock down to about 1:10 before punting. If the 3rd-down play is an incomplete pass, the clock will stop at about 1:49.
The conclusion is that if New England runs the ball on 2nd down, or completes a pass, the Bengals have bought themselves an extra 5 seconds by using their timeout at 2:04. This advantage persists regardless of the outcome of the 3rd-down play.
However, calling timeout at 2:04 has one important drawback: It increases New England's play-calling flexibility on 2nd down. Since the game clock stops after that play for the two-minute warning, an incomplete pass does no damage to the Patriots, at least from the standpoint of clock management. Therefore, the Patriots have the option of passing the ball up the field, when they would otherwise have a strong inclination to run.
It's hard to place a precise value on that play-calling flexibility, but it's probably worth more than 5 seconds on the clock, which is the most the Bengals can gain by calling timeout at 2:04. Therefore, we would have let the clock run.
With 9:53 remaining in the 4th quarter, Jacksonville led 21-17, and faced 4th and goal at the Green Bay 3-inch line. Jacksonville decided to go for it.
Although the commentators described the call as "gutsy," it appears to have been the correct choice by a wide margin. According to the
if the Jaguars kick the field goal, their probability of winning the game is 0.846. If they go for the touchdown, their probability of winning is 0.955 if they score but 0.808 if they are stopped. Assuming a 0.6 probability that they score from 3 inches out, Jacksonville's probability of winning if they go for it is
Late in the 4th quarter, with the score 21-21, Minnesota had the ball deep in Detroit's end. With 1:52 left, on 2nd and 4, the Vikings ran for two yards to the Lions' 11-yard line, and the Lions called their final timeout at 1:44.
On the next play, Minnesota running back Moe Williams found a hole up the middle. Overpowering a Detroit tackler near the goal line, Williams scored the go-ahead touchdown with 1:37 left.
Detroit then marched down the field and scored a touchdown with 0:08 remaining, but missed the extra point on a botched snap to give Minnesota a 28-27 victory.
If Minnesota had thought through the situation during the timeout at 1:44, they wouldn't have needed such good luck. A first down on that 3rd-down play is important, but a touchdown is counterproductive. Notice that if Williams had been stopped at the 1-yard line, giving Minnesota 1st and goal, the correct tactic for Minnesota would have been to run down the game clock and kick a walk-off field goal. As we described in detail in a
it would be wrong for Minnesota to try to score a touchdown — even though Detroit would presumably stand aside and invite them to do so. If you agree with this, it's logically inescapable that Minnesota is better off if Williams doesn't score on his run at 1:44. During the timeout that preceded that run, the coaches should have told Williams that if he's fortunate enough to find a big hole, he should down himself short of the goal line. Detroit can then win the game only if the field goal misses (probability 0.02) and then Detroit wins in overtime (probability 0.5). Minnesota thereby reduces Detroit's probability of winning to
An interesting situation arose following the pass interference call that gave Detroit 1st and goal at the Minnesota 1-yard line with 0:12 remaining. As we described in a previous article, normally in equilibrium Minnesota would select a defense (i.e. personnel and their positions on the field) against which a run and a pass are equally likely to score. However, Detroit had no timeouts. Therefore, time would expire following a failed running play, whereas Detroit could run as many as three plays if the first two were incomplete passes. We won't go through the algebra here, but the not-very-surprising result is that in equilibrium, Minnesota has to practically dare Detroit to run, with a defense that is heavily geared toward stopping a pass play — more like a "prevent" defense than the usual goal-line defense.
With 7:36 remaining in the 4th quarter, and Pittsburgh leading 14-13, Pittsburgh quarterback Ben Roethlisberger was sacked, bringing up 4th and 15 at the Jacksonville 36-yard line. The Steelers then deliberately let the play clock expire, and after the officials moved the ball to the 41-yard line for delay of game, the Steelers punted.
There is a good reason to take a delay penalty here, but it's not the one Pittsburgh presumably had in mind. We assume that the Steelers thought the pooch kick would be more effective from the 41-yard line. However, it's hard to see how that can be a significant benefit, because Jacksonville has the option of declining the distance penalty. The better reason to let the play clock expire is that it's in Pittsburgh's interest at that point to take time off the game clock. Actually, Pittsburgh missed a good opportunity. The game clock restarted after the penalty, with 25 seconds on the play clock. The Steelers could have consumed almost the entire 25 seconds, but instead punted with 14 seconds on the play clock. (We described this tactic in a guest article at Football Outsiders.)
(Notice that a desire to punt from farther back is independent of clock management: If a team prefers to punt from farther back but wants to retain time on the game clock, they can line up quickly and false start.)
Teams continue to be oblivious to clock management.
Late in regulation, Atlanta had the ball, trailing 31-24. With 3:13 left, from their own 41-yard line, the Falcons connected on a 54-yard pass play to the Carolina 5-yard line.
Up to that point, there was a possibility that Atlanta would run out of time, or at least that time pressure would be a constraint on their play calling. In other words, the clock was on Carolina's side. But that situation reversed following Atlanta's long pass play. With 1st and goal at the 5, and almost three minutes left, Atlanta might or might not score a touchdown, but if they don't it won't be because they're short of time. On the contrary, it's in their interest to run time off the clock. At that point it's essential for Carolina to call timeout, so that if the Falcons do score the tying touchdown, the Panthers will have adequate time for a potential game-winning score before the end of regulation.
Carolina could have called timeout as early as 2:59, but didn't. In fact, the Panthers didn't call timeout until 2:27, at which point the play clock was down to :10 and the Falcons were about to snap the ball anyway.
With 5:26 remaining in the 1st quarter, Baltimore trailed 3-0, and faced 4th down and a half yard to go at the Indianapolis 48-yard line. The Ravens sent in the punting unit.
We will assume that if the Ravens punt, the Colt's expected starting field position is their own 10-yard line. Then according to the Model, if Baltimore punts, their probability of winning the game is 0.438.
If instead the Ravens go for the first down, their probability of winning is 0.484 if they make it but 0.391 if they fail. If we assume that the probability of picking up a half yard near midfield is 0.7, then Baltimore's probability of winning the game if they go for it is
With 2:31 remaining in the 3rd quarter, and the score 28-28, Tennessee faced 4th and 1 at the Kansas City 46-yard line. The Titans brought in punter Craig Hentrich, but lined up with a group of five players toward the right sideline, and two toward the left sideline. Hentrich then walked up to center Ken Amato, obviously suggesting a trick play.
Tennessee did almost the same thing in Week 8 versus Cincinnati. In that game, Hentrich took the snap and ran for the first down against the almost undefended center part of Cincinnati's line.
This time, though, Amato snapped the ball diagonally (and not between his legs) to Troy Fleming over toward the right sideline. Fleming gained 2 yards for a first down.
We watched the snap carefully on video tape. Amato, holding the ball with his left hand, first brought the ball off the ground and toward himself, and then, preceded by what appears to be a slight "backswing," tossed the ball toward the sideline to Fleming. Although there was no pause between these two parts of the snap, it's not clear if the motion complied with the requirements of Rule 7-3-3-b, which says that "The impulse must be given by one quick and continuous motion of hand or hands of snapper." That's something to keep in mind in case this sort of trick play becomes more common.
The Jets had the ball late in the first half, trailing 7-6. With 0:47 left before halftime, on 3rd and 10 from their own 37-yard line, the Jets completed a pass for a 3-yard gain.
Houston should have called timeout immediately, and could have done so with 0:39 remaining. There is really no downside to doing this. If, following the Jets' punt, the Texans find themselves deep in their own end, they have the option of running out the clock. The Jets, with two timeouts, would be powerless to prevent that. But if the Texans get a good punt return, they have the possibility of adding to their lead before intermission.
The Texans were asleep, however, and didn't call timeout until 0:03. The Jets then erred by punting. A better tactic at that point is to throw a long pass, hoping for a touchdown or a pass-interference call. Almost always, the half will end without another score, but the probability of a score by the offense is larger than the probability of a score by the defense.
Even if the Jets decide not to attempt to score, punting still unnecessarily risks a block or a return for a touchdown. A better tactic in that case is to throw a long pass beyond a receiver who is running down the sideline. By the time the ball lands safely out of bounds, the half is over. (New England used this tactic at the end of its divisional-round game against Tennessee in January.)
Tennessee attempted three onside kicks in the first quarter of this game. We can use the Model to estimate the probability of success that is required to justify these attempts. We will assume that after an onside kick, whichever team gains possession will do so at Tennessee's 45-yard line.
The first attempt came with 10:37 remaining in the 1st quarter, and Tennessee leading 7-3. According to the Model, Tennessee's probability of winning the game is 0.579 if they kick deep. If they kick onside, their probability of winning is 0.634 if they recover the kick, but 0.548 if Indianapolis gains possession. From these numbers it follows that the onside kick is justified if its probability of success exceeds 0.36.
The second attempt came with 8:08 left in the quarter, and the score 10-3 in favor of Tennessee. A similar calculation shows that in this case, the onside kick is justified if its probability of success exceeds 0.37. The third attempt occurred with 3:54 left in the quarter, and Tennessee leading 17-10. Not surprisingly, this attempt also requires a 0.37 probability of success in order for it to make sense.
The Colts didn't use an onside prevent for any of these kickoffs; in fact, even on the third attempt, the Indianapolis players were already moving toward their own goal when the ball was kicked. So Tennessee's chance of recovering the kick was probably fairly high in each case.
Copyright © 2004 by William S. Krasker