A model-based approach to football strategy.
|January 18, 2005|
In this article we discuss some notable coaching decisions from selected games. Many of the analyses use the footballcommentary.com Dynamic Programming Model.
Trailing 6-3 with 9:54 left in the 3rd quarter, Indianapolis faced 4th down and just under 1 yard to go at the New England 49-yard line. Indianapolis coach Tony Dungy elected to punt.
We will assume that if Indianapolis punts, New England's expected starting field position is their own 10-yard line. In this case, according to the Model, the Colts' probability of winning the game if they punt is 0.388.
If the Colts go for the first down and fail, their probability of winning is 0.325. If they make it, their win probability is 0.454. (Here we have assumed that conditional on making the first down, the Colts' expected gain on the play is 3 yards.) With just under a yard to go near midfield, 70% would be a typical likelihood of making the first down, in which case the Colts' probability of winning if they go for it is
0.7 × 0.454 + (1 − 0.7) × 0.325 = 0.415.
This is noticeably better than punting. Actually, one can verify that it makes sense to go for it as long as the probability of picking up the first down exceeds 0.49. Therefore, it's right for Indianapolis to go for it in this situation even if their chances against New England's defense are somewhat below average.
If you end up kicking a chip-shot field goal on 3rd down on the final play of the first half, when you still have a timeout, it's a good bet that you made a clock-management error along the way. It certainly appears that the Colts did in this game.
After they achieved 1st and 10 at the New England 12-yard line, the Colts called their second timeout to stop the clock with 0:22 left before intermission. The next play was a completed pass. The Colts could have used their final timeout to stop the clock at 0:17, but instead they moved expeditiously to the line of scrimmage and snapped the ball at 0:08. The play was a pass into the end zone that fell incomplete, stopping the clock at 0:02. Indianapolis then brought in the field-goal unit on 3rd down.
Notice that on 2nd down, Indianapolis has the option of running or passing, because they still have a timeout with which to stop the clock if a running play fails to reach the end zone. Nevertheless, the Colts are better off if they use their timeout at 0:17, following their 1st-down play. They still have the option of running, because if the run doesn't score, they have enough time to spike the ball on 3rd down. But if they choose to pass on 2nd down, and the pass is incomplete, they have the opportunity for another pass attempt on 3rd down before sending in Mike Vanderjagt. Therefore, calling timeout at 0:17 dominates not calling timeout: it causes no restriction in the choice of play, and allows an extra play in some scenarios.
Much has been written about how the Patriots supposedly kept Peyton Manning off the field by winning the time-of-possession battle. But obviously, since football teams alternate possessions, they always get about the same number of opportunities. (New England coach Bill Belichick actually pointed this out to a reporter during his press conference on January 11.) In this game both teams had ten possessions (which is somewhat below the average); the problem for the Colts wasn't that they didn't get their share of opportunities, it's that they didn't score when they got them.
Of course, if running the ball proves to be an effective way to score, that's another matter. By all means run. And once you have the lead, taking time off the clock is clearly beneficial. But in a tie game between teams that are regarded as evenly matched, there is no real advantage to taking time off the clock. (As we explained in a previous article, there is an advantage to doing so if you're the underdog.)
With 0:06 remaining in the 4th quarter, and the score 17-17, the Jets faced 3rd and 8 just outside the Pittsburgh 23-yard line. On the next play Jets' quarterback Chad Pennington surprisingly took a knee, and the Jets called their second timeout at 0:04. They then attempted a 43-yard field goal as time expired. The kick was well left, and the game went into overtime.
The analysis presented below suggests that compared to attempting the field goal on third down, taking a knee was like chicken soup: it didn't help, but it really didn't hurt either. Running a real play on third down in an attempt to gain yardage would have been better, but not by very much. (We have attempted no analysis to try to determine if the Jets should have called different plays on 1st and 2nd down.)
Note that by taking a knee, the Jets increased the length of the field goal by almost 2 yards. This decreases the probability of success by about 0.02. Let p41 be the success probability on a 41-yard field goal, let p43 be the success probability on a 43-yard field goal, and let pR be the probability of a kickoff return for a touchdown.
If the Jets take a knee on third down, they win if the subsequent field goal is good, or if it misses but they win in overtime. So their probability of winning is
p43 + (1 − p43)0.5.
If the Jets attempt the field goal on 3rd down and it misses, the Steelers take over at their own 31-yard line with a second or two on the clock. Presumably the Steelers would run out the clock rather than try to score. So the Jets win if their field goal is good and the Steelers fail to score on the ensuing kickoff, or if the field goal misses and the Jets win in overtime. Their probability of winning is therefore
p41(1 − pR) + (1 − p41)0.5.
Now p41 and p43 are approximately 0.74 and 0.72 respectively. (The exact probabilities aren't so important for comparing the strategies; what matters is that the success probability on a field goal of that length decreases by a little over one percentage point per yard.) If the field goal is good, the ensuing do-or-die kickoff return would presumably feature multiple laterals, and so Pittsburgh's probability pR of scoring would be around 0.01. If we plug these values into the above expressions, we find that kicking on 3rd down and taking a knee on 3rd down give the Jets almost exactly the same probability of winning the game, roughly 0.86. The possibility of a kickoff return for a touchdown affects the calculation more than one might think, because a return doesn't send the game to overtime: it wins outright.
We now turn to the third option, which is running a real play on 3rd down in an attempt to gain yardage. When he rejected this course of action, we wonder if Jets' coach Herman Edwards was thinking about what happened to Denver near the end of their Week-2 game in Jacksonville. Instead of trying a 41-yard field goal on 3rd down, Denver coach Mike Shanahan elected to run a play in an attempt to get closer. When Quentin Griffin fumbled, costing Denver its chance to win, Shanahan was predictably subjected to a certain amount of second-guessing. (We examined that decision in our Week 2 Strategy Analysis, and re-examined it in a guest column at Football Outsiders.)
If the Jets run a play on 3rd down, their expected gain is around 3 yards. (The Jets can't even try for a long gain, because time would expire.) If they don't turn the ball over, they win if they make the subsequent 38-yard field goal, or if it misses and they win in overtime. If there is a turnover, they can still win in overtime. So if pt is the probability of a turnover, the Jets' probability of winning the game is
(1 − pt)[p38 + (1 − p38)0.5] + pt0.5.
If we use 0.01 for pt and 0.77 for p38, we find that the Jets' probability of winning if they try to gain yardage on 3rd down is about 0.88, which is better than the 0.86 obtainable by taking a knee on 3rd down. However, this calculation ignores two additional risks from running a play. First, it's possible that the Jets will be unable to stop the clock before time expires. And second, the chance of a penalty on the offense (particularly a false start) exceeds the chance of a penalty on the defense. All things considered, we think the Jets lowered their probability of winning by only about 0.01 by taking a knee on 3rd down rather than running a play.
With 0:53 remaining in the 3rd quarter, Minnesota trailed 21-7, and faced 4th and 22 at the Philadelphia 31 yard line. Vikings' coach Mike Tice decided to go for it rather than punt or attempt a field goal. We will examine whether it can make sense to do so with so many yards to go for the first down.
We will assume that if Minnesota punts, Philadelphia's expected starting field position is their own 10-yard line. Then according to the Model, Minnesota's probability of winning the game if they punt is 0.036.
If the Vikings go for it, we will assume that the play is a pass, and is at least long enough to pick up the first down. There are three main possible outcomes: an incomplete pass (or interception in the end zone, which is similar); a touchdown; or a first down but not a touchdown. Readers are welcome to supply their own probabilities for these three outcomes, but for our analysis here, we will suppose that there is a 0.85 probability that the pass is incomplete (or intercepted), a 0.1 probability of a touchdown, and a 0.05 probability that the pass results in a first down but not a touchdown.
If the pass is incomplete, then according to the Model Minnesota's probability of winning is 0.029. If the Vikings score a touchdown, their probability of winning is 0.159. (This value takes into account that it would be slightly beneficial to attempt a two-point conversion.) If the pass results in a first down but not a touchdown, we assume that the expected line of scrimmage is the Philadelphia 5-yard line, in which case Minnesota's probability of winning is 0.129. It follows that if the Vikings go for it, their probability of winning is
0.85 × 0.029 + 0.1 × 0.159 + 0.05 × 0.129 = 0.047.
With these assumptions, then, going for the touchdown is better than punting.
The final alternative is a field-goal attempt. If the kick is good, Minnesota's probability of winning is 0.063. If it misses, and Philadelphia takes over at their own 39-yard line, Minnesota's probability of winning is 0.027. It's easy to check that that in order for a field-goal attempt to be preferred to going for the touchdown, the probability of making the field goal has to exceed 0.56. Now, NFL place kickers make about 61% of their kicks from 49 yards. However, these were not average conditions. The temperature was
Copyright © 2005 by William S. Krasker