A model-based approach to football strategy.
|October 13, 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 game, trailing 16-10, the Cowboys faced 4th and 1 at their own 43 yard line. Dallas coach Bill Parcells decided to go for it. However, Vinny Testaverde's completed pass to Darian Barnes was stopped for no gain, and the Giants took over on downs. Parcells was accused of panicking, not playing the percentages, and — this one really hurts — disregarding convention.
Parcells confessed after the game that he hadn't played the percentages, but perhaps his confession was misguided. According to the
if Dallas goes for it, their probability of winning the game is either 0.272 or 0.133, depending on whether or not they make it. Assuming that the probability of success is 0.7, Dallas's probability of winning the game if they go for it is
Parcells was also criticized for going for it on 4th and an inch at the Giants' 5 yard line, trailing 3-0 with 2:01 left in the first quarter. If the Cowboys attempt a FG, their probability of winning the game is either 0.5 (if it's good) or 0.42 (if it misses). Assuming that the probability of making it is 0.985, Dallas's probability of winning the game if they go for the FG is
With 6:55 left in the 3rd quarter, Denver had 4th and goal at the Carolina 1 yard line. Denver, leading 13-10, decided to go for it. Their actual choice of play, in which Jake Plummer ran backwards and to his right and threw an off-balance pass from the Carolina 13 yard line, was a disaster. We will base our analysis on the assumption that the Broncos call a play more appropriate for the situation — a run, for example.
According to the Model , if the Broncos score a TD their probability of winning the game is 0.849, whereas if they go for it and fail, their probability of winning is 0.652. If they attempt a FG their probability of winning is 0.71 is they make it, and 0.61 in the unlikely event that it misses and Carolina takes over at the 20 yard line. From a glance at these numbers it's clear that going for it is the right choice, and the intuition is that a 10-point lead is much better than a 6-point lead. Even if the FG is a sure thing, it's easy to check that Denver needs only a 30% chance of scoring the TD to justify going for it. The actual probability of success from the 1 yard line is about 57%. (And using 57%, the decision to go for it stands up even to a substantial probability of a turnover that the opponents run back for a touchdown.)
With 12:28 left in the 3rd quarter, Jets quarterback Chad Pennington's third-down completion to Wayne Chrebet came up two feet short of a first down at the Buffalo 38 yard line. The Jets, leading 10-0, lined up as if to go for it in an attempt to draw Buffalo offside, but ultimately took an intentional delay-of-game penalty at 11:44, and punted.
According to the
if the Jets go for it their probability of winning the game is either 0.886 or 0.816, depending on whether they succeed or fail. Using 0.7 as the probability of success, the Jets' probability of winning if they go for it is
Neither team displayed very good clock management at the end of the game as the Jets, trailing 14-13, were driving for the eventual game-winning score. After Curtis Martin ran to the Buffalo 21 yard line with 1:50 left, the Bills should have begun using their two remaining timeouts. The Jets, with all three timeouts left, were not going to run short of time, so Buffalo had to conserve the clock for a scoring drive of their own that they would very likely need. The Jets, for their part, neglected to let the play clock run all the way down — and then passed the ball (incomplete) on second down instead of running.
The Jets did use good clock management technique prior to their FG at the end of the first half, patiently letting the game clock wind down to 0:03 before calling timeout.
Much of the commentary on the Rams' astonishing comeback against the Seahawks relates to the way the comeback was facilitated by Seattle's poor clock management. Leading 27-24 with 2:40 left in regulation, on 1st and 10 at their own 36 yard line, Seattle threw an incomplete pass which stopped the clock at 2:35. Seattle's motive for passing is clear: Since St. Louis has no timeouts, one more Seattle first down settles the matter. However, as Russell Levine noted in an article at Football Outsiders, if Seattle simply runs the ball three times, being careful to use the play clock each time, their worst case is that the Rams get the ball back with just under 0:30 remaining. A St. Louis score is then very unlikely, though not impossible.
What should Seattle do after throwing the incomplete pass on first down? To try to analyze this question, we built an ad hoc dynamic programming model that operates at the level of individual plays. It's computationally feasible because the Rams have no timeouts, and a Seahawk first down ends the game. We will probably describe the model in detail in an article during the off-season (following much more testing), but the main features are as follows: On fourth down, Seattle punts, and St. Louis's probability of winning is proportional to the time on the clock when they get the ball. On first, second, or third down, Seattle chooses whether to run or pass. There is a probability distribution for the yards gained on a run. We assume a pass is thrown far enough to pick up the first down, and that its probability of completion is a decreasing function of the number of yards to go. The model includes the possibility of a sack. The number of seconds consumed on a play is modeled in detail, including its interaction with the two-minute warning.
Using plausible parameter values, the model says that the correct play on 2nd and 10 at the 36 yard line, with 2:35 left, is to run the ball and let the clock wind down to the two-minute warning. The strategy then becomes more interesting. On 3rd down, the model says to pass if there are between 5 and 10 yards to go for a first down, and run otherwise. This unexpected result actually makes some sense. If it's 3rd and short, Seattle has a good chance to pick up the first down even with a run, which has the additional virtue of keeping the clock moving. If it's 3rd and long, neither a run nor a pass has a high probability of gaining the required yardage, so once again it's better to guarantee that the clock runs. But in the intermediate range, the chances of picking up the first down by passing are good enough to risk stopping the clock.
And by the way, on 1st and 10 at the 36 with 2:40 left, the model does indeed say that Seattle should run, and then run again on 2nd and 3rd down regardless of the yardage gained or lost on the previous play or plays.
With 9:01 left in the 3rd quarter, the Redskins led 10-0, and faced 3rd and 6 at their own 37 yard line. Quarterback Mark Brunell dropped back to pass, but Baltimore safety Ed Reed knocked the ball loose and ran it in for a touchdown. Washington coach Joe Gibbs challenged the ruling, claiming that Brunell's arm was moving forward. However, the ruling was upheld, and Washington was charged with a timeout.
At the time Gibbs had to make his decision there had been only one replay, from which it seemed unlikely that the call would be reversed. However, the probability that the call will be reversed is not the sole factor. One also has to take into account the consequences.
According to the Model , if the play stands as called, Washington's probability of winning the game is 0.647. If the ruling is reversed, the pass is incomplete and Washington presumably punts. In this case their probability of winning the game is 0.846. It follows that even if the likelihood of reversing the call is only 10%, Washington still increases its probability of winning the game by about 0.02 by challenging, before taking the costs into account. The costs are the loss of a challenge and the likely loss of a timeout. With only twenty-two minutes left until the two-minute warning, the Redskins were unlikely to need two challenges. The timeout is a more serious issue. In the absence of a model for valuing timeouts (a project for the off-season), we're somewhat diffident; but with the Redskins still leading, it feels unlikely that an extra timeout at that stage of the game could be worth 0.02 toward Washington's probability of winning. So the decision by Joe Gibbs to challenge was probably correct.
Leading 10-0 with 9:23 left in the 2nd quarter, the Patriots chose to attempt a 47-yard FG on 4th and 1 at the Miami 29 yard line. Unfortunately for New England, Adam Vinatieri's kick was wide right.
If the Patriots make the FG, then according to the
their probability of winning the game is 0.835. If they miss, Miami takes over at the 37 yard line, and New England's probability of winning is 0.758. NFL place-kickers make about 65% from 47 yards, and if we use this value, we find that New England's probability of winning the game if they attempt the FG is
If instead the Patriots go for the first down, their probability of winning the game is either 0.843 or 0.766, depending on whether or not they make it. Using 0.7 for the probability of success, we find that New England's probability of winning the game if they go for it is
Houston scored a TD with 3:00 left in regulation to narrow their deficit to 28-20 prior to the try for an extra point or points. Naturally Houston coach Dom Capers elected to kick the extra point, as would every coach in the League, but in this situation it's actually better to go for two. To see why, notice that up to a good approximation, Houston can win only if they score one more TD while preventing Minnesota from scoring. So for purposes of examining extra-point strategy, we can assume that scenario prevails. For simplicity, assume also that a kicked extra point is a sure thing. Under these conditions, if Houston chooses to kick the extra point, the game will be decided in overtime.
If instead Houston elects to go for two following the first TD, they will be better off if they make it (which has probability 0.4), and worse off if they miss both this two-point conversion and the next one (probability
We analyzed this situation in more detail in a previous article .
With a comfortable 21-7 lead, and 7:19 remaining in the 3rd quarter, San Diego faced 4th and goal at the Jacksonville 3 yard line. The Chargers chose to kick a field goal.
According to the
if San Diego makes the FG their probability of winning the game is 0.964, whereas if they miss and Jacksonville takes over at the 20 yard line, San Diego's probability of winning is 0.935. Assuming that the probability of success on the FG is 0.985, San Diego's probability of winning the game if they attempt the FG is
If the Chargers instead go for the TD, their probability of winning the game will be either 0.986 or 0.948, depending on whether or not they score. One can check that the probability of scoring has to be at least 0.4 to make going for the TD better than kicking the FG. However, 0.4 is approximately the probability of a successful two-point conversion, for which the ball is spotted at the 2-yard line, and hence the probability of scoring from the 3-yard is smaller. So, San Diego did the right thing by kicking. Had they been leading by fewer than 14 or trailing, the result of the calculation might have been different.
Copyright © 2004 by William S. Krasker