A model-based approach to football strategy.
|November 23, 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 7:59 left in the 4th quarter, the Packers trailed 13-10, and had the ball at the Houston 21 yard line, 4th down and about two feet to go for a first down. Green Bay coach Mike Sherman elected to attempt the 39-yard field goal rather than go for the first down.
According to the
if the Packers attempt the field goal, their probability of winning the game is 0.449 if it's good but 0.225 if it misses. NFL place-kickers make about 81% from 39 yards. Using that value, we find that Green Bay's probability of winning if they kick is
If the Packers try for the first down, their probability of winning is 0.543 if they make it but 0.24 if they fail. The probability of gaining two feet is about 0.72. It follows that Green Bay's probability of winning if they go for the first down is
With 0:11 left in a scoreless 1st quarter, Cleveland faced 4th and 2 at the Jets' 42 yard line. The Browns elected to punt. Derrick Frost's kick sailed into the end zone for a touchback.
For our analysis we will assume that if Cleveland punts, the Jets' expected starting field position is their own 10 yard line. In that case, according to the Model , Cleveland's probability of winning if they punt is 0.526.
If instead the Browns go for the first down, their probability of winning is 0.588 if they make it and 0.482 if they fail. Assuming that the probability of picking up 2 yards near midfield is 0.53, we find that Cleveland's probability of winning if they go for it is
With 0:47 left before halftime, Cleveland had two timeouts remaining, and the Jets had none. On 3rd and 1 at their own 37 yard line, Cleveland ran the ball for no gain. The clock continued to run, with one second more on the game clock than on the play clock. Cleveland then inexplicably called timeout at 0:12, forcing them to punt to Santana Moss. The correct tactic is to let the play clock expire with 0:01 left in the half, and then, following the five-yard penalty for delay of game, to take a knee on 4th down.
Finally, with 2:00 left in the game and the Jets leading 10-7, the Jets' LaMont Jordan ran for a first down at the Cleveland 43 yard line. The Browns belatedly called their final timeout at 1:46, but even if they had used it promptly, it wouldn't have prevented the Jets from taking a knee three times and running out the clock.
As we explained in our article on intentional fouls , Cleveland needs to take a penalty at the conclusion of the play on which Jordan gains the first down. The simplest way to accomplish this is for a Cleveland player to take off his helmet (Rule 12-3-1-g). The resulting 15-yard penalty moves the Jets into field-goal range. But the important thing is that the clock stops, and doesn't restart until the snap. Combined with Cleveland's remaining timeout, this forces the Jets make another first down in order to run out the clock. Even if the Jets kick a field goal, the Browns get the ball back trailing by 6 points with about 0:25 left, and have a slight chance to win.
With 3:56 remaining in a scoreless first period, Dallas faced 4th and goal at the Baltimore two-foot line. The Cowboys decided to kick a field goal.
Assume for simplicity that the field goal is a sure thing. Then according to the Model , if Dallas kicks, their probability of winning the game is 0.548.
If Dallas goes for the touchdown, their probability of winning is 0.668 if they score but 0.498 otherwise. From two feet out, the probability of scoring is around 0.59. If we use that value, we find that Dallas's probability of winning if they go for it is
With 14:17 left in the 4th quarter, Minnesota scored a touchdown to close the deficit to 19-13 prior to the try. The Vikings elected to attempt a two-point conversion.
As the Chart shows, a two-point conversion in that situation is appropriate only if the probability of success exceeds 0.46. We generally assume that the actual success probability is 0.4, in which case Minnesota would have been better off kicking the extra point. It's unusual for a coach to call for a two-point conversion in a situation in which the Model says to kick (although the reverse happens all the time), but this isn't the first time Mike Tice has done it. In 2002 he went for a two-point conversion when trailing by 1 point with 0:05 left in the game. That decision makes sense only if the probability of success exceeds about 0.5.
Of course, there is undoubtedly some team-to-team variation in the probability of a successful two-point conversion. It's possible that the Vikings think their success probability exceeds 0.46. However, in Week 10 versus Green Bay, Minnesota scored a touchdown with 2:53 remaining to pull to within 8 points before the try. The Chart shows that in this case, Minnesota should go for two as long as the probability of success exceeds 0.38, yet they kicked the extra point. Teams can form their own opinions of the probabilities, but they should at least be consistent.
Leading 13-7 more than halfway through the third quarter, San Diego arrived at 1st and goal at the Oakland 1 yard line. On 1st down LaDainian Tomlinson was stopped for no gain, and the next two plays resulted in incomplete passes. San Diego then kicked a field goal with 5:22 left in the quarter, which the Model says gives San Diego a 0.833 probability of winning the game.
If instead the Chargers go for it on 4th down, their probability of winning is 0.918 if they score. (This number incorporates the fact that it's optimal to attempt a two-point conversion.) If San Diego is stopped, their probability of winning is 0.768. Using these numbers, it's easy to check that San Diego should go for it as long as the probability of scoring exceeds 0.44. So notwithstanding the results of the previous three plays, the Chargers should have gone for the touchdown on 4th down.
With 6:48 remaining in the 3rd quarter, Kansas City trailed New England 17-10, and faced 4th and 2 at the New England 5 yard line. The Chiefs elected to kick a field goal.
For simplicity we will suppose that the field goal is a sure thing. According to the Model , it gives the Chiefs a 0.29 probability of winning the game.
If the Chiefs go for it, their probability of winning is 0.47 if they score a touchdown on the play, 0.438 if the play picks up the first down but doesn't score, and 0.223 if the play fails to make the first down. We will assume that the probabilities of these three outcomes are 0.15, 0.35, and 0.5 respectively. From these assumptions it follows that Kansas City's probability of winning if they go for it is
0.15 × 0.47 + 0.35 × 0.438 + 0.5 × 0.223 = 0.335.
Since this exceeds Kansas City's probability of winning if they kick the field goal, we conclude that they should have gone for it.
With 0:37 remaining before halftime, Buffalo had the ball, 4th and 2 at the St. Louis 3 yard line. The Bills, trailing 17-14 and with no timeouts, decided to bring in Rian Lindell to kick the chip-shot field goal. According to the Model , this gives Buffalo a 0.475 probability of winning the game. (It's less than 0.5 because the Bills kick off to start the second half.)
Alternatively, the Bills can go for the touchdown. If they score a touchdown before halftime, their probability of winning the game is 0.632, but if they fail to get any points, their probability of winning is 0.369.
For our analysis we will assume that if the Bills pick up the first down without scoring, they will spike the ball and have time for another play. At that point they would be inside the 1 yard line, from which the probability of scoring a touchdown is about 0.59. Since
0.59 × 0.632 + (1 − 0.59) × 0.369 = 0.524 > 0.475,
it would make sense for the Bills to go for it in that case.
Returning to the original 4th and 2 situation, we will assume that if Buffalo goes for it, there is a 0.6 probability that they fail to pick up the first down, a 0.3 probability that they score on the play, and a 0.1 probability that they pick up the first down without scoring. Buffalo's probability of winning if they go for it is then
0.6 × 0.369 + 0.3 × 0.632 + 0.1 × 0.524 = 0.463.
Since this is less than Buffalo's probability of winning if they kick the field goal, the Bills did the right thing by kicking. The intuition is that one of the usual benefits of going for it near the opponent's goal — that if you fail, the opponents have bad field position — doesn't come into play so close to halftime.
With 2:20 remaining in the game, and Pittsburgh leading 19-14, Pittsburgh quarterback Ben Roethlisberger ran for a first down to the Cincinnati 35 yard line. The Bengals had no timeouts, so the clock ran down to the two-minute warning. The Steelers then took a knee three times and ran out the clock.
Once Pittsburgh made the first down, Cincinnati assumed the game was over. However, as we described above and explained in detail in our article on intentional fouls , Cincinnati still had a slim chance. The Bengals need to commit a foul after Roethlisberger makes the first down, but before the clock reaches the two-minute warning. The game clock stops for the penalty, and doesn't restart until the snap. Therefore, unless the Steelers make another first down, they can't simply run out the clock. Even if the Steelers kick a field goal, the Bengals get the ball back trailing by 8 points, with almost 0:40 left in the game.
Copyright © 2004 by William S. Krasker