A model-based approach to football strategy.
|October 27, 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 6:55 remaining in the game, and New England leading 13-7, the Jets faced 4th down and about an inch to go at their own 23 yard line. In a controversial decision, Jets' coach Herman Edwards decided to go for it.
According to the
if the Jets go for it their probability of winning the game will be either 0.196 or 0.057, depending on whether or not they make it. We will suppose that the probability of gaining one inch is 0.75. It then follows that the Jets' probability of winning if they go for it is
The decision whether to punt or go for the first down depends on the score, the field position, the time remaining, and the probability of picking up the first down. Calculations using the footballcommentary.com Dynamic Programming Model require those inputs. To make the results of the Model accessible to readers, we have prepared a series of "Go For It" Tables (which we also link to on our home page ). By interpolating within and between the Tables, one can find the probability of making the first down that is required to justify going for it. For example, the 0.48 probability described in the previous paragraph could have been found using the Tables.
With the score 7-7 and 0:35 left in the 2nd quarter, Miami quarterback Jay Fiedler threw an incomplete pass on 3rd and 18 at the Rams' 32 yard line. However, Miami was called for holding. St. Louis coach Mike Martz elected to take the penalty, bringing up 3rd and 28 at the Rams' 42 yard line with 0:29 left in the half. On the next play Fiedler completed a pass to Randy McMichael, who caught the ball at the 27 yard line and ran it in for a touchdown.
Martz was criticized for accepting the penalty, which allowed Miami to repeat 3rd down. That decision merits some analysis. We will base the analysis on the Model , which says that when the Rams kick off to start the second half, their probability of winning the game will be either 0.474, 0.369, or 0.229, depending on whether Miami's lead is 0, 3, or 7 points.
If the Rams decline the penalty, Miami presumably attempts a 50-yard field goal. The average NFL place-kicker makes about 60% from 50 yards. But since Matt Bryant is relatively untested and has never attempted a kick of 50 yards or more, we will assume his probability of success is 0.5. The Rams' probability of winning if they decline the penalty is therefore
If the Rams take the penalty, we will suppose that there is a 0.7 probability that the Dolphins don't get into field goal range, a 0.25 probability that they get into good FG range from which they have an 80% chance of success, and a 0.05 probability of a touchdown before halftime. From these assumptions it follows that if the Rams take the penalty, their probability of winning is
0.7 × 0.474 + 0.25 (0.8 × 0.369 + 0.2 × 0.474) + 0.05 × 0.229 = 0.441.
If anything, our assumptions feel skewed toward declining the penalty. We therefore conclude that Martz was right to accept the penalty.
With 4:41 remaining in the 1st quarter, Cincinnati led 7-0, and faced 4th and about two feet at the Denver 5 yard line. Bengals' coach Marvin Lewis decided to go for it.
For simplicity assume that a 23-yard field goal is a sure thing; this has no meaningful impact on the analysis. Then the Model says that if the Bengals kick the FG, their probability of winning the game is 0.742.
If instead they go for the first down, their probability of winning is 0.811 if they make it but 0.695 if they don't. If the probability of picking up the first down is 0.6, it follows that Cincinnati's probability of winning the game if they go for it is
With 3:57 left in the game, Cincinnati led 23-10, and had the ball at midfield, on 2nd down and 6 yards to go. Denver had just used its last timeout. This is an obvious situation for a run, to keep the clock moving. Cincinnati running back Rudi Johnson found a hole, but after picking up the first down, he drifted toward the sideline and allowed himself to be pushed out of bounds. If the ball carrier goes out of bounds inside 5:00 in the 4th quarter, the game clock doesn't restart until the snap. Therefore, by not staying in bounds, Johnson gave Denver an extra 40 seconds.
It didn't matter in this case, because the Bengals made one more first down and ran out the clock. And of course, Denver's chances were miniscule regardless. Occasionally, though, being oblivious to clock management proves costly.
In overtime, the Eagles won the coin toss and elected to receive. Philadelphia drove into Cleveland territory, and reached 4th and 1 at the Cleveland 47 yard line. Philadelphia coach Andy Reid then chose to punt.
We can analyze Philadelphia's decision using a model we built to examine the effects of the wind in overtime. Wind was not a major factor in this game, but the model provides a way to estimate a team's probability of prevailing in overtime if it arrives at 1st and 10 at any particular yard line.
That model says that if the Eagles go for it and make the first down, their probability of winning the game will be about 0.80. If the Eagles go for it and fail, the Browns take over at their own 47 yard line, and Cleveland's probability of winning will be about 0.76. If we use 0.7 as the probability of picking up 1 yard when you're near the middle of the field, it follows that Philadelphia's probability of winning the game if they go for it is about
Cleveland coach Butch Davis also chose to punt on 4th and 1 in overtime, from the Browns' 48 yard line. The analysis is similar. According to our overtime model, if the Browns go for it and make it, their probability of winning is about 0.77. If they fail, the Eagles take over at the Cleveland 48, and have a 0.79 probability of winning. So, if Cleveland's probability of picking up the first down is 0.7, it follows that their probability of winning the game if they go for it is about
This game featured two important fourth-down decisions on the same possession.
With 9:39 remaining in the 2nd quarter, and the score 7-7, the Giants faced 4th down and about three inches to go, at the Detroit 10 yard line. The Giants decided to go for it.
According to the
if the Giants go for the first down their probability of winning the game is 0.67 if they make it and 0.527 if they fail. If the probability of picking up the three inches is 0.75, then the Giants' probability of winning if they go for it is
If instead the Giants attempt a field goal, their probability of winning the game is 0.596 if they make it and 0.511 if they don't. NFL place-kickers make about 92% from 28 yards, and if we use that figure, we find that the Giants' probability of winning if they kick is
On the same drive, with 7:26 left in the half, the Giants reached 4th and goal from just inside the 1 yard line. This time, the Giants kicked. According to the Model , this gives them a 0.597 probability of winning.
If instead they go for it, their probability of winning is 0.729 if they score but 0.543 if they are stopped. Using 0.57 for the probability of scoring, it follows that the Giants' probability of winning the game if they go for it is
Field position — the fact that Detroit is pinned back if the TD attempt fails — is a relatively small part of the reason why it's better to go for it in this case. Even if (contrary to the rule) the Giants were required to kick off regardless of the outcome of the play, it would still be better to go for it as long as the probability of success exceeds 0.426. (This differs slightly from the 3/7 that one would anticipate using an expected-points calculation, because a TD here is disproportionately beneficial.)
With 3:17 left in the 3rd quarter, Jacksonville trailed 14-10, and faced 4th and 2 at the Indianapolis 4 yard line. The Jaguars decided to kick a field goal.
For simplicity we will assume that the 22-yard field goal is a sure thing. Then according to the Model , if the Jaguars kick the FG their probability of winning the game is 0.397.
If instead Jacksonville goes for the first down, their probability of winning is 0.58 if they make it and 0.314 if they fail. If we assume that the probability of success is 0.4 (which is what we use for two-point conversions), then Jacksonville's probability of winning if they go for it is
It's instructive to contrast this with our finding for an ostensibly similar situation in the Houston-Kansas City game in Week 3. Leading 7-3 with 2:00 left in the first half, Kansas City chose to go for it on 4th and 2 at the Houston 6 yard line. In both our original analysis and a re-examination in a guest column at FootballOutsiders , we found that the Chiefs should have kicked a field goal. There are two important differences between that situation and this one. First, in the Kansas City case there was too little time before halftime for the effects of field position to be felt fully. Second, a 4-point lead is relatively favorable for kicking a field goal, but a 4-point deficit is relatively unfavorable.
On the game's opening drive, Atlanta reached a decision point at 12:19 in the 1st quarter, when the Falcons faced 4th and goal at the Kansas City one yard line. The Falcons elected to kick a field goal.
For simplicity we will assume that the chip-shot field goal is a sure thing. According to the
if the Falcons kick the FG, their probability of winning the game is 0.545. If they go for the TD, their probability of winning is 0.655 if they score but 0.498 if they don't. If we use 0.57 for the probability of scoring, we find that Atlanta's probability of winning if they go for it is
This situation — tie score early in the game, 4th and goal at the 1 yard line — arises frequently. Teams kick more often than not, but that decision significantly reduces the probability of winning the game.
We thought that the Miracle of the Meadowlands had taught coaches the virtues of taking a knee, but evidently not in New Orleans. With 1:10 remaining, the Saints led 31-26 and had 1st down. The Raiders had only one more timeout, so all the Saints had to do is take a knee three times and the game would be over. Instead, on first down, New Orleans risked a fumble or injury by having Aaron Brooks hand off to Deuce McAllister.
Copyright © 2004 by William S. Krasker