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A model-based approach to football strategy.

November 3, 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 8:47 left in the game, Houston led 10-3. Facing 4th and 2 at the Jacksonville 26 yard line, Houston lined up for an apparent field goal attempt. However, the formation was a fake; holder Chad Stanley ran for 5 yards and a Houston first down.

According to the
Model ,
if Houston attempts the field goal, their probability of winning the game is 0.952 if the kick is good and 0.846 if it misses. NFL place-kickers make about 71% from 44 yards, and if we use that figure, we find that Houston's probability of winning if they kick is

If the Texans go for the first down, their probability of winning is 0.952 if they succeed but 0.859 if they fail. It's easy to check that in order for it to be correct to go for it, the probability of picking up the first down has to exceed 0.67. This is higher than the actual probability with two yards to go, whether they go for it openly or from a field goal formation. So Houston coach Dom Capers should have settled for the field goal.

With 0:02 left in the 2nd quarter, Tennessee led 6-3, and faced 4th and goal inside the Cincinnati 1 yard line. In a controversial decision , Titans' coach Jeff Fisher decided to go for it.

This situation is interesting because one of the commonly cited reasons to go for it — if you're stopped, the opponents are pinned back near their goal line — doesn't apply. Regardless of what happens on this down, play will resume with Cincinnati kicking off to start the 3rd quarter. (We explored this situation in detail in a previous article .)

According to the Model , when the second half begins, Tennessee's probability of winning the game will be either 0.632, 0.731, or 0.845, depending on whether they lead by 3, 6, or 10 points. Therefore, assuming for simplicity that the chip-shot field goal is a sure thing, Tennessee's probability of winning if they kick the FG is 0.731.

If we assume that the Titans have a 0.57 probability of success if they go for the TD, then their probability of winning if they go for it is

With 10:28 remaining in the 1st quarter, and no score, Kansas City faced 4th and 1 at the Indianapolis 17 yard line. The Chiefs decided to go for the first down rather than kick a field goal.

According to the
Model ,
if the Chiefs attempt a field goal, their probability of winning the game is 0.582 if they make it but 0.503 if it misses. NFL place-kickers make about 84% from 35 yards, and if we use that figure, we find that Kansas City's probability of winning if they kick is

If instead the Chiefs go for it, their probability of winning is 0.629 if they make it and 0.523 if they are stopped. If we use 0.65 for the probability of picking up a yard at that point on the field, we find that Kansas City's probability of winning if they go for it is

With 2:18 left in the game, Kansas City led 38-35, and had 3rd and 5 from just inside the Indianapolis 15 yard line. The Colts had no timeouts. On a "free" play due to an Indianapolis offsides penalty, Trent Green threw into the end zone to Tony Gonzalez, who made a fine catch for a touchdown.

Our initial reaction was that Kansas City had made a poor choice of play. It seemed that any completion beyond 5 yards, but short of the end zone, would win the game for Kansas City. All they would have to do is let the clock run down to the two-minute warning and then take a knee three times. By scoring, the Chiefs risked a quick Indianapolis score and an onside kick.

Then we remembered that the clock stops if there is a penalty, and in the last five minutes of the game, it doesn't restart until the snap regardless of whether the penalty is accepted or declined. So even if the Chiefs had made a first down and declined the offsides penalty, they would still have needed to run a play before the two-minute warning, and couldn't have run out the clock by taking a knee. We doubt Trent Green worked all this out as he dropped back to pass, but all things considered, the TD was Kansas City's best outcome on the play. (If our understanding of the rule is incorrect, please let us know at ` feedback@footballcommentary.com`.)

With 1:49 left in the game, Greg Wesley intercepted Peyton Manning's pass five yards deep in his own end zone. According to the NFL Recap , Wesley's 65-yard return sealed Kansas City's victory, but of course what really sealed the victory is that he was finally tackled. If Wesley had simply taken a touchback, the game would have been over. He shouldn't have risked a fumble or injury by running the ball out of the end zone.

With 0:09 left in the first half the Giants, already leading by a comfortable 17-0, faced 3rd and goal at the Minnesota 12 yard line. The Giants had no timeouts. [Note: The NFL Gamebook erroneously says the Giants had 0:05 and one timeout.] Rather than try a pass into the end zone, the Giants chose to kick a field goal on third down.

We will base our analysis on the Model , which says that when Minnesota kicks off to start the second half, the Giants' probability of winning the game will be either 0.954, 0.974, or 0.99, according to whether the Giants' lead is 17, 20, or 24 points.

NFL place-kickers make about 90% from 30 yards. If we use this figure, we find that the Giants' probability of winning if they attempt the field goal immediately is

If the Giants instead attempt one more pass into the end zone, the main possibilities are a touchdown, a sack or interception, or an incompletion. (A penalty just makes the FG a bit longer or shorter.) If the pass is incomplete, the Giants then kick a field goal. Coincidentally, the Giants' probability of winning if they attempt a FG (0.972) is exactly midway between their probabilities of winning if they score a TD (0.99) or are sacked (0.954). So in this case, the decision simply comes down to whether a TD is more or less likely than the combination of a sack or interception. Surely the probability of a TD is larger, as long as Kurt Warner throws the ball away if he can't quickly locate an open receiver. It follows that the Giants should have run another play.

With 11:44 left in the game, Detroit trailed 21-14, and faced 4th and 1 at the Dallas 37 yard line. The Lions decided to go for the first down. Center Dominic Raiola, apparently believing (incorrectly) that a Dallas lineman was in the neutral zone, snapped the ball early , which allowed unblocked Dallas cornerback Nathan Jones to sack Joey Harrington for a 10-yard loss.

Although the play was a disaster, the decision to go for it shouldn't be controversial. According to the
Model ,
if the Lions punt their probability of winning is 0.147. If they go for it, their probability of winning is 0.237 if they make the first down and 0.115 if they are stopped. If we assume the probability of making it is 0.7, then Detroit's probability of winning if they go for it is

Detroit could also have tried a 55-yard field goal. If the kick is good, Detroit's probability of winning is 0.221, but it's only 0.107 if the kick misses. One can check that in order for a FG attempt to give the Lions a higher probability of winning the game than going for the first down, the probability of success on the FG has to exceed 0.82. From 55 yards, that's clearly not the case for any NFL place-kicker.

With 12:19 left in the first quarter, and no score, Philadelphia had the ball on 4th and goal at the Baltimore 3 yard line. The Eagles chose to kick the field goal.

If we assume for simplicity that the FG is a sure thing, then according to the Model , Philadelphia's probability of winning the game if they attempt the FG is 0.581. If instead they go for the TD, their probability of winning is 0.689 if they make it and 0.534 if they fail. It's easy to check that in this case, the Eagles should go for it if their probability of success exceeds 0.31. From the 3 yard line, if the actual probability does exceed 0.31, it's not by very much. (Two-point conversions succeed about 40% of the time.) So in this case, kicking was appropriate.

With 2:22 left in the game, Baltimore trailed 15-10, had two timeouts, and faced 4th and 6 at their own 38 yard line. The Ravens elected to punt.

If Baltimore punts, their only real hope is to force Philadelphia to go three-and-out. In that case, the Ravens can expect to get the ball back roughly where it is now, but with no timeouts and about 1:30 on the clock. So far this year the Eagles have gone three-and-out on only 25% of their possessions, so it's unreasonable for the Ravens to suppose that their probability of forcing the Eagles to go three-and-out exceeds about 0.35.

If instead the Ravens go for the first down and make it, they are at least 6 yards farther up the field, and have about 2:16 and two timeouts. In addition, even if the Ravens are stopped, they could still win, as Jacksonville showed in a similar situation in Week 6 against Kansas City. So as long as Baltimore's probability of picking up the first down is as high as their probability of forcing Philadelphia to go three-and-out — which it is — they definitely should go for the first down.

With 11:23 remaining in the 1st quarter, and no score, Washington arrived at 4th and 6 at the Green Bay 34 yard line. The Redskins chose to punt.

We will suppose that Green Bay's expected starting field position following a pooch kick is the 10 yard line. In this case, according to the Model , Washington's probability of winning the game if they kick is 0.486.

If the Redskins go for the first down, their probability of winning the game is 0.563 if they succeed and 0.456 if they fail. If the probability of picking up the first down is 0.35, then Washington's probability of winning if they go for it is

Washington also has the option of attempting a 52-yard field goal. If they do, their probability of winning is 0.545 if it's good but 0.443 if it misses. It's easy to verify that a field goal attempt is better than punting if the probability of success exceeds 0.42. Since 42% is not far from the true success rate, there is no advantage to attempting a field goal here. This is one of those rare cases in which punting, going for the first down, and attempting a field goal are roughly equal.

Trailing 17-7, Washington attempted an onside kick to start the second half. Washington's probability of winning is 0.204 if they recover the kick, but only 0.132 if Green Bay gets possession. On the other hand, if Washington kicks deep their probability of winning is 0.156. Using these numbers, one can check that the onside kick doesn't make sense unless its chance of success exceeds 33%.

With 12:03 remaining in the 2nd quarter, the Jets led 7-0, and faced 4th and just over 2 yards to go at the Miami 43 yard line. The Jets decided to punt.

If we assume that Miami's expected starting field position following a Jets punt is their own 10 yard line, then according to the
Model ,
if the Jets punt their probability of winning is 0.742. If they go for the first down instead, then their probability of winning is 0.785 if they make it but 0.702 if they don't. If the probability of picking up the first down is 0.5, then the Jets' probability of winning the game if they go for it is

With just 0:05 left in the first half, the Jets had 1st and 10 at the Miami 37 yard line. They still had one timeout. Rather than attempt a pass into the end zone or a 55-yard field goal, the Jets decided to risk having time expire by throwing a short pass to set up an easier field goal. Chad Pennington passed 6 yards to Wayne Chrebet, who immediately downed himself as the Jets called timeout. The clock stopped at 0:01, allowing Doug Brien to kick a 49-yard field goal to give the Jets a 17-7 halftime lead.

Our first reaction was that the clock operator must have been slow to restart the clock at the snap, but a review of the video tape shows that not to be the case. Unlike the television commentators, the Jets knew how long that play would take. And given how unpromising the alternatives were, the Jets were right to try it even if there was a significant chance that time would expire.

Copyright © 2004 by William S. Krasker