A model-based approach to football strategy.
|September 16, 2004|
In this article we discuss some notable coaching decisions from selected games. Many of the analyses use the footballcommentary.com Dynamic Programming Model . Those who are unfamiliar with the application of the Model can examine detailed calculations in our analysis of Super Bowl XXXVIII .
Trailing by 3 points with 5:50 remaining in the 3rd quarter, Indianapolis faced 4th down and a half yard to go at the Patriots' 41 yard line. The Colts lined up to go for the first down, prompting commentator Al Michaels to speculate that the Colts might just be trying to draw the Patriots offside. However, the Colts did go for it, and there is little question that Tony Dungy made the correct choice. According to the
if the Colts go for the first down, their probability of winning the game will be either 0.459 or 0.322, according to whether they succeed of fail. Assuming a 0.7 probability of picking up the first down, the Colt's probability of winning the game if they go for it is
With 1:30 left in the 2nd quarter, on 1st and goal at the New England 5 yard line, Edgerrin James gained 4 yards to the New England 1. However, the Patriots were called for encroachment. Indianapolis therefore had the option of either 2nd and goal from the 1 yard line, or 1st and goal from the
Near the end of the game the Patriots made a potentially fatal clock management error, from which they were rescued by Mike Vanderjagt's improbable missed FG. When Willie McGinest sacked Peyton Manning on 3rd down, there was still 0:45 left in the game. New England should have immediately used one of their two remaining timeouts. Then, if Vanderjagt makes the FG, the Patriots have time for at least the possibility of a game-winning score. Instead, the clock ran down to 0:24 before the Patriots woke up and called time.
One of the worst in-game coaching decisions of the week was Steve Mariucci's decision to have Detroit kick the extra point after scoring a touchdown with 9:54 left to go ahead 19-14. According to the
Detroit's probability of winning the game following the try is either 0.75, 0.764, or 0.846 according to whether they lead by 5, 6, or 7 points. Using 0.985 and 0.4 as the probabilities of successful one- and two-point conversions, we find that Detroit's probability of winning the game is
With 1:59 remaining in the game, leading by 6 points and facing 4th and 11 at their own 7 yard line, Detroit took an intentional safety. The thought process is presumably that Chicago, with no timeouts, is unlikely to score twice; and whether Detroit leads by 6 or 4, a Chicago TD beats them while a FG does no harm. So, there is a rationale for trading 2 points for 25 yards of field position. On the other hand, if following the safety Chicago scores a TD, a subsequent FG by Detroit only gets them to OT. So without considerable further analysis, it's hard to say if the intentional safety was the correct strategy. (This decision was reminiscent of Bill Belichick's decision to take an intentional safety in New England's game against Denver last year. Of course, the Patriots were at their own 1 yard line rather than the 7, so a punt would have entailed a serious risk of a block resulting in a Denver TD. Still, New England trailed by 3 following the safety, so that a FG would no longer win outright. It's not completely clear that Belichick did the right thing, although when it works there's never second guessing.)
On 2nd down with 0:42 remaining in a tie game, the Steelers ran the ball to the Raider 24 yard line, let the clock run down to 0:11, called their second timeout, and brought in the field-goal unit. Presumably they were thinking that in case of a bad snap, they could use their final timeout and try the FG again on 4th down.
We analyzed this situation in a previous article , and found that there are two strategies that are approximately equally good. One is to let the clock run down to 0:02, to be sure that time will expire during the FG attempt. The second is to leave 0:04, to allow some chance to call time if the snap is bad, while retaining a substantial probability that time will expire during the kick.
However, there doesn't seem to be any justification for leaving 0:11. Even if the snap is bad, and Pittsburgh calls timeout to try the kick again, there will still be time on the clock after the FG, forcing the Steelers to kick off.
Leading by 7 points, the Jets faked a punt on 4th and 5 at the Cincinnati 36 yard line, with 9:05 left in the first half. Unfortunately for the Jets, the attempt to pick up the first down failed. Actually, it's not clear whether going for it was the right thing to do. Calculations using the Model (analogous to those performed earlier ) suggest that in that situation, the Jets needed a 0.389 probability of successfully picking up the first down to justify going for it. The situation would be clearer if the Jets were behind at the time. As can be seen from the Tables , to justify going for it, you need a higher probability of success if you're ahead than if you're behind. Of course, Herman Edwards presumably felt that his chances of gaining the 5 yards were enhanced by faking the punt.
The Dolphins punted three times on 4th down and 1 yard to go; in each case the Model suggests they should have gone for it. The most compelling situation came at the start of the 4th quarter, with the Dolphins facing 4th and 1 at the Tennessee 49 yard line. Down by 14 points, intuition says you have to try for the first down, and indeed the Model says that Miami needed only a 0.373 probability of picking up the yard to justify going for it. Of course, at that point Miami was highly likely to lose regardless of their choice: Assuming that the actual probability of picking up the first down was 0.7, the Model says that Miami's probability of winning the game was 0.043 if they went for it and 0.033 if they punted. But you have to keep trying.
With 14:36 left in the 2nd quarter, Washington coach Joe Gibbs chose to kick a FG on 4th and 1 from the Tampa Bay 2 yard line. Washington led by 7 points at the time.
To analyze Washington's decision, we first have to estimate their probability of scoring a TD if they eschew the FG. One possibility is to score the TD on the first attempt; this presumably has probability 0.4, since it's equivalent to a two-point conversion. Alternatively, Washington can pick up a first down by gaining a yard.
assembled by Football Outsiders suggest that there is about a 0.57 probability of gaining a yard when very near the opponent's goal line, so we will use
According to the
Washington's probability of winning the game is 0.868 if they score a TD, and 0.746 if they go for the TD and fail. So, their probability of winning the game if they go for the TD is about
With 3:33 to go in a scoreless first quarter, the Packers had 4th down and about 3 inches to go at the Carolina 24 yard line. Mike Sherman decided to attempt a FG rather than go for the first down.
The probability of picking up 3 inches must be at least 0.75. Using that figure, and performing
calculations analogous to those shown
we find that Green Bay's probability of winning the game if they go for the first down is 0.545. If a 41 yard FG were a sure thing, then kicking the FG would actually be slightly better, achieving a probability of winning the game of 0.548. However, NFL kickers make only about 77% of FG attempts from 41 yards. If the FG misses, Carolina takes over at their 41 yard line, and Green Bay's probability of winning the game is just 0.456. It follows that if the Packers attempt the FG, their probability of winning the game is
Tuesday Morning Quarterback
lambasted the Panthers for their decision to punt with 10:05 remaining in the game, down
Two-point conversion attempts with nearly a full quarter to play are rare. The coach is apt to be criticized for "chasing points" if the try fails — although, judging from the columnists' silence, not if it succeeds.
With 14:27 left in the game, the Rams scored a TD to take a 5-point lead. The Chart says that it is clearly better to go for two: St. Louis needed only about a 0.23 probability of success to justify the attempt. The Rams did in fact go for two. Direct calculations using the Model (analogous to those shown earlier ) show that the Rams have a 0.754 probability of winning the game if they attempt a two-point conversion, versus a 0.738 probability of winning if they kick.
This week, teams attempted only three two-point conversions, although there were nine situations in which a two-point conversion was the better option.
Despite being down by 3 points at the time, the Chiefs chose to punt on 4th and 3 at the Denver 46 yard line, with 9:31 left in the game.
Assuming Kansas City's probability of picking up the first down would have been about 0.5, the Model says that their probability of winning the game if they choose to go for it is 0.320. On the other hand, if they punt their probability of winning the game is 0.297. So it appears that they should have gone for it, and in fact, going for it is better as long as the probability of picking up the first down exceeds 0.38.
One of the more amusing moments from this week's broadcasts came on Kansas City's final offensive play, when commentator Paul Maguire commended Trent Green for avoiding a sack by throwing the ball into the ground in front of a prostrate Priest Holmes. What Green actually accomplished by his action was sealing his team's defeat. He needed to throw the ball up in the air in the general direction of a receiver, and pray. But to be fair, Kansas City's chances were virtually zero at that point.
Copyright © 2004 by William S. Krasker