A model-based approach to football strategy.
|October 6, 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 12:26 left in the 4th quarter, having just scored to close the deficit to 24-10, Titans coach Jeff Fisher decided to attempt an onside kick.
Trailing by 14 points at that stage, Tennessee's chances of winning the game are slim. According to the Model , if they choose to kick deep, their probability of winning the game is 0.02. If they kick onside, their probability of winning will be either 0.035 or 0.014, depending on whether or not they recover the kick. So the question comes down to the probability of recovering the kick. One can check that it makes sense to try the onside kick if Tennessee's probability of recovering it exceeds 0.29.
During the Monday Night Football broadcast on September 13, the commentators reported that during the last five NFL seasons, the kicking team has recovered 24% of "anticipated" onside kicks, and 61% of "surprise" onside kicks. The second percentage in particular is surely based on too small a sample to be a reliable estimate of the corresponding probability. But the lack of data is unavoidable: When "surprise" onside kicks cease to be rare, they cease to be a surprise. One potentially interesting piece of information is that according to the Model , if the probability of recovering an onside kick exceeds 0.39, then teams should attempt onside kicks on the opening kickoff. Clearly coaches don't believe that the probability of recovering an onside kick can ever be 0.61, nor do we.
At any rate, given how much time was left, the kick probably was a surprise to San Diego, and we find it easy to believe that Tennessee's probability of recovering it exceeded 0.29. If that's true, then Jeff Fisher made a good call.
Much earlier in the game, with 0:28 left in the first quarter and the Titans trailing 7-0, they decided to go for the first down rather than kick a FG on 4th and 1 at the San Diego 5 yard line. The probability of picking up the first down is about 0.6. According to the
if the Titans go for it, their probability of winning the game is either 0.424 or 0.281, according to whether they succeed or fail. So, if they choose to go for it, their probability of winning the game is
San Francisco's long opening drive reached a decision point with 9:51 left in the 1st quarter, when the 49ers faced 4th and 14 at the St. Louis 30 yard line. San Francisco chose to punt.
A punt from the opponent's 30 yard line will not net too many yards, on average. If we assume that the Rams' expected starting field position following a pooch kick is the 10 yard line, then according to the Model , San Francisco's probability of winning the game if they punt is 0.485.
The 49ers could instead have attempted a FG. According to the Model , if they do so, their probability of winning the game is either 0.545 or 0.45, depending on whether or not the kick is good. One can check that a success probability of just 0.37 is sufficient to make the FG attempt superior to the punt. The average NFL placekicker makes about 63% of his field-goal attempts from 48 yards.
Alternatively, San Francisco could have tried to pick up the first down. For the sake of argument, suppose that if the 49ers go for the first down and make it, their expected gain on the play is 16 yards. Then the Model says that if the 49ers go for it, their probability of winning the game is 0.59 if they succeed and 0.46 if they fail. One can check that San Francisco needs only a 0.2 probability of success to make going for the first down superior to punting. It appears, then, that punting was actually the worst of the three possible choices.
Following the St. Louis touchdown that put the Rams ahead 24-0, and the subsequent kickoff, the 49ers took over at their own 27 yard line with 0:25 remaining in the first half. Although the 49ers didn't take a knee to run out the clock as commentator Joe Theismann suggested they would, they did almost the same thing: a run up the middle on first down, and a 2-yard pass on second down.
According to the Model , if San Francisco is down 24-0 when they kick off to start the second half, their probability of winning the game is only about 0.01. If they can get a FG before halftime, their win probability doubles to about 0.02, which is still tiny, but perhaps offers a glimmer of hope. With a TD before halftime, their win probability rises to almost 0.05. A touchdown is quite unlikely, but with all three timeouts remaining, there is time for four plays, and a FG is a real possibility. However, the 49ers have to throw the ball down the field and hope for a completion (or a pass interference penalty). Playing it safe is pointless.
With 14:09 remaining in the 2nd quarter, and the score 10-10, New England faced 4th and 1 at their own 46 yard line. The Patriots decided to punt.
According to the
New England's probability of winning the game if they choose to punt is 0.477. If they go for it, their win probability is 0.523 if they make it and 0.425 if they don't. Assuming that their probability of making it is 0.7, their probability of winning the game if they go for it is
Later in the game, with 12:25 left in the 4th quarter, the Patriots kicked a 32-yard FG to take a 20-17 lead. However, Buffalo was called for offsides on the play. The Patriots therefore had the option of "taking points off the board" and resuming their possession with 1st and goal at the Buffalo 9 yard line, which is in fact what they did. According to the Model , if New England declines the penalty and keeps the points, their probability of winning the game is 0.636, whereas if they take the penalty, their win probability is 0.754. So this is not a close call. In fact, according to the Model , it would be right to take the points off the board regardless of the field position, as long as they were close enough to have kicked a FG in the first place. (Of course, this only applies when the score is tied and about 12:25 remains. With a different score or time remaining, it might be right to decline the penalty.)
It's noteworthy that at various times during the first half, with the score tied, the Bills went to a no-huddle offense. As we explained in a previous article , the underdog should actually employ a slowdown tempo unless they lead by a sufficient amount. (Of course, the Bills might have felt that hindering Patriot substitutions trumped clock-management considerations.)
With 2:21 left in the game, leading 17-13, and facing 4th and 4 at the Washington 28 yard line, Cleveland lined up for an apparent field-goal attempt. However, in a controversial decision, Cleveland coach Butch Davis chose to have holder Derrick Frost attempt to pass. Since the Redskins were out of timeouts, a Cleveland first down would have virtually sealed the victory. Unfortunately for the Browns, Frost was tackled before he could get the pass off, and Washington took over on downs.
We will derive a rough estimate of the probability of picking up the first down that is required to justify going for it. Notice that regardless of what Cleveland does on that play, Washington has to score a touchdown to have a chance to win the game. Moreover, Washington's probability of scoring a touchdown is roughly the same whether they get the ball back on downs, or on a kickoff after a Cleveland FG, or after a missed Cleveland FG attempt. We will denote that probability by q. Let p denote Cleveland's probability of picking up the first down if they go for it, and let pFG denote Cleveland's probability of making the FG if they attempt it.
(Washington's expected starting field position is actually better following a missed Cleveland FG than it is if they take over on downs or if they receive a kickoff. Therefore, the assumption that each of these situations yields the same probability q for a Washington TD actually biases the analysis in favor of Cleveland kicking the FG.)
Suppose the Browns go for the first down. Then Washington wins the game if the Browns fail to pick up the first down and then the Redskins score a TD. This has probability
Suppose instead that the Browns attempt a FG. Then Washington wins if the FG misses and then Washington scores a TD; or if the FG is good, Washington scores a TD, and Washington wins in overtime. This has probability
(1 − pFG)q + pFGq0.5.
It follows that Cleveland should go for the first down if
(1 − p)q < (1 − pFG)q + pFGq0.5,
which reduces to
With 8:58 remaining in the first quarter, on the opening drive of the game, New Orleans faced 4th and goal at the Arizona one-foot line. The Saints called for a quarterback sneak, but Aaron Brooks fumbled. The Cardinals recovered in their end zone for a touchback, and took over at their 20-yard line.
Many coaches would have attempted a FG. If the Saints do so, then according to the
their probability of winning the game is either 0.546 or 0.471, depending on whether or not they make it. If the probability of success is the same 0.985 we use for extra points, then the Saints' probability of winning the game if they attempt the FG is
If the Saints go for the TD, their probability of success from a foot away is about 70%. Of the remaining 30%, we should recognize that some will be due to fumbles recovered by the Cardinals in their end zone. So we will assume probability 0.7 of a touchdown, probability 0.28 that the Cardinals take over near their own goal line, and probability 0.02 that the Cardinals recover a fumble in their end zone and take over at their 20-yard line (which is the same spot at which they start following a missed FG).
If New Orleans goes for the TD and succeeds, then according to the
their probability of winning the game is 0.66, whereas if they fail and Arizona takes over near their own goal line, New Orleans has a 0.498 probability of winning. It follows that if the Saints go for it their probability of winning is
The Jaguars trailed 17-9 with 10:45 remaining in the 4th quarter, and faced 4th and 1 at the Indianapolis 40 yard line. Rather than simply try to pick up the first down, Byron Leftwich went deep to Jimmy Smith, who caught the ball at the Indianapolis 12 yard line and ran it in for the touchdown. Was Jacksonville right to go for broke?
If the Jaguars merely try to pick up the first down, then according to the
their probability of winning the game is 0.165 if they succeed and 0.071 if they fail. If the probability of success is 0.7, then Jacksonville's probability of winning if they just try to pick up the first down is
To analyze the long pass, we have to make assumptions about what happens if the pass is complete. Suppose that if the pass is complete there is a 0.5 probability that Smith scores on the play, and a 0.5 probability that he is tackled at the Indianapolis 6 yard line. In the former case, according to the Model , Jacksonville's probability of winning the game is 0.374, whereas in the latter case their probability of winning is 0.312. If we let p denote the probability that the pass is completed, it follows that Jacksonville's probability of winning the game if they attempt the long pass is
p (0.5 × 0.374 + 0.5 × 0.312) + (1 − p) 0.071.
One can check that in order for this expression to exceed 0.137, so that going for the long pass is better than merely trying to pick up the first down, p must exceed 0.24. This seems a bit high for the probability of success on such a long pass play, although the play was presumably sufficiently unexpected that its chances of success were enhanced.
Following the touchdown, and trailing 17-15 prior to the try, the Jaguars attempted a two-point conversion. As can be seen from the Chart , this was the correct decision. (In fact, according to the Model , a deficit of two points is the score differential most favorable for going for two: Trailing by 2 points prior to the try, it's correct to go for two as early as 13:00 remaining in the 2nd quarter.)
After apparent confusion induced Kansas City to burn its final timeout with 1:38 left in the 1st quarter, commentator Al Michaels said that the absence of timeouts is not that big a deal in the first half, except that the Chiefs could no longer challenge. This view that first-half timeouts have little clock-management value is too limited, and it took less than an hour for a game situation to arise that illustrates why.
At the two-minute warning in the second quarter, Kansas City faced 2nd and 13 at their own 7 yard line. Leading by 7 points, the Chiefs would have been happy to run out the clock, and if the Ravens had been out of timeouts as the Chiefs were, Kansas City could have ensured that Baltimore would get the ball back with less than 0:30 remaining. But since Baltimore still had two timeouts, they could be sure to get the ball back with plenty of time for a score, provided they could deny Kansas City a first down. (As it turned out, Baltimore didn't need time; B.J. Sams returned Kansas City's punt for a touchdown.)
There is one sense in which first-half timeouts actually have more clock-management value than second-half timeouts: Late in the second half, timeouts are useful only for the team that trails, but late in the first half they can be useful to either team.
Copyright © 2004 by William S. Krasker