A model-based approach to football strategy.
|September 22, 2004|
In this article we discuss some notable coaching decisions from selected games. Many of the analyses use the footballcommentary.com Dynamic Programming Model .
Trailing 7-6 near the end of the game, Denver was driving toward the Jacksonville goal line. On 2nd and 10 from the Jacksonville 24 yard line, Denver ran the ball for a 1-yard gain, and Jacksonville used its second timeout to stop the clock with 0:37 left. In one of the more controversial decisions of the week, Denver coach Mike Shanahan decided to run one more play before bringing in the field goal unit. Unfortunately for Denver, Quentin Griffin fumbled, and the game was over.
Running another play does four things, three of which are good: It consumes a few seconds, it forces the Jaguars to use their final timeout, it picks up a few yards on average, and it risks losing a fumble.
From data on all FG attempts during the 2003 regular season and playoffs, which we described in a
previous article ,
it appears that NFL place kickers make about 76% of their field goals from 41 yards. Moreover, the success probability rises about 1% per yard as the distance decreases. Therefore, to a first approximation, a play that (expectationally) gains 3 yards increases the probability of making the FG from 0.76 to 0.79. So, if we let pf denote the probability of losing a fumble, we find that Denver's probability of taking the lead is
We have seen no data to support the notion that calling timeout to "ice" the opponent's FG kicker is an effective strategy — though teams continue to try it. Sometimes it's harmless, as in Super Bowl XXXVIII — but not when it uses a timeout that you're likely to need later.
With the clock already stopped with 1:57 left in regulation, and Miami's Olindo Mare preparing to attempt a 47-yard FG that would tie the game, the Bengals called timeout in an attempt to "ice" him. But if, as is likely, Mare makes the FG, then the Bengals get the ball back with 1:53 left, and have a chance for a game-winning score. Cincinnati's probability of scoring is definitely higher with an extra timeout.
With 10:25 remaining in regulation, on 3rd and 21 at their own 32 yard line, leading 27-14, the Jets gained 7 yards. The clock stopped at 10:18 when the Jets were called for holding on the play. The Chargers therefore had the option of giving the Jets 4th and 14 at their 39 yard line, or 3rd and 31 at their 22.
San Diego's probability of winning the game at that point was not high. According to the Model , if they decline the penalty and force the Jets to punt, their probability of winning the game is 0.031. The Chargers did in fact decline the penalty.
If San Diego had accepted the penalty, the best strategy for the Jets would probably have been a running play or a screen pass, to keep the clock running. A reasonable assumption is that accepting the penalty gains (in expectation) about 10 yards of field position, at a cost of about 0:40 on the clock. Interestingly, according to the Model , this trade is roughly a wash, so that San Diego's slim probability of winning the game is about the same whether they accept or decline the penalty. On the other hand, San Diego's best hope is that the Jets pass the ball incomplete on a replayed 3rd down. For that reason, we would have accepted the penalty.
One of the worst coaching decisions of the week was Mike Tice's decision to settle for a FG with 12:10 left in the first half. The Vikings had 4th and goal from inside the Philadelphia 1 yard line, trailed 7-3, and would be kicking off to start the second half.
According to the
Minnesota's probability of winning the game is 0.55 if they score a TD, and 0.364 if they go for it and fail. It's 0.42 if they make a FG, and 0.336 if they attempt a FG and miss (in which case the Eagles take over at the 20 yard line). Assuming that the probability of making the FG is the same 0.985 we use for extra points, Minnesota's probability of winning the game if they attempt the FG is
It appears that Tice also erred by not challenging Terrell Owens's TD reception with 7:40 left in the game, which put Philadelphia ahead by 15 points. Tice reportedly said that his coaches didn't see a good replay until after David Akers kicked the extra point. But Minnesota should have challenged even without seeing a definitive replay, because if the play stands, the game is essentially over. (According to the Model , Minnesota's probability of winning falls to 0.007.) So there is little to lose by challenging.
Having just scored a TD with 1:33 left in the 3rd period to close their deficit to 5 points, Arizona attempted a two-point conversion. As can be seen from the
Arizona needs only about a 0.26 probability of success to justify going for two, so they certainly made the correct decision. Indeed, according to the
Arizona's probability of winning the game at that point is either 0.237, 0.261, or 0.325 depending on whether they trail by 5, 4, or 3 points. If kicked extra points and two-point conversions have success probabilities of 0.985 and 0.4 respectively, then Arizona's probability of winning the game is
With 12:16 left to play in the 1st quarter, on the game's opening drive, the Cardinals faced 4th and 1 at their own 48 yard line. This sort of situation arises often, and coaches generally punt, as Dennis Green did here. However, the correct choice is to go for it. According to the
if Arizona goes for it and picks up the first down, their probability of winning the game is 0.523. If they fail, their probability of winning the game is 0.436. So, assuming a 0.7 probability of success, Arizona's probability of winning the game if they go for it is
With 11:33 remaining in a tie game, the Tennessee faced 4th and 2 at the Indianapolis 27 yard line. The Titans chose to go for broke, passing into the end zone, but cornerback Nick Harper snatched the ball from receiver Derrick Mason for an interception and touchback. None of the commentators has pointed out that if Harper had simply dropped the ball rather than hold on to it, the Colts would have taken over at their 27 yard line rather than their 20, but that's not what concerns us here. We want to compare Tennessee's decision to go for the TD to the alternatives of just trying to pick up the first down, or kicking a FG.
According to the
if the Titans successfully kick a FG their probability of winning the game is 0.645. Following a failed FG attempt, Indianapolis takes over at their 35, and Tennessee's probability of winning the game is 0.442. Since NFL kickers make about 68% of their field goals from 45 yards, Tennessee's probability of winning the game if they attempt the FG is
If instead the Titans merely try to pick up the first down, their probability of winning the game will be either 0.669 or 0.461, according to whether they succeed or fail. Assuming a 50% chance of success, Tennessee's probability of winning the game if they go for the first down is
Finally, Tennessee's probability of winning the game if they score a TD is 0.776. If the Titans pass into the end zone, let p denote the probability of a completion for a TD. Then Tennessee's probability of winning with this strategy is
There were two situations during the game in which, following a Houston TD, the correct choice was to attempt a two-point conversion. The first of these came with 2:31 left in the 3rd quarter, when Houston trailed 14-9. Using Model calculations analogous to those shown above , we find that Houston's probability of winning the game is 0.277 of they go for two versus 0.267 if they kick the extra point. Houston kicked the extra point, though.
With 12:20 left in the game, Houston scored a TD to trail 21-16. This time Houston went for two, undaunted by the criticism John Fox sustained for going for two in an almost identical situation in Super Bowl XXXVIII . According to the Model , Houston's probability of winning the game is 0.243 if they go for two and 0.227 if they kick.
Copyright © 2004 by William S. Krasker