A model-based approach to football strategy.
|November 9, 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 10:49 remaining in the 3rd quarter, Minnesota's Nate Burlson returned a punt for a touchdown. The Vikings still trailed 14-12 before the try. Minnesota coach Mike Tice elected to attempt a two-point conversion.
According to the
if Minnesota chooses to kick the extra point their probability of winning the game is 0.421. If they go for two, their probability of winning is 0.473 if they make it and 0.394 if they fail. If we assume that the probability of success is 0.4, then Minnesota's probability of winning if they go for two is
Minnesota's squandered timeouts and poorly executed two-minute drill at the end of the first half, which forced them to settle for a field goal, were justifiably criticized by the commentators. However, where the Vikings really wasted time was before the two-minute warning. They took possession at their own 8 yard line with 5:16 left in the half. From that field position, nearly half of drives that culminate in touchdowns use more than 5:16, so if the Vikings were interested in scoring, they should have been trying to conserve time from the outset. During that possession, and prior to the two-minute warning, the Vikings ran six plays for which the game clock was running at the time of the snap. For those six plays, the average real time that elapsed from the end of the previous play was 34 seconds. If the Vikings had been paying attention, they could easily have run two more plays before the two-minute warning.
With 1:53 left in the game, and the score 28-28, Peyton Manning's left-handed shovel pass to Edgerrin James resulted in an Indianapolis first down at the Minnesota 15 yard line. Because the Vikings had only one timeout, the commentators suggested that Minnesota should let Indianapolis score. Even if Minnesota could be sure that the Indianapolis ball-carrier would take the bait, it's not obvious that it's in Minnesota's interest. It's true that Mike Vanderjagt isn't likely to miss from 36 yards (the average NFL place-kicker makes about 83% from that distance), but the Vikings aren't likely to score a touchdown in the last 1:40 either. However, the real risk to letting Indianapolis score is that the ball-carrier might instead down himself at the one yard line, turning the game-winning field goal into a chip shot. So, if both teams are rational, the correct strategy for the Vikings is to try to prevent the Colts from getting better field-goal position. That's exactly what they did.
Finally, the Colts irrationally stopped the clock at 0:06 in preparation for the game-winning field goal. Since it was 4th down, there was no possible advantage to leaving so much time. Predictably , the field goal left 0:02 on the clock, and forced the Colts to kick off to the Vikings before the game ended.
The Jets won the coin toss prior to the game. Herman Edwards then made the puzzling decision to defend the west goal rather than receive the kickoff, and Buffalo elected to receive. The wind was from the southwest at about 25 miles per hour.
If the coin toss were for the start of overtime, then as we discussed in a previous article , there would be a threshold for the wind above which it would be correct to take the wind rather than receive the kickoff. It's not clear if the wind exceeded that threshold in this game; the ease with which Doug Brien made a 41-yard field goal into the wind in the 2nd quarter gives us doubts. But the point is, the start of the game is not overtime. Because the teams change ends after the 1st and 3rd quarters, each team gets the wind for half the game regardless of who kicks off for either half. Buffalo, naturally, elected to receive to start the second half. Therefore, the effect of the Jets' decision not to receive the opening kickoff was simply to reduce their expected number of possessions in the game. According to the Model , coach Herman Edwards' decision lowered his team's probability of winning the game from 0.5 to 0.464.
With 12:40 left in the 1st quarter, and no score, Buffalo faced 4th and six inches at their own 41 yard line. The Bills elected to punt.
Normally we assume that a punt (other than a pooch kick) is expected to net 40 yards. But because of the stiff headwind, we will assume that the punt is expected to net 30 yards, in which case Buffalo's probability of winning if they punt is 0.499. If instead they go for the first down, their probability of winning is 0.552 if they make it and 0.465 if they fail. With six inches to go, the probability of making it should be about 0.75. Therefore, Buffalo's probability of winning if they go for the first down is
With 11:33 left in the 3rd quarter, Baltimore led 12-10, and faced 4th down and 1 yard to go at the Cleveland 45 yard line. The Ravens chose to punt. According to the Model , this choice give the Ravens a 0.585 probability of winning the game, assuming that Cleveland's expected starting point is their own 10 yard line.
If instead the Ravens go for it, their probability of winning is 0.648 if they pick up the first down but 0.523 if they are stopped. Assuming that they have a 0.7 probability of making the first down, their probability of winning if they go for it is
With 10:19 left in the 4th quarter, the Ravens punted, and the officials ruled that Baltimore downed the ball inside the Cleveland 1 yard line. The Browns challenged at 10:05, claiming that it was a touchback. Cleveland led 13-12 at the time.
According to the Model , Cleveland's probability of winning is 0.6 if the ruling on the field stands, but 0.66 if it is reversed and the Browns start at their 20 yard line. From the view of the play that was available when Cleveland had to make the decision to challenge, it seemed to us that there was about a 0.5 probability that the ruling would be reversed. So the expected gain from challenging was about a 0.03 increase in the probability of winning, before taking into account the costs, which are the loss of a challenge and the possible loss of a timeout. With only 8:05 before the two-minute warning and Cleveland still leading, if feels unlikely that these costs could be worth 0.03. We think Cleveland was right to challenge.
When Baltimore scored a touchdown with 7:03 left in the game to go ahead 18-13 before the try, they elected to go for two. Assuming a success probability of 0.4, Baltimore's probability of winning if they go for two is 0.818, versus 0.79 if they kick, so Baltimore did the right thing. In fact, it turns out that it's right to go for two in this situation as long as the probability of success exceeds 0.1. (The same result can be found by consulting the Chart .)
The latest in a series of counterproductive individual achievements came with 0:45 left and the Ravens leading 20-13, when Baltimore's Ed Reed intercepted Jeff Garcia's pass 6 yards deep in his own end zone and ran 106 yards for a touchdown and the longest interception return in NFL history. Cleveland had no timeouts, so if Reed had taken a touchback the game would have been over. At least he slowed down as he approached the goal line.
ESPN showed a replay of Baltimore coach Brian Billick's reaction during Reed's runback. We were hoping to hear Billick shouting "Get down! Get down!" but he was actually shouting "Run it back! Run it back!"
With 0:13 left in the first half, San Diego had 1st and 10 at the New Orleans 23 yard line. The Chargers led 20-7, and had no timeouts. They had to decide whether to try another play before halftime, or kick an immediate field goal. The Chargers chose to run another play, but Drew Brees was sacked, and the half ended.
We will base our analysis on the Model , which says that when the Chargers kick off to start the second half, their probability of winning the game will be either 0.877, 0.928, or 0.966, according to whether their lead is 13, 16, or 20 points.
NFL place-kickers make about 78% from 41 yards. Therefore, if San Diego chooses to kick immediately, their probability of winning the game is
If the Chargers attempt another play, it really has to be a pass into the end zone, because time will expire if the ball carrier is tackled inbounds short of the goal line. Let p denote the probability of a touchdown, and let q denote the probability of a sack or interception. The probability of an incomplete pass is then
It follows that in order for trying another play to be better than kicking immediately, we must have
0.966p + 0.877q + 0.917(1 − p − q) > 0.917,
which reduces to
p > 0.82 q.
In short, the probability of a touchdown has to be almost as high as the combined probability of a sack or an interception. From the 23 yard line, when the opponents know you're passing, that feels like a close call. On this decision, we wouldn't criticize the coach either way.
With 14:11 left in the 2nd quarter, and Oakland leading 3-0, the Raiders had the ball, 4th and goal at the Carolina 1 yard line. Oakland elected to go for the touchdown.
For simplicity, assume that a chip-shot field goal would be a sure thing. Then according to the
if Oakland kicks their probability of winning is 0.641. If they go for it, their probability of winning is 0.754 if they score and 0.59 if they are stopped. Assuming that the probability of scoring is 0.57, it follows that Oakland's probability of winning if they go for it is
The endgame was almost surreal. With the score 24-24, and 1:18 left, Oakland had 1st and goal at the Carolina 3 yard line. Oakland had three timeouts, Carolina none. It's an intellectually interesting
to determine whether it's best for Oakland to take the clock down to 0:02 before calling timeout and kicking the field goal, to ensure that time expires on the kick, or to leave 0:04 on the clock, to allow for a re-kick in case of a bad snap. But let's not split hairs. If Oakland simply takes a knee twice, centering the ball between the hashmarks, and calls timeout at 0:02, Carolina can win only if the field goal misses (probability 0.02) and then they win in overtime (probability 0.5). Oakland therefore reduces Carolina's probability of winning to
This plan seems straightforward enough, but instead of following it, Oakland coach Norv Turner had his offense try to score a touchdown on both 1st and 2nd down. Carolina coach John Fox, evidently convinced that it's better to give than to receive, had his defense try (successfully) to stop both attempts when he should have told them to step aside. (Stepping aside can't hurt in this case, in contrast to the situation in the Minnesota-Indianapolis game .) Fox reportedly considered letting Oakland score, but decided — we're not making this up — that it was a low-percentage play.
Oakland finally saw the light and set up for a field goal. Even then, Oakland erred by stopping the clock with 0:09 left, guaranteeing that they would have to kick off to Carolina following the field goal, and virtually doubling Carolina's probability of winning the game.
With 13:15 remaining in the 2nd quarter, Houston trailed 7-0, and faced 4th and inches at the 50 yard line. Houston coach Dom Capers called for a quarterback sneak, but David Carr was stopped short, and Denver took over on downs.
According to the Model , Houston's probability of winning if they punt is 0.27.
If the Texans go for it, their probability of winning is 0.31 if they make it but 0.228 if they are stopped. On 4th and inches at midfield, the probability of picking up the first down is about 0.75. Therefore, Houston's probability of winning if they go for it is
Copyright © 2004 by William S. Krasker