Gruden Goes For Two: Foolish Folly or Genius Gamble?

Washington's painful one-point loss to Tampa Bay yesterday was about as gut-wrenching a seesaw battle as I've seen in a while, with huge momentum-changing plays every few minutes, four critical instant-replay reviews, and one unreviewable blown call.*

The most interesting sequence of the game came after the Bucs' final touchdown. With the score 35-34 in Washington's favor Tampa Bay opted to kick the extra point and tie the game. Washington's Shawn Springs and Walt Harris timed the snap and flew around the left and right ends to block the kick (Harris was credited). But wait: They both jumped offsides giving the the Bucs another chance from the 1.

Rather than kicking again Gruden deployed his heavy set and Mike Alstott plowed in for the score and the 36-35 lead. Or did he? Replays seemed to show Alstott's elbow down short of the goal line, and the replay official ducked under the hood to sort it out. Deciding there wasn't conclusive evidence to convict, er, overturn the line judge who called the score, he let the conversion stand. The Redskins received the kickoff, gained one first down to near midfield, and then ran four plays gaining zero yards, handing the ball and the game to the Bucs.

So was Gruden's call for two the best choice? The announcers certainly thought so, comparing his decision favorably with Dick Vermeil's touchdown call to win the game in last week's Kansas City vs Oakland matchup. I wasn't so sure.

In that instance the Chiefs elected to go for the win with five seconds on the clock, meaning Oakland had no chance to get the ball back and score. As Gregg Easterbrook pointed out last week in his NFL.com column, the Chiefs had probably an 80-90 percent chance or better of scoring from inside Oakland's 1, while kicking to send the game into overtime offered no better than a 50 percent shot at victory. In Sunday's game, however, the Redskins would get the ball back and only needed a field goal to recapture the lead. Gruden's call increased the Skins' chances of winning outright if Alstott failed, and didn't prevent the Skins from winning even if Alstott scored. On further review, it turns out that not only was Gruden's call probabilistically the right one, but he should have gone for two points and the win even before the Skins' offsides penalty moved the ball a yard closer. To calculate this I coarsely modeled the likeliest outcome paths with back-of-the-envelope estimates of the probabilities involved at each step.

One path, for example, was Bucs Go For 2/Bucs Score/Bucs Stop Wash. This is the path that actually occurred, and it happens be the single likeliest path out of the 16 paths I modeled.

Some other likely paths were Bucs Kick XP/Bucs Make Kick/Wash 50 Yd Dr/Wash 42 Yd FG and Bucs Kick XP/Bucs Make Kick/Bucs Stop Wash/Bucs OT Win or Wash OT Win. The least likely path was Bucs Kick XP/Bucs Miss/Bucs Onside Rec/Bucs 30 Yd Dr/Bucs Miss FG.

According to my model, the Bucs chances of winning were just 32 percent had they opted to kick the extra point and 55 percent by going for two (assuming an 80 percent chance of converting). If there had been no Skins penalty and you drop the Bucs chances of converting from the 2-yard line to 70 percent, that's still the better option with a 48 percent chance of ultimate victory!

The key is that by going for two the Bucs eliminate the outcomes where the Redskins have two opportunities to win. In other words, if the Bucs kick for the tie, Washington gets a chance to win in regulation (33 percent) and another chance of winning in overtime (50 percent). When the Bucs go for two they lose outright nearly 20 percent of the time but the other 80 percent of the time Washington just gets one 33 percent chance of victory. (Actually the Bucs lose outright 19 percent of the time--the other one percent they recover their onside kick, drive 30 yards with no timeouts, and kick a 42 yard field goal!)

UPDATE: I read today that NFL teams make just over 50 percent of two-point conversions from the 2-yard line. I'm not sure whether that number is accurate--it wasn't from an authoritative source. If it is, the sample size may be fairly small. I'd prefer to look at the percentage of all plays from the 2 which scored. But even assuming the worst-case 50 percent odds of success, going for two is still the slightly better option in this scenario, offering a 35 percent chance of winning vs a 32 percent chance of winning when teams kick the extra point!

One interesting side note on my probability estimates: I guestimated the average kicker's chance of hitting a 42 yard field goal at 65 percent. Ned Macey at FootballOutsiders happened to mention today that NFL kickers hit 62 percent of all 46-yard field goals. That was a pretty darn good guestimate! NFL.com stats so far this season show kickers hitting 69 percent of 40-49-yard field goals.

UPDATE II: More actual probabilities: On fourth-and-goal from the 1-yard line over the past four seasons teams score 67 percent of the time overall and 74 percent of the time when they run.

UPDATE III: I was asleep at the switch on this one (not paying much attention to the blog over Thanksgiving weekend) but thanks to Gregg Easterbrook for the link from his NFL.com column!

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Current Washington Post Redskins stories: Skins Blame Selves, Wilbon, Wise, Kornheiser, Gruden: Easy Choice, Gibbs Gouges Refs, Skins Peek at Giants, Turner Still Stinks.

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* Joey Galloway's out-of-bounds catch at Washingon's 3 in the first quarter was unreviewable because the official said Galloway was forced out of bounds by the defender.

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Model Details

(Click for larger Image.) Each step includes outcome descriptions, the probability of each outcome, and the number of outcome occurences. The orange rows indicate an ultimate Bucs win, the red indicate an ultimate Skins win. For example, here are the steps in the topmost path which starts when the Bucs Go For 2:

1. Bucs score 80 percent of the time (16 of 20 outcomes on branch)

2. Wash drives 50 yards 50 percent of the time (80 of 160 outcomes on branch)

3. Wash kicks a 42 yard field goal 65 percent of the time (1040 of 1600 outcomes on branch)

4. No more decisions on this path so Wash wins 100 percent of the time (20,800 of 20,800 outcomes on branch).