Kicking a field goal down by 18 this late in the game is a poor decision unless it’s fourth and impossible. Since 1940, do you know how many teams have kicked a field goal, when trailing by 18 or more points in the *second half*, and went on to win the game? **THREE**. The “They Are Who We Thought They Were” game, when Chicago kicked a 23-yard field goal down 20-0 midway through the third quarter. After that field goal, Mike Brown, Charles Tillman, and Devin Hester scored touchdowns for the Bears, which doesn’t seem like the best model to follow in the future since none of those players played offense.

In 1998, the Rams kicked a field goal in Buffalo to make it 28-13 in the third quarter, ultimately winning 34-33 on a touchdown run in the final seconds. And in 1996, in Bill Parcells’ return to the Meadowlands to face the Giants, Adam Vinatieri kicked a third-quarter field goal down 22-0, and then Terry Glenn, Dave Meggett (on a punt return), and Ben Coates scored fourth quarter touchdowns.

You know what hasn’t happened? A team kicking a field goal, down by 18 or more points in the *fourth quarter*, and going on to win the game. Including the two teams this year, 117 teams since 1940 have kicked a fourth quarter field goal when trailing by more than 17 points, and none of them have ever won. I know, trailing by 18, it’s so comforting to kick a field goal and think “hey look, all we need to do is stop them, score a touchdown, stop them again, score a touchdown, convert a two-point conversion, and then win in overtime.” But that’s never, ever happened before.

According to Brian Burke, the Cardinals had a 3% chance of winning the game if they kicked the field goal, a 1% chance of winning if they failed on 4th down, and a 10% chance if they converted and scored a touchdown. Those numbers seem reasonable to me, but maybe you want to use different numbers. It doesn’t really matter. When you’re that big of an underdog, you need to play aggressively. You’re almost certainly going to lose, and you’re only chance of not losing is having some high-leverage plays go your way. For the avoidance of doubt, a 22-yard field goal is not considered a high-leveraged play.

Using Burke’s numbers, Arizona would have needed only a 22% chance of converting on 4th-and-goal from the 4 to make it the right move mathematically, as he estimates that the league-average conversion rate is 42%. You might think “well sure, but against the Seahawks defense, Arizona’s chances were much lower of converting.” To the extent that such a proposition is correct, what does that mean for the chances of the Cardinals to put together two touchdown drives over the rest of the game?

In a vacuum, Arians didn’t give up much, reducing his team’s win probability from five percent (by choosing to go for it, without knowing the outcome) to three percent (of course, while a different of two percent in win probability is small, a reduction of 40% is quite large). But the more important takeaway is that Arians, coaching a huge underdog, chose the most conservative option possible. He picked a route that has literally never led to victory in NFL history.

(On an unrelated note, I will give Arians credit for going for two later in the game with the team (before the score) trailing by 18, an analogous situation to one I outlined last year.)

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Despite your cogent argument, citing historical precedent and statistical analysis for the math, I can’t really give Arians too much grief on this. Yes, a touchdown would have been better than a field goal. A touchdown is ALWAYS better than a field goal, whether it’s the first quarter or the fourth. But a field goal is better than failing to convert. To come away with no points at all is disastrous. He’ll still be down by three scores and will have basically thrown away the possession and all the time that it took off the clock.

1. The possession and time taken is a sunk cost, it’s gone no matter what happens that drive, so it doesn’t do any good taking that into consideration.

2. Chase just showed us that kicking a field goal is EQUALLY disastrous to getting no points, because no team has ever come back from that deficit. Scoring a TD there is your only hope.

You’re a very kind person, but you should still give him grief when he makes a blatantly boneheaded decision that shouldn’t require any advanced mathematics or historical precedent to understand.

Nice analysis, but it leaves out an important fact. What is the record of teams behind by 18 in the 4th quarter who choose not to try for a field goal on 4th down? Have they had better success than those who took the field goal? If not, then why is kicking a worse choice?

While it would be nice to know the statistic you mention, Allen, it’s really not necessary. No strategy will be worse than 100% failure.

Nonsense. If you’re going to criticize a coach for selecting a strategy, you need to be able to show that your strategy has a measurably better chance of success. Saying “it can’t be worse” doesn’t mean it’s better. If the other strategy hasn’t been successful either, it means his choice is just as valid as yours.

The criticism is based on the math, not the history.

The criticism is that the Cardinals made a decision that was not only a negative EV proposition, but it was also one that reduced the team’s variance. Arians should be looking to maximize the team’s EV, or increase their variance, but certainly not neither.

The historical fact that no team has won a game while kicking a field down in the 4Q when down by 18 isn’t shown to prove that kicking was the wrong decision, but was shown as a response to someone who thinks the smart move is to always take the points.

I was watching the Broncos-Colt game and even the TV commentators noted that Matt Prater’s 42 yard field goal attempt in the waning moments of the third quarter was an unusual choice.

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