## Belichick’s Decision: Flip a Coin, or Trust your Team?

By David Roher

If you write, talk, or scream about football for a living, you probably had something to say about Bill Belichick’s decision last night. In short, the Patriots had the ball with just over 2 minutes to go on their own 28. It was 4th and 2, and instead of electing to punt, Belichick decided to go for it. The pass play came up just short, and the Colts gained possession and went on to score a touchdown for a 35-34 victory.

This post is not really about the correctness of that call, though. As I see it, it’s been handled quite convincingly. Bill Barnwell shows here, (as well as Brian Burke here, and Wayne Winston here) that Belichick likely gave his team a better chance to win the game by going for it on 4th and 2. Instead, it’s about the consequences of making a choice that is mathematically correct when it’s going to make everyone upset.

It’s hard to say precisely how much better the Patriots were off going for it. But let’s say the win probability difference is not greater than 10%. Is that 10% worth the inevitable firestorm that would result if he gambled and lost?  This might not be true for Belichick, but almost any other coach would have to think about the effect it would have on his job security and on his relationship with the players.

Let’s say you’re an Olympian. You’re about to enter a final race, one that you have a 49% chance of winning. A corrupt French judge offers to flip a coin to determine the outcome of the race. Heads, you win, tails, you don’t. After making it that far, would you really take the offer? I have a feeling that very few would. Even fewer would like it if their coach took the offer for them.

When a coach makes a decision like Belichick’s, he’s doing something very close to that. If the Patriots had converted on 4th down, they would have had roughly an 100% chance of winning the game. If they didn’t, they probably had somewhere between a 15-50% chance of winning the game (depending on how the Colts offense and Pats defense are evaluated). That means that Belichick singlehandedly based 50-85% of the outcome of the game on just one play. Granted, a play is not a coin flip – it is based on the players’ performance. But the outcome of one play is a lot more random than the outcome of one drive.

My guess is that the average Patriot doesn’t understand the win probabilities behind the decision evaluation. But I’m almost positive that the defense got the following message from that decision: “I’d rather base the outcome of the game on one play run by the offense than on you guys making a stop over the course of an entire series.” Is that an unfair characterization of the complex decision that Belichick had to make? Certainly. But it’s what inevitably results.

This sort of decision happens all the time, in all sports – do you shoot a 2 at the buzzer to send a game into overtime or a 3 to try and win it in regulation? Do you play small ball to get 1 tying run in the bottom of the 9th, or swing away to get 2 or more to win? In both of these cases, the mathematically correct decision is probably to go for the win in the moment. But the reason for that involves the team’s relatively lower chances of winning the game itself through more skill.

So what does all this mean? If you’re of the opinion that player psychology and coach-team relationship is negligible, then this is worthless. Judge based on math. But it’s a lot murkier if you think that these aspects of sports matter. Belichick not only has to crunch the numbers, but he has to ask himself, is that extra 10% in win probability worth the potential problems in the locker room afterward? Does it cost the Pats more than 10% in win probability over the course of the regular season?

I have no clue. But a good coach should.

UPDATE: Here’s a nifty Belichick 4th-and-2 calculator from Football Outsiders.

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### 4 Responses to Belichick’s Decision: Flip a Coin, or Trust your Team?

1. Rogersworthe says:

Interesting piece. However, does a defense really feel that rejected and upset if a coach goes for it there? If they do, shouldn’t the answer be “If you want me to have confidence in you, then play better”?

I just think you have to play in the moment and not contemplate how your defense might react. How would the offense feel if Belichick punts it and the defense lets Manning drive right down the field for the win? How would the defense feel?

I think some of this “You gotta have confidence in your offense/defense” is a totally overrated cliche.

2. bubqr says:

Not a big fan of the comparison with the corrupt judge/coin flip. It’s still football, the coinflip comparison is good statistically, but it’s going a bit too far.
A better comparison would be a soccer team willing to accept that the outcome of the game be decided by a penalty shot instead of playing the 2nd half, if the game is tied at half time.
And “Is that 10% worth the inevitable firestorm that would result if he gambled and lost?” yes, yes and yes. I’m not a Pats fan, but I have to admire Bellichick when he makes that decision, because if it fails, like it did, he’ll be the scapegoat. He’s a coach wanting to give his football team the best chances to win and willing to take all the blame if it doesn’t. The NFL need more coach like that.

3. Jeff Clarke says:

This is an interesting piece.

It gives a little more rational voice to the “he’s disrespecting the defense argument” that frankly doesn’t make a lot of sense.

If I was him, I’d invite the entire team in and go over the math in detail. They might not understand all the specifics, but they’d get the overall picture that it was actually the correct call for the moment. I think that would help any hurt feelings.

I generally don’t buy the hurt feelings argument. It is sort of predicated on the idea that football players are a lot more sensitive than I think they are. Plus, this argument doesn’t come up in any other context. If a coach calls a pass to the tight end, is he disrespecting the wide receivers and running backs? Will their morale be so hurt by the call that they won’t be able to perform on the next play? Almost everybody would say they should suck it up and accept that the coach needs to maximize the possibility of success. If that means someone else’s number is called, so be it. Yet somehow, hurt feelings are a legitimate point in this debate.

4. Guy Incognito says:

Belichick went for it on 4th-and-13 from 31 yards out in Super Bowl 42, and on 4th-and-1 from his own 25 earlier this year (both non-endgame situations). I’m pretty sure that his defense had some idea that going for it was a possibility and knows not to take it personally.