Bills showing why being too aggressive backfires.

It was easily the right decision. Fourth and less than 1 QB sneaks in the NFL succeed at a very high rate even when you don’t have a human-moose hybrid as your QB. Let’s say that succeeds 80% of the time, and then let’s say since they were inside the 5 yard line, let’s say that they score 80% of the time that they convert. I would guess these numbers are conservative and would put it closer to 90%, but let’s say .8 * .8 = .64% of the time they win the game right there. Overtime is much closer to 50/50. You can adjust those numbers a little bit if the situation favors you, like you’re the better offense and their defense is gassed, but most of the time teams go to overtime is because they’re very evenly matched that day and who gets the ball next is random so it makes sense that it’s probably near 50%.

People in general but it seems especially football fans are very results oriented. If a decision works out, then obviously it was the right call. If it doesn’t, then the coach is obviously an idiot! But that doesn’t make sense. The outcome is going to be probabilistic due to very slight differences in the situation. If you run that 4th and 1 decision a thousand times with slightly different unpredictable conditions, you’re going to get something like 83% successes and 17% failures. Rolling the dice and getting that 17% doesn’t make it a bad decision any more than betting even money that you’ll roll a die and win if you get any number 2-6 and then rolling a 1. It was still a great bet, you just happened to lose.

There’s also the issue of diffusion of blame, or being unable to declare a clear failure point. If the Bills go for it on 4th and one and fail, you have an easy point where they lost it to point to, a single decision and a single lack of execution. If they kick the field goal, go to overtime, Tennessee wins the coin toss and then over 7 plays goes down and scores the TD, you don’t have an easy single point of blame. Was it the decision to go for overtime that lost you the game? Was it losing the coin toss? Was it the bad tackle on play 3, or the dropped interception on play 5 that cost you the game? Now you don’t have a single decision you can point to and say “the coach is an idiot! he lost us the game!” So even though the coach made the decision (kicking the FG) that gave you a lower chance to win, it diffuses and deflects the criticism away from his playcalling decisions.

That’s why NFL coaches are almost always too passive and usually make the wrong decision in these situations. Because the fans are too results-oriented and can’t understand the decision-making process, and look for that single point of blame. And so NFL coaches try to avoid that single point of blame by diffusing the loss over a bunch of sub-optimal decisions rather than take the single correct decision that leaves a clear point of blame.

To say the Bills made the wrong decision there is not just to say “well they lost, and I can find the decision they made that most directly lead to the loss, so it’s a bad decision”, you have to show that the outcome of the decision was less likely to secure a win than the alternative. And I think you’d have a hard time making the case that the Bills win overtime more often than they convert a 4th and less than 1 and then score from within the 5 yard lane.

I am happy to see the Bills lose, but Allen looked the like the real deal there. And I don’t know who the Bills OC is, but they are creative and effective. Even with this loss, I don’t see how the Bills don’t walk away with the AFC East (barring injury, of course).

Brian Daboll. He’s on the short list of guys I hope the Bears take a very close look at.

Yeah, the stat that I saw last night was that Allen was something like 17-1 in running a QB sneak with a yard or less to go.

But…the play before, Allen had gotten rocked when he tried to dive for a first down by the sidelines. Now, I have no idea if that affected him, but he did get hit pretty hard on that play.

Don’t think so, he just slipped. He tried to dig in and plunge into the pile and his feet slipped out from under him. Not sure you can blame anyone for that, it’s not like it was raining. Just bad luck and maybe Allen was rushing it.

I think the problem with football is that the long run never plays out. With each game being so important, results are important. If an “unconventional” choice only gives a slight edge it may never bear fruit in a season.

I think the Bills made the right call but I don’t have a rooting interest in either team so I find the more aggressive choice interesting.

It doesn’t really matter if you end up having a large sample size - that’s just to demonstrate evaluating decisions in a probabalistic way. You go with whatever gives you the highest chance of winning. You would always want to roll the dice on a 75% chance to win over a 50% chance to win, and just because that 1/4 chance came up and you lose doesn’t mean that taking the 50/50 was somehow better. The 50/50 chance is always worse than the 75/25 chance whether you do it once or a million times.

Yes, but …

Consider a game where you bet on the throw of a fair 6-sided die. You can bet ‘low’, in which case you win if the result of the throw is 1, 2, 3 or 4 - or you can bet ‘high’ and win with 5 or 6. A rational person would always bet ‘low’ - but we’ve probably all run into the type who says “It’s comin’ up 6 - I just know it !” If he bets ‘high’ and the result is indeed a 6, he wins - and (with some justification) feels his was the better choice.

Yes, but in a situation this complicated, you can’t know what the true probabilities are. You can manufacture a die as accurately as possible, and you can roll it thousands of times to see how often each number comes up. You’ve got a pretty good basis to conclude that the probability on the next roll is 1/6 for each side.

Every play and every situation in a football game is unique; the players on the field, the coaches calling the play, the turf, the score, the weather, etc. No one can say “there’s a 73.2% chance of winning if they go for it on fourth down.” The best you can do is try to estimate it based on how similar situations have turned out in the past; and in that case having a large sample size does help.

Then the coach makes his choice and the team runs a play. And the result of the game becomes part of the calculation for the next time the choice has to be made.

You never know the exact true probabilities, but you can get a good estimate, and adjust things based on the exact situation. In some of the cases the math is so overwhelming that the details usually don’t matter much, like the one about going for 2 when you’re down 14 and score a touchdown.

The other thing about this is everybody actually does this approach on normal plays, they just don’t phrase it the same way. Nobody thinks the Bills should’ve kicked a FG on third down, right? But the reasoning of the argument for why they shouldn’t is the same as it is on fourth down.

The Chargers over the last two weeks are a good example for why going for 4th downs can be a good strategy, even through it obviously doesn’t always work. They made a bunch of 4ths against the Browns, and missed a bunch against the Ravens. A more conservative coach would have kept the Ravens game closer, but probably still lost, but would have also lost the Browns game.

I’m not following your logic here. The Bills shouldn’t kick a FG on 3rd down because they still can run a play to attempt to get the first down (or score a TD). But on 4th down they have no such luxury.

I think @borschevsky’s argument is that the same probability analysis applies. Kick the field goal on third down, and the best you can do is 3 points. Run a play and you have the chance to score more than 3 points, with the likelihood that you can still kick the field goal on fourth down. Your win percentage is maximized by running a play.

It’s not a sure thing. Maybe you fumble the ball and the other team recovers, or you lose yardage and wind up missing the field goal on fourth down. You’d have been better off kicking the easier field goal when you had the chance. It’s rare that things turn out that way, though. You could do the same probability analysis as you do for tough decisions, but no one does because the answer is obvious.

I like the new emphasis on data.

It wasn’t long ago coaches would only go for it on 4th down when there was no other option. Now, it happens every week and not always in the 4th quarter.

The conventional wisdom was that fans would excoriate a coach who went for it and failed. And maybe that happens a little but generally, it seems like fans love seeing a coach get aggressive when the situation says it’s appropriate, even if it doesn’t always work out.

And by moving the ball to the center or one side of the field and gaining yards, improve the probability of making the field goal. Look at it as an expectation problem.

Right. I was being glib about it, but I was trying to say that the reasoning for not kicking on third down is a probability analysis of the plays that are coming, just like it is on fourth down.

I disagree with the “with some justification” part. It’s not like the guy somehow predicted the random event through clairvoyance. He made the worse bet and winning through chance isn’t an indication of a good decision. That’s exactly the sort of irrational results-oriented thinking I was speaking about.

No one here has really criticized the decision, but I saw on reddit how hundreds of people were blasting the decision and they were doing exactly what I said. You can design a formula and plug the numbers in yourself. I remember threads where people on the SDMB went after Bill Bellichick for going for aggressive 4th down numbers, made a formula for the situation, and asked them to plug in numbers they estimated for each part of the formula (what are the chances of converting the 4th down, what are the chances the other team would score after a turnover on downs vs a punt, etc), and none of them ever disputed it because they knew, after plugging in the numbers, that their intuitive decision was wrong but still stuck to the idea that he was somehow being arrogant by making the correct aggressive decision that gave the Patriots the highest chance of winning.

This one is really simple. What are the odds that Josh Allen gets a 4th and less than 1 in that situation? I read that he’s 17-1 in that situation. Maybe you say Houston’s defensive line is unusually good or has been on the ball with the snap counts and adjust it down a little bit. Let’s call it 85%. Now, let’s say that he doesn’t score during that play but they’re inside the 5. How often do score a touchdown after converting that 4th and 1? Let’s call it 75%. I think these numbers are conservative, but even if you plug in those numbers, it’s 63.75% chance to win, compared to OT which is much closer to 50/50.

(Technically I’m leaving out the chance that they convert the 4th down, fail to get a TD, but then kick the field goal for OT - that wouldn’t change the numbers much and I left it out for simplicity of explanation).

You would have to think that the chance of the moose in the football uniform converts is significantly less than 80%, or that their chance of scoring a TD after conversion is way lower than 75%, for the numbers to work in favor of the FG.

It’s really hard to argue that overtime would’ve been more like 70/30 or 60/40 Bills - after all, we have a lot more data at that point that suggests that the teams are pretty evenly matched since they’re tied after 60 minutes, and you don’t know who is going to get the ball first.

I would say that the range of reasonable numbers (Josh Allen has a 80-98% chance to convert, and the Bills score a TD if they convert 70-90% of the time) - even the worst end of those numbers is about even with the most optimistic numbers you can predict for an overtime win.