I'm not sure I buy your numbers. Where do they come from anyway?
The win probability (WP) numbers are from actual teams playing actual games. They’re average win rates based on recent NFL history. They are not theoretical or simulated outcomes. They’re simply how often teams win given certain situations. In many cases where there are too few games for a reliable estimate, other similar situations are used to smooth the gaps. There are some sophisticated statistical tools that help make sure we do that right, but underneath it all are actual games and actual wins and losses.
Football is a game of momentum. If a team goes for it and fails, it will lose all its momentum and its players will be deflated.
Momentum in sports, for the most part, is an illusion. People naturally expect to see events alternate more often that they really do. Streaky outcomes are a natural part of the world, and momentum is not needed to explain it. Flip a coin a few times and you’ll see that there are streaks of the same result, and no one would ever say the coin had momentum.
Here’s a quarter. Go ahead and start flipping now. I’ll wait. Half out of every set of two flips will be the same two results in a row. One in four sets of three flips will be a streak of the same result…And one out of eight times you’ll see four straight of the same result. There are at least 20 drives in an NFL game, plenty of opportunity to witness perfectly natural streaks.
Despite this illusion, emotion can be an important part of a sport like football. No one can deny that. And I agree that large successes and failures are an important part of players’ emotional states. But the momentum/emotion argument always assumes failure. It assumes momentum/emotion can only be lost. It can be gained too, perhaps from a 4th down conversion. Besides, what happens to your opponent’s emotional state when your team successfully converts a 4th down?
But that offense was only 1 for 3 in converting short yardage situations in the game. No way the chance of conversion was close to 75%. More like 33%!
If I flip a coin four times and get heads three times, does that mean the coin is weighted three quarters towards heads? Or does it mean that it’s a fair 50/50 coin, but sometimes you get variable results, especially when you have so few trials? Although prior results from the particular game might be helpful, they are far more likely to be due to the effect of small sample size. The long-run probabilities are far more likely to be representative of the true chance of success.
The math is too confusing.
Once the WP numbers are in place, the math is 5th grade arithmetic. If you can multiply and add decimals, you're all set.
I don’t understand how you can say the decision to go for it was worth a "net WP"? Either they make it or they don’t.
Let's use a gambling analogy. Assume every dollar in your pocket is equally valuable to you. I offer you the choice between a certain $10 or a coin flip for $20. What’s better? They’re theoretically equivalent. What if I offer you the choice between $10 or a 75/25 proposition for $20? I’m sure you see that the gamble is preferable to the certain ten bucks (.75*20 = $15).
Now, what if I offer you a certain $40 or I offer you a 75/25 proposition at $60 (.75*60=$43). Further, what if I sweeten the deal and say, even if you lose the 75/25 gamble, I’ll still give you $15 bucks? Well, that clinches it. The gamble is the better deal.
Ok...now...pretend you’re a football coach, and I, the football god, offer you a certain 40% chance at winning the game or a 75/25 gamble at a 60% chance at winning? Which should you prefer? You’d prefer the gamble. And if I sweeten the deal and let you have a 15% chance at winning even if you lose the gamble, that’s just a bonus. The gamble gives you then best overall chance to win. See what I did there?
But dollars and winning football games aren’t the same thing.
In this case, they are. Recall my assumption above—“every dollar is equally valuable to you.” The same is true for chances to win a football game. Think of WP as chances to win out of 100. A 0.40 WP is 40 wins out of every hundred games. So 20 chances is exactly twice as good as 10 chances to win, and 40 chances to win is exactly twice as good as 20. And so on. Every chance of winning is equally valuable as the next. (Economists call this linear utility, and the gamble analogy above is known as expected utility.)
But if they go for it and fail, they’ll definitely lose. You can’t bet the whole game on one play!
Sure you can, when the odds are in your favor. The speed at which you win or lose is irrelevant.
If you fail, handing the other team the ball in field goal range is suicide!
It’s not suicide. Turnovers happen. Just last Monday night, we saw a team lose a fumbled quarterback snap when a game-winning field goal was well within range. Field goals get missed. Just yesterday, 23 of the 75 attempted field goals were missed, including a potential game-winning kick that was only a 22-yarder! (The line of scrimmage was the 4.) And last year in a Falcons-Saints overtime game, the Saints missed a supposedly automatic 38-yard FG, allowing the Falcons to steal the win. It happens--not often--but enough to matter.
Well, since it didn’t work out and the team lost, that proves going for it was the wrong decision.
By that logic, the team that missed the 22-yard game-winning field goal should have gone for it, right? Or should they have punted from the 4? That kind of thinking is called outcome bias.
OK. I understand everything you just said. I understand where the numbers come from. I understand the math and the concepts, but I still can’t bring my head around to think that going for a super-risky fourth down was the smart thing to do.
So far we’ve only been looking at it from the side of the coach who has to make the decision. Let’s put ourselves in the shoes of a fan of the other team. Consider what was going through the head of a Saints fan yesterday as Mike Smith decided to go for it in OT:
Yay! We made the stop on 3rd down! Here comes the punt team. We’re gonna’ get the ball back and win this thing...Hey wait, what’s going on?…
Where’s the punter going?... Why is their offense…? Crap, they’re going for it….Oh, $#!+ ! They're going to make this. It's so short.
$#!+! $#!+! $#!+!...Oh, thank God.
If you gave the Saints coaches the choice between receiving the punt and letting the Falcons roll the dice on 4th and inches, they’d take the punt every time and twice on Sunday. That tells you something, doesn’t it?
I'm not sure I buy your numbers. Where do they come from anyway?