Kickers Make 80% From 43 Yards. That Told Chicago Nothing.

Gene, a Bears man, asks a good question. If the long run is so reliable, why does it seem to quit at the last second? Kickers make 80.3% from 43 yards. It never quit; it was never a fact about one kick.

The Sports Page · The Professor · answering Gene

The question, roughly as Gene put it: a team wins 75% of its games over a season. So why, at the nitty-gritty last second, is the probability something else entirely?

The answer: nothing about the team changed. That 75% was a fact about a crowd of games. It was never sitting inside the team like a fuel gauge, waiting to be read off on Sunday.

Here is the surprising part. Most of us have it backwards. We treat the long-run percentage as the real thing and the single game as a wobble around it. It is the other way round. The single game is the only real thing; the percentage is a summary of a crowd that game happens to belong to.

What you get from it: two questions that make any quoted probability behave.

The law of large numbers promises less than you think

The law is real and it is not in doubt. It says that as cases pile up, the average settles down toward the true rate. Read it again and notice what is missing. It says nothing at all about the next case.

It cannot. A single kick is not an average of anything. It goes through or it does not, and afterwards it is a 1 or a 0, never an 0.8.

This is where the gambler goes wrong, in the other direction. He thinks a run of misses means one is “due,” because the average has to come back. The average does come back — by drowning the old results in new ones, not by correcting them. The coin has no memory and neither does the season.

A number about the crowd, quoted about the man

There are two ways of knowing a thing, and philosophers named them in 1894. You can look for a law that holds across many cases, or you can try to understand the one case in front of you. The first is nomothetici; the second is idiographic.

A percentage is nomothetic to its bones. Quote it about one man on one Sunday and you have quietly changed the subject.

Watch the number move as you narrow the crowd

The mechanism is simple, and once you see it the mystery goes away. Every probability you are quoted is a conditional one: the chance of a thing given some stated circumstances. Change the circumstances and you change the number.

Across all field goals in the last ten seasons, kickers make 84.6%. Narrow to 43-yarders: 80.3%. Narrow again to the last two minutes of a one-score game and it falls to 71.1%.

Nothing about any kicker changed between those three sentences. The kickers were the same men. Only the crowd we were describing got smaller.

Now push the narrowing all the way, the way Gene’s question does. What is the crowd for this kick? Forty-three yards, ten seconds left, one point down, playoff game, iced by a timeout, a rookie’s fingertip in the flight path.

It has one member, and it has already happened. Narrow far enough and every event is unique. Stay broad enough to have data and you are no longer talking about the thing you care about. That squeeze has no tidy escape; knowing its name is most of the defense.

Two camps, and they are arguing about this

Gene also asked how a Bayesian differs from a frequentist. This is exactly where they part company, and the split is easier than the jargon suggests.

A strict frequentist says a probability simply is a long-run frequency in a repeatable class. On that view, “what is the chance this kick goes in?” is not a hard question; it is a broken one. There is no long run of that kick.

A Bayesian treats probability as a degree of belief about a particular case. You are allowed to state one about an event that happens only once; it is supposed to move when you learn something. Ask the two camps what the number means and you get a fight. Ask them what to bet and they mostly agree.

So why do the odds never sit still?

Because every one of them is really this: the chance of the thing, given what we know so far. And what we know grows on every play.

When a win probability drops from 71% to 4% in one snap, nothing has been caught out. A great deal just became known. A number that never moved would not be more rigorous. It would only be deaf.

Now, Gene, about Da Bears

You support a club that went 11–6 last year. I support one that went 3–14. On the face of it there is nothing to discuss.

Look under the records, though, and it gets more interesting for you and no better for me. Chicago outscored its opponents by 26 points across the whole season, which ranks eighteenth in a league of thirty-two. Your record says contender; your scoreboard says average with a gift for close games.

My Jets have no such consolation. Minus 203 points, and last in the league by the schedule-adjusted measure. Dead last. Not unlucky. Just last.

So take the widest gap in professional football — your team against mine — and put it on a neutral field. It comes to about 12.6 points a game, which is a win probability of 82.4%.

Now here is the number I want you to keep. To show that 82.4% is really better than a coin flip, you would need about sixteen games between us. An NFL season is seventeen.

The widest gap in football, and it takes nearly a whole season of playing each other before that gap could be told apart from luck. That is Sunday for you. That is why we all keep watching, and it is the honest answer to your question.

What to take home: two questions

Ask them of any percentage anyone ever quotes you. What crowd is this a fact about? And what does it already know?

The first tells you whether the number is about your case or somebody else’s thousand. The second tells you why it will be different tomorrow.

You will need this far away from football. A treatment with 90% survival — among whom, at what stage? A 30% chance of rain — over what area, over what hours? A poll at 52% — among people who answered, when? Every one is a crowd and a condition wearing a single number as a disguise.

And on the kick itself, Gene: the 80.3% was true. It was true of 355 kicks. Yours was not one of them until it landed.