Seven Hundred Best Days

There is a moment, most evenings, that almost nobody describes accurately afterwards. You open the feed. Somebody is in Lisbon. Somebody has closed a round. Somebody's child has done something photogenic on a beach, and somebody else has run a marathon in a time you could not manage downhill. Seven hundred of these, in the time it takes the kettle to boil. Then you look up from the phone into a kitchen that has not changed, and something in you files a report: behind.

The report is wrong, and it is wrong in a way you can write down. Not because those people are lying — mostly they are not. Not because the good things did not happen — mostly they did. It is wrong because of what a feed is. A feed is a filter, and this particular filter keeps one thing: the maximum.

The tool below is that filter, taken apart. Give everybody the same life — the same spread of good days and bad — let each of them post the best day out of every thirty, then turn up yourself on an ordinary Tuesday and see where you rank. The answer is not below average. The answer is below all of it, and it stays there if you are better than most people, and it stays there if you are better than nearly everyone.

A feed is a filter, and this one keeps the maximum

Start with the honest version of a life, which is a distribution. Some days are better than others; nobody disputes this about themselves. Draw it as a bell — most days near the middle, a few well above, a few well below — call the middle an ordinary day, and call one step the size of a normal swing. This is not an assumption about how good the life is. It is only the assumption that days vary, and the whole argument runs on that and nothing else.

Now ask what gets posted. Not the median day. Nobody photographs the median day; there is no photograph in it. What gets posted is the best of some run of days — the one weekend out of the month, the one dinner out of the quarter, the year's one paragraph in the Christmas letter. Call the length of that run k. A person who posts about once a month, and posts the day worth posting, is publishing the maximum of thirty draws.

The maximum of thirty draws is a known object. Statisticians call it an order statistic, and the arithmetic is one line long: the chance that all thirty days fall below some level is the chance that one does, raised to the thirtieth power. Solve for the level that half of all best-of-thirty days clear and half do not, and the typical post sits two full steps above an ordinary day. Almost to the decimal. Best of seven: 1.3 steps. Best of a year: 2.9.

Nobody in the feed is lying. Every one of them is reporting the maximum, and the maximum of thirty ordinary days is a two-sigma day.

Everyone identical, everyone below average

Here is the part that should stop you. Make everyone in the feed the same. Not similar — identical: the same distribution of days, no better life anywhere among the seven hundred. Each posts their best of thirty. You open it on an ordinary day. What share of the feed is above you?

All of it. The chance that a best-of-thirty day falls below an ordinary one is one half to the thirtieth power, about one in a billion. So seven hundred people with a life exactly as good as yours will, every one of them, appear to be doing better than you on any day you happen to look — and, since the arithmetic is symmetric, you appear to be doing better than every one of them on the day you post. The feed is seven hundred people all feeling behind, in a room where nobody is.

Now make yourself better. Genuinely better: put your whole life a full step above everyone else's, which is better than 84 percent of people. On an ordinary day you are below 99 percent of the feed. Push it to two steps — roughly the top two percent of everyone alive — and you finally reach the middle of it: half the posts above you, half below. That is what it costs to feel average in a monthly highlight reel. The top two percent of the human race.

Run it the other way. Of your own days, how many would clear the typical post? At best-of-thirty, about one in forty-four. At best-of-a-year, one in five hundred. Those are the days you post. The other forty-three you spend looking at other people's one.

To feel average in a feed of monthly highlights you would need to be in the top two percent of lives. Most people are not, and the ones who are feel behind too.

The neighbours could not do this

Comparison is not new, and neither is its unfairness. Festinger wrote it down in 1954: where there is no objective yardstick, people measure themselves against other people, and they cannot easily stop. What is new is the sample. For most of history the comparison group was whoever you could see, and you saw them on ordinary days. The neighbours had their bad Tuesday in full view. Their car broke down in front of your house. The maximum was in there somewhere, but so was everything else, and the typical sighting of a neighbour sat, on average, exactly where your typical day did. In the model that is k = 1, and at k = 1 the gap is zero.

The Christmas letter was the first machine for raising k. One page a year, the year's best paragraph, from twenty families. Everybody knew to discount it. Nobody could have said by how much, and the answer is 2.9 steps: a best-of-365 day is nearly three standard deviations above the one you were having when the letter arrived. But twenty of them, once a year, was survivable. Then the letter became daily, the twenty became seven hundred, and a machine was placed between you and them whose one job is to decide which of the seven hundred maxima you see first.

Notice what the size of the feed does and does not do. Raising N from twenty to seven hundred does not move the typical post at all; a best-of-thirty day is a best-of-thirty day regardless of how many people are posting one. What it moves is the top. The best post in a feed of seven hundred monthly maxima is the best of twenty-one thousand days, and that sits four steps up — a one-in-thirty-thousand day. It happened to somebody, once, and it is the one your memory keeps, because the loud thing is never the common thing. You do not walk away from the feed comparing yourself with its median. You walk away comparing yourself with the one you remember.

The half you never see

So far the model assumes people post the best day and merely omit the rest. The evidence says the omission is not neutral. In four studies published in 2011, Alexander Jordan and colleagues found that people report their negative emotions as more private than their positive ones, underestimate how common ordinary bad experiences are among their peers, and overestimate the good ones — and that the error survives even for peers they know well, partly because those peers are suppressing the bad half. Lower estimates of other people's misery went with more loneliness, more rumination, and lower satisfaction with life. The paper's title is the finding: misery has more company than people think.

That was measured on people who could see each other in person. On the platforms the norm is explicit. A survey of twelve hundred Dutch users aged fifteen to twenty-five, published in 2018, found positive expressions rated more appropriate than negative ones on every platform tested, and the platform on which a bad day was least acceptable to post was Instagram. So k is not only the number of days between posts. It is also the number of bad ones that were never eligible.

And the belief lands where the arithmetic says it should. In a 2012 survey of 425 students at a state university in Utah, the longer people had used Facebook, the more they agreed that others were happier than they were and the less they agreed that life is fair; the more hours they spent on it each week, the more they agreed that others were happier and having better lives. It is a correlation on a questionnaire, and the authors say so. But it is the correlation the filter predicts, with the sign the filter predicts, and it is hard to see what else would produce it.

Nobody is watching, and there is arithmetic for that too

The comparison runs in both directions, and the return leg is where the money goes. A great deal of spending — the car, the watch, the restaurant chosen for the photograph — is a bet on an audience. The bet has been measured, once, with a T-shirt.

In 2000, Thomas Gilovich and colleagues had people walk into a room of strangers wearing a shirt with Barry Manilow's face on it, then leave and estimate how many in the room had noticed. The wearers said about 46 percent. The room said 23 percent. Half. They named it the spotlight effect, and it held with a flattering shirt as well as an embarrassing one: it is not shame that inflates the estimate. It is that you are the only person for whom you are the centre of the picture.

The general case needs no experiment, only bookkeeping. Attention is conserved. Everybody has one day of it and spends most of it on themselves; whatever is left is spread across everybody else they know. So the total attention that lands on you, from all seven hundred, is exactly the total you hand out to them — and the amount any one of them spends on you is what you spend on any one of them. You already know that number. It is the share of your day you spent thinking about the person in Lisbon, which was about four seconds, most of it envy.

How much of their day did they spend thinking about you? Exactly as much of yours as you spent thinking about them. You know that figure. It rounds to zero.

There is an old line: in your twenties you worry what everyone thinks of you, in your thirties you decide you do not care, and in your forties you realise nobody was thinking about you at all. The T-shirt study is that line with an error bar. The audience you have been dressing for is a quarter of a room, and the quarter that did notice had moved on before you reached the door.

And now you

None of this says the feed is evil or that you should live in a cave. It says the instrument is miscalibrated in a known direction by a known amount, which is a more useful thing to know than either. Calibrate for it.

Four ways this is wrong

People are not identical. The model gives everybody the same life, and lives differ. But that is the point rather than the flaw: the gap appears with zero difference, so the identical case is the floor of the effect, not an estimate of it. Add real differences and you get the honest version — the feed contains people who are genuinely doing better than you, and you cannot tell which ones from the posts, because a two-sigma day from an ordinary life and an ordinary day from a two-sigma life are the same photograph.

Days are not normal. The bell is a convenience. Real good days probably have a fatter right tail — the promotion, the birth, the round that closes — and the maximum of fat-tailed draws runs further from the middle than the maximum of normal ones, not less far. The normal assumption is the conservative one. If the truth is fat-tailed, every offset on this page is too small.

Not every post is a maximum. Plenty of people post their Tuesday. The dial handles that — k is not thirty for everyone, and at k = 1 the gap is zero, which is what the neighbours were. But the platforms select on the posters as well as the posts: the accounts that post ordinary days are the ones the machine shows you least, which quietly raises the k of what reaches you above the k of what was written.

The evidence is thinner than the arithmetic. The 46/23 figure is one experiment, in one lab, on students in 2000. The Facebook result is a questionnaire in Utah. The Dutch survey is about norms, not behaviour. The arithmetic does not depend on any of them; they are here because the arithmetic predicts a direction, and the direction has appeared every time anyone has looked. Nothing on this page says by how much you are miscalibrated. It says which way, and that a monthly feed of perfectly ordinary lives will produce a two-step gap out of nothing at all.

Seven hundred best days are not seven hundred better lives. Push the dials yourself in The Highlight Reel. The Cemetery is the same filter running over people instead of days — you hear from the survivors and the rest stay quiet — and The Unanimity Filter is what a filter does to a distribution when it keeps the middle instead of the top.