An illustration of various animals partying
Tom Bingham

A Mathematical Formula for the Right Time to Show Up at a Party

We made an interactive calculator—with help from a mathematician—that bypasses the confusion about what “fashionably late” means and tells you definitively when to arrive.

My role at parties is, unfortunately, to be the one who shows up way before everyone else. Even when I actively try to show up later, to seem more like a normal human, I still somehow end up among the first to walk in the door.

I was generally spared this fate earlier in the pandemic, when many parties became dangerous and I had far fewer to attend. Now that parties are back for many people, so is the timeless question of when you should show up. Because if you arrive at the stated start time, chances are that, like me, you’ll be the first one there.

The optimal arrival time accounts for several different, sometimes competing considerations: If you’re the first one there, it can be a little awkward (trust me), and the host might not be quite ready. If you show up long after everyone else, you might miss the best parts or risk rudeness. Most likely, you want to arrive just as the party’s gaining real momentum, a Goldilocks window of time that’s neither early nor late.

When we go to a party, we all run our own little calculations (consciously or not) to try to identify this golden moment. For instance, my friend Sam Brodey, a political reporter in Washington, D.C., has a “38-minute rule”: For low-key parties with friends and food, he typically likes to show up 38 minutes after the stated start time. “30 minutes would [be] too early, and 45 too late,” he explained. (For a larger, rowdier house party, he shoots for an hour after the start time.)

I like the simplicity of the 38-minute rule, but for help with some more complicated arrival-time calculus, I reached out to someone with a deep understanding of, well, calculus: Daniel Biss, a mathematician who appreciates how quantification can veer into absurdity. Years ago, when a friend of his, the novelist John Green, wanted to have a precocious character in one of his books develop a formula for predicting the outcome of a romantic relationship, Biss drew up a delightfully complex one with variables such as the “Dumper/Dumpee differential.” It appears in the book An Abundance of Katherines and produces results that can be plotted on a graph.

Biss, a former math professor at the University of Chicago (and the current mayor of Evanston, Illinois), accepted my request to make a similarly preposterous formula for calculating the perfect time to arrive at a party. The result, which you can see—and plug your own numbers into—below, accounts for how punctual your friends are, how early or late you prefer to be, how excited you are about the party, and how accurately you tend to predict the time you’ll get there.

The formula then spits out how many minutes after the party’s start time you should aim to arrive. It’s math, so it can’t be wrong.

Okay, so maybe a formula like this is a little silly. Although Biss doesn’t plan to use it himself anytime soon, he did say that writing it was instructive; listing out possible arrival-time considerations prompted him to think about whether his own arrival times line up with what he wants to get out of parties. “If you don’t think carefully about all the different factors, then you might wind up … showing up five minutes after the person who you really wanted to spend time with left,” he said.

The fact that people typically don’t show up to parties all at the same time is so standard in American culture that it seems perfectly normal. But if you really think about it, it’s also a bit curious in a society where meetings and appointments tend to have stricter start times. How and why did we collectively decide that, at parties, a start time is usually only a rough suggestion?

Part of it has to do with a fundamental tension between what’s called “clock time”—as in the numbers on a clock—and “event time,” a more fluid framework that follows our social rhythms, in which “activities are allowed to transpire according to their own spontaneous schedule,” as the late social psychologist Robert Levine wrote.

The precision of clock time governs much of our daily comings and goings, but at parties, we get a break from it and relax into event time. “Parties are supposed to be conceptual and experiential opposites of business meetings or classes,” Kevin Birth, an anthropologist at Queens College, City University of New York, told me. “Part of this contrast is that the start time of parties is not supposed to be serious.”

On top of that, unlike many other events, parties don’t feel like they start at a single, clearly delineated moment—there’s no starting gun or curtain-raising. “The real party doesn’t begin until the number of guests … crosses a certain threshold—hard to define, sometimes difficult to identify,” David Henkin, a historian at UC Berkeley who has studied timekeeping, wrote to me in an email. Perhaps parties’ “porous boundaries,” he suggested, naturally lead to staggered arrivals.

This laxity has its limits, though. Even if a party’s start time is not taken literally, guests would be lost if the host didn’t provide one at all—such is the dominance of clock time.

Of course, societies had ways of coordinating activities before everyone had timepieces. Many people used to tell time by public bells that rang from churches or town halls. Anthony Aveni, an emeritus professor of anthropology and astronomy at Colgate University, told me that several hundred years ago, in Munich, Germany, an intricate system of bells that rang in different tones and sequences communicated to different groups of workers in the garment industry—cutters, dyers, and so on—when they each needed to report to work.

This got me thinking ahead to the next party I’ll host. Because nobody comes at the stated start time anyway, I started wondering whether there are any nonclock reference points I could give to my guests and have any hope that, like those cutters and dyers, they’d show up at a similar time.

Public bells aren’t really an option anymore, but the experts I interviewed mentioned some rudimentary cues that would probably work well enough: I could tell people to come over right after work, after dark, or perhaps after they put their kids to bed. Their other suggestions were more poetic. Birth, for instance, said I could notify my guests that the party would begin “after the evening primroses bloom.” He also mentioned that in the area where he did his doctoral research in Trinidad, flocks of parrots would fly home to their roosts at a similar time each evening, which could perhaps serve as a prompt to leave for a party, at least if you live somewhere with a local parrot population.

Aveni also went in a floral direction—he said my party could start when nearby sunflowers faced a certain way—but my favorite idea of his was more interactive. “I’d give everybody a stick 12 inches long,” he said, “and I’d tell them, ‘Go out into your backyard, find a flat place, put the stick in the ground, and when [its shadow] reaches a certain point—maybe when it’s three feet from the base—that’s when I want you to come.”

So if you ever get a stick in the mail from me, you know you're in for a good time.