I recently attended a conference where I didn’t know how many participants there were, but was too lazy to ask the organizers.
So instead I began thinking about how to estimate the number in interesting, preferably statistical, ways, which can be done by an ordinary attendee in their head or by trivial observation.
To keep the game amusing, I’ll impose 3 requirements: (1) we must do without requiring fancy measurements (eg. aerial footage, acoustic sound recordings, WiFi snooping/AP counting, social media analytics); (2) or methods with hopeless error bars (eg. feeling how hot a venue gets from body heat or CO2 levels); (3) or methods which estimate some other population (eg. just turns out to quantify our observation sample size, or a different population of people than physically present).
Here are some weird statistical approaches to estimating how many people are attending a convention:
Easiest:
wisdom of crowds: just ask random people what they think and average it.
Easy: Little’s law (“the long-term average effective arrival rate λ multiplied by the average time W that a customer spends in the system. Expressed algebraically the law is L = λ · W”, cf. Olber’s paradox):
Example: look at current room, count number of people, estimate how long on average they spend in it, multiply; sum over all known rooms. (This assumes convenient rooms. If that is not the case, one can sample in whatever unit is convenient, like a grid of square meters for a large hall.)
Little’s-law-like stock × flow estimates can be done in many ways:
Parking lot: if an event is primarily reached by cars, rather than housing on-site or public transit or rideshare, then Little’s law might apply here too.
Registration queues: as everyone may have to go through registration, and it can be a major bottleneck (requiring heavy optimization), this can be a good chokepoint to apply Little’s law to, by counting the number in line, and how long one is in line.
If bathrooms, elevators, cafeteria tables, or stairs are chokepoints, this may work for them too.
Management overhead: organizations and events often operate with a certain small overhead, eg. charity or Medicare overhead ratios. One could try to estimate from that. An example would be, estimating from the number of staff to the number of attendees.
(Checking, it seems like the ratio tends to be 1:50–100, so that is a simple multiplier once you estimate # of staff, and since staff are much fewer, they can be more easily counted than attendees, and many of the previous methods could be applied to just the staff.)
Economic gravitational model (eg. Reilly’s law of retail gravitation): Estimate conference size based on the “economic gravity” needed to justify the venue cost, speaker fees, rented A/V equipment like video cameras, and catering expenses you observe.
Intermediate:
Garbage index (Little’s law): watch a fixed group of people, like at a talk, to estimate what fraction have a coffee cup or packaged food item etc (eg. 1 person out of 10); look inside a trash can and count them; multiply by # of trash cans, and then by the fraction to get a total.
Difficult to sample reliably given that staff may be cleaning regularly.
Drink index: coffee/tea is often quoted by event-planning sources as being ~1–2 cups⧸person⧸session range (“Expect ~60% to drink hot beverage (coffee or tea) in the morning…Expect ~35% to drink hot and 65% cold beverages in the afternoon.” Sources: 1, 2, 3, 4, 5, 6)
So that is a simple rule: # of morning break coffees = # of attendees. If cups are unavailable, one can watch for coffee urn swaps, as the urn capacities are fairly standard.
This may apply to food in general: it would be risky to cater for <100% of attendees, so simply count food like pizza to extrapolate a headcount.
Swag exhaustion: Conferences provide items like tote bags, lanyards, or program books. These are usually stocked once at the beginning, and then run out.
So, guesstimate the total at the beginning, watch for a time to see what percentage of attendees take any, and see how much is left at the end.
Power-Up index: In the age of laptops and phones, power outlets are a critical, limited resource—it’s increasingly common to see phones abandoned at wall sockets charging, or crowding at USB hubs. Count the number of outlets and the number of people using them or waiting to use them.
This gives you a “pressure” metric. In a session room, do a quick scan of how many laptops are plugged in versus running on battery. A high ratio of plugged-in devices suggests a large population competing for scarce resources over a long conference duration.
Hard:
capture-recapture: count how many times you’ve seen each person; use one of the many estimators.
An example might be to walk a hallway twice, in the morning and afternoon. If you see 100 people each time, and 10 people twice, then you could use an estimator like the Lincoln index: (100 · 100) ⧸ 10 = 1,000 people total.
indirect capture-recapture: observe how often attendees hold doors for people or do not appear to introduce themselves to the other person (eg. a handshake almost always means a new encounter);
Birthday paradox: how many people do you meet with the same first name (eg. ‘Rachel’)?
With population statistics about first names (eg. US Census), you can infer the total conference size for which your subsample would yield n collisions.
Galaxy brain:
anthropic argument: estimate how many people like you would attend a conference like this, what % of your life you have spent attending conferences like this, and infer the necessary conference size if you were a random person-day.
Poincaré recurrence time: Assume people are gas particles in the venue’s “phase space.” Time how long it takes for the same person to randomly reappear near you (eg. “I saw that green hat twice!”). The average recurrence time T relates to total attendees N by:
Benford’s law: processes which ‘grow’ are often characterized by a Benford-like distribution; crowds or groups of people talking at a conference are clearly governed by preferential attachment processes—the larger the group, the more people who will get ‘stuck’ to it. It would be reasonable—although still highly speculative—to assume that they are described by Benford’s law.
So one can observe the largest group, and work backwards over the distribution, and infer the total, including the n = 1 groups, and thus the total population.
?:
Lost-and-found time-series: the count of items in the event lost-and-found might not be useful without big assumptions… but perhaps the variance over time / ebb-and-flow can give a good estimate?
For example, one could make an anthropic-Doomsday-style mediocrity principle argument that if one traveled x kilometers to attend, that x is the 50th percentile and attempt to infer from that.
Social density physics: people have been observed to act like particles in a gas.
Is there an equivalent of an ideal gas law which would let one take a total venue size (volume) and measure density (distance between people), and then back out the total number, similar to Little’s law?
Attention economy: Measure the “attention scarcity”—how difficult it is to get speaker attention, how long networking conversations last, how long people are willing to wait in a queue before abandoning it for another thing (see optimal foraging) etc. This reflects the competition for finite social resources.
If these scaling laws have not been measured before, they might be an interesting topic.