Why emergency wait estimates should under-promise: the 70th-percentile finding

It seems obvious that telling people how long they will wait should make waiting easier. The evidence says it is not that simple. In a randomized trial of 1,011 patients in an emergency department fast track, adding process information and wait estimates had no effect on satisfaction; what did matter was the actual time in the waiting room, with each extra 10 minutes cutting the odds of a "very good" rating by 8%.^[1] Two more randomized trials that gave patients an estimated wait found no difference in satisfaction either.^[2][3]

Yet patients clearly want the information. In a needs assessment, 90% of patients wanted wait times shown in the waiting room and 77% said it would improve their experience.^[4] In one of the null trials, 70% of patients still preferred having an estimate.^[2] So the question is not whether to give an estimate, but what kind.

David Maister's classic analysis of waiting lines explains why. Uncertain waits feel longer than known, finite waits; unexplained waits feel longer than explained ones; and anxiety makes any wait feel longer.^[5] He also describes what could be called appointment syndrome: once a promised time passes, even a short extra wait becomes very irritating.

An estimate at the median is, by definition, wrong in the unpleasant direction for half of the people who read it. Each of them watches the promised time pass, and the wait that follows feels longer than if no number had been given.

The same study points at the active ingredient. In a before-and-after study of 1,209 patients, those who were told about delays rated their care better on every item.^[6] The explanation, not the number, moved the ratings.

A field experiment that showed emergency patients machine-predicted waits at different percentiles found a clear pattern: estimates at the median (p50) had no effect, estimates at the 70th percentile raised satisfaction the most, and estimates at the 90th percentile helped less.^[7] The authors explain it with loss aversion: waiting longer than announced hurts more than waiting less than announced helps.

There is a limit to how far to lean. In a scenario experiment with 303 participants, satisfaction peaked when the estimate matched the actual wait; errors of about 10 minutes were still better than no information, and errors of about 20 minutes were not.^[8] Under-promise a little, not a lot.

In EDFlow, each estimate has three parts, always in this order:

1. A usual range, for example "Usually 40 min to 1 h": roughly the middle half to three quarters of past visits for the same step, rounded up to 5 minutes.
2. The "most people" line, for example "Most people (9 in 10) are done within about 1 h 30 min. Sometimes it takes longer." This is the 90th percentile, deliberately not called "at the longest", because it isn't.
3. The basis, for example "Based on past Tuesdays around 7 p.m. at this hospital." The patient can see that the number is local, recent and specific to the hour.

Once a step passes the 90th percentile, the numbers are replaced with plain words: "This is taking longer than usual. If you haven't heard from anyone recently, please check with a nurse." The screen never claims the team knows, and never implies the patient did something wrong.

When there isn't enough history for a step at that hour, the estimate falls back to a reviewed default and says so, or is hidden. A wrong number is worse than none.

Canada's emergency physicians recommend medians for public reporting because lay readers understand them best, and warn that averages mislead in skewed data like emergency waits.^[9] That is why patient copy never says "average". It is also why the estimate is a range, not a point.

Estimates carry a real risk: in the same needs assessment, 19% of patients said they would be more likely to leave without being seen if they saw a long wait.^[4] Before a physician has seen them, patients see ranges together with the reason ("the sickest people are seen first"), and a "Thinking of leaving?" request asks them to talk to a nurse before they go. Left-without-being-seen rates are watched as a safety measure throughout a pilot.

Finally, calibration: a department can only ask patients to trust its estimates if it checks them. The target is simple: at least 9 in 10 visits should finish a step within the "most people" time. If they don't, the estimate is wrong and the history behind it needs attention.