The 85% Rule for Goal Difficulty: What Wilson et al. Showed

In 2019, Robert Wilson, Amitai Shenhav, Mark Straccia and Jonathan Cohen published a paper in Nature Communications (volume 10, article 4646) with a title that states its own result: “The Eighty Five Percent Rule for optimal learning.” Its claim is that a learner improves fastest when it gets about 85% of its training trials right, an error rate of 15.87%. Whether that number governs human goals is a separate question, and the paper does not answer it.

What did the paper actually show?

The authors worked in a narrow setting. The task is binary classification: the learner sees a stimulus and picks one of two answers. The learner improves by gradient descent, meaning it nudges its internal parameters after each trial to reduce error. Difficulty is a dial the experimenter can turn, for instance by making two stimuli harder to tell apart.

Given those assumptions, they derived the error rate that makes the learning signal, and so the speed of improvement, as large as possible. With Gaussian noise the answer is 15.87%, the standard normal distribution’s value at minus one. Too-easy tasks leave little to learn from, and too-hard tasks give almost no consistent signal, so the best rate sits between them.

They then checked the prediction against two kinds of learners: artificial neural networks trained on classification problems, and a model of perceptual learning meant to represent how animals learn. They also reported that existing animal-learning data was consistent with the 85% figure. That is the evidence base, and it is machines and animals in simple discrimination tasks.

What does it not show?

It does not show that humans pursuing goals learn fastest at 85%. Nobody in the paper’s data was setting a savings target or a gym schedule. The limits, itemized:

• One task type. Binary classification, with a clear right and wrong answer on every trial. Most goals have no such trial structure.
• One learning rule. Gradient-descent-style updating. Humans also learn by instruction, imitation, and insight, none of which is modeled.
• One noise model. The 15.87% depends on the Gaussian assumption. Change it and the optimum moves.
• One outcome. The quantity maximized is learning speed. Motivation, enjoyment and persistence are not in the objective.

Applying 85% to a personal goal is an extrapolation. It may be a useful one, but it is a hypothesis about people that this paper motivates and does not test.

How does it relate to Csikszentmihalyi’s flow channel?

Csikszentmihalyi’s flow model, developed in the 1970s and popularized in Flow (1990), plots challenge against skill. When challenge far exceeds skill, people report anxiety. When skill far exceeds challenge, they report boredom. The band between, where the two are roughly matched and both are high, is the flow channel.

The two ideas share a shape: a middle band between too easy and too hard. They differ in what they claim. The flow channel is a description of experience, built largely from self-reports. The 85% rule is a quantitative prediction about learning speed in a formal model, with a specific number attached. A person can be in flow at 60% accuracy, and a network can learn fastest at 85% without anything like an experience of absorption. Treating them as one finding lets the precision of the second borrow credibility it has not earned in the first domain.

Where does James Clear’s Goldilocks Rule fit?

Atomic Habits (2018) calls it the Goldilocks Rule: people stay motivated on tasks at the edge of their current ability, and Clear ties this to flow, commonly summarized as a task roughly 4% harder than what you can do now. Two points on precision. The 4% figure is repeated in flow-research popularizations that attribute it to Csikszentmihalyi and Steven Kotler, and it appears without a primary experiment attached, so read it as a rule of thumb. And because the book appeared a year before Wilson et al., it cannot have cited them; the 85% rule and the Goldilocks Rule arrived at similar-sounding advice independently.

The advice is also not identical. A task 4% beyond your ability does not translate into a stated success rate, so the two cannot be compared as figures. Both say: avoid the extremes.

How would you use 85% on a new wake time?

Treat each morning as one binary trial: you were up by the target time, or you were not. That matches the structure the paper studied better than most goals do, which is why it is a reasonable place to try the idea, still as an experiment and not as a proven rule.

A worked example. Your current average wake time is 7:15 and you want 6:30. Three steps.

1. Move the alarm 15 minutes earlier, to 7:00. Hold it for 14 mornings.
2. Log hit or miss each evening. A hit means out of bed and upright by the target.
3. On day 14, compute hits divided by 14 and read the table.

Hits in 14 mornings	Hit rate	What to do
14	100%	Too easy. Shift another 15 minutes now, or 30 if this was your second easy step in a row.
13	93%	Slightly easy. Shift 15 minutes.
12	86%	Target zone. Hold for another week to confirm, or shift 15 minutes if the misses were oversleeps you can’t explain.
11	79%	Near the zone. Hold the time and look at what caused the 3 misses (bedtime, alcohol, travel).
10	71%	Too hard for now. Return to the previous time for a week, then try a 10-minute step.
9 or fewer	64% or lower	Step back a full 15 minutes and fix bedtime before shifting again.

At 15 minutes a step, the trip from 7:15 to 6:30 is three steps, about six weeks if you hold each for two weeks and never step back. That is slower than most advice recommends, and the pace is the point of the exercise.

The table has a limit that belongs beside it. The cutoffs come from the paper’s optimum, rounded to what 14 trials can resolve, and nothing here has been validated for human wake times. A 79% and an 86% fortnight are within noise of each other. If the table gives you a different answer than your own sense of how the fortnight went, trust the sense and log another fourteen days.

For a fixed-time log kept for a month, see the first-person accounts in a 28-day same-wake-time experiment. For why the plan you make the night before tends to overestimate the person who has to carry it out, see why night-you can’t predict morning-you. And a target that gets a visible tally as you hit it can feel closer than it is, a bias covered in the endowed progress effect.

Where does an app fit?

If you want the miss rate to be honest, you need some way to know a miss was a miss. DontSnooze asks for a 30-second video when the alarm fires and sends a random camera-roll photo to your chosen friends if you skip it (see how it works). That produces a clean hit-or-miss record, which is what the table needs. It does not choose your step size, and it will not tell you 85% is the right target.

The sober summary is that a well-derived number from machines and animals has made its way onto posters about human ambition. Fourteen logged mornings will tell you more about your own optimum than the poster will.