I want to show you an experiment that will make you distrust every confident forecast you hear.

The Setup

Researchers ask educated subjects to provide a range. The instruction: "Give me a low estimate and a high estimate such that you are 98% confident the true answer falls somewhere between them."

The question might be: "What is the distance from Earth to the Moon in miles?" Or: "What is the weight of a Boeing 747?" Or: "How long is the Nile River?"

You have to commit to a range where you are willing to say, with 98% certainty, that the true answer lives inside it. For a perfectly calibrated person—someone whose subjective confidence matches their actual accuracy—the true answer would fall outside their range only 2% of the time.

What Actually Happens

The true answer falls outside the range approximately 15% to 30% of the time.

In other words: people's stated 98% confidence corresponds to roughly 70–85% actual accuracy.

This gap—between the confidence people feel and the accuracy they achieve—is enormous. It is systematic. It persists across different questions, different populations, and different expert levels. Even after researchers teach people about the bias and show them their own data, subjects barely improve.

What's most striking is that the pattern does not improve with training or expertise. Educated subjects do not perform better than less educated subjects. Experts do not perform better than novices. In fact, experts often perform worse, because expertise inflates confidence without improving accuracy, especially at the extremes.

Why Your Narrow Range Is Overconfident

You intuitively know that uncertainty exists. You know the future is unpredictable. But when I ask you for your "98% confident" range, something in your mind reaches for precision.

The range that feels right is usually too narrow.

If you say "oil will be between $70 and $90 per barrel next year, 98% confident," your subjective feeling might be that this range captures almost all plausible scenarios. It probably captures 70%.

The reason is that you are not accounting for what you don't know. You are not accounting for what could change that you haven't conceived of. You are anchoring on recent history and recent experience and treating that as the boundary of plausibility.

But the actual world is wider and more contingent than your model permits. A war. A pandemic. A technological disruption. A policy shock. A financial event. A supplier failure. A regulatory change.

Your 98% range, in the moment it felt right, was actually a 70% range. The wide, uncomfortable range would have been right.

The Two-Percent Rule That Actually Works

Here's what decades of calibration research concludes: whatever range feels like your 98% confidence interval, double the width.

You will still be overconfident, but you will be far less dangerously so.

If your instinct says "2–3% growth," report "0.5–4.5% growth." If your instinct says "$70–$90 oil," report "$40–$140 oil." If your instinct says "90–110 IQ points," report "50–150 IQ points."

The doubled range looks humiliatingly uncertain. It looks like you don't know anything. That feeling of embarrassment is information telling you that the actual world is humiliatingly uncertain, and your narrow range was a comfortable fiction.

The doubled range is still probably overconfident. But it's in the ballpark of realistic.

Why This Matters Beyond Statistics

This is not a technical problem that only affects academics. This is the mechanism behind real-world catastrophes.

A bank uses a risk model that produces narrow confidence intervals around "value-at-risk." The model says there is a 1% chance of losses exceeding a certain amount. In reality, given the gap between subjective and actual calibration, there is probably a 10–20% chance. The bank positions itself accordingly—with vastly insufficient capital. When the tail event arrives, the bank fails.

A company forecasts sales for next year. The finance department produces a narrow range. Half-consciously, everyone in the organization treats that range as the distribution of plausible outcomes. It's actually half the width of reality. When actual sales fall outside the narrow range, the organization is caught flat-footed.

A surgeon tells a patient "95% of people survive this procedure." The surgeon believes this with high confidence based on personal experience. The actual historical survival rate is 85%. The patient makes a decision based on the overconfident number.

The gap between confidence and accuracy is not just a statistics problem. It's a decision problem. Every decision made by an overconfident forecaster is a decision made on false information.

The Wider Range as an Admission of Reality

The psychologically hardest part of this is accepting that the wide range is not a failure of your knowledge. It is an accurate representation of your knowledge.

You know more than a complete ignorant person. Your wide range reflects genuine expertise. A surgeon's 40–90% survival rate is still much more useful than a layperson's "I dunno, 50–50?" The surgeon's range, though wide, is genuinely constrained by knowledge of the procedure, patient factors, comorbidities, and hospital quality.

But the surgeon's initial instinct—95% confidence—was an underestimate of uncertainty, not a true estimate.

This is the key insight: your narrow range does not reflect confidence. It reflects overconfidence. Your wide range reflects something closer to truth.

Once you accept that, the wide range stops feeling like a failure and starts feeling like intellectual honesty.