Power Sample Multiplier
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Power is the probability that a study correctly detects a real effect when one actually exists, commonly set at 80% or 90% as a target. Low power means a real effect could easily be missed, producing a false negative.

To reliably detect smaller and smaller differences from random noise, you need more data to reduce the uncertainty around your estimate; power and sample size trade off directly, so increasing one target (power) increases the other requirement (sample size) for a fixed effect size.

Smaller expected effects require dramatically larger sample sizes to detect reliably, since the signal-to-noise ratio is lower; a study looking for a subtle effect needs a much bigger multiplier applied to its base sample size than one expecting a strong, obvious effect.

An underpowered study has a meaningfully high chance of failing to detect a real effect (a Type II error) even when one exists, and any significant results it does find tend to overestimate the true effect size, a phenomenon known as the winner's curse.

It's a widely used convention rather than a strict law, chosen as a reasonable balance between resource cost and risk of missing a true effect. Some fields or high-stakes studies opt for 90% or higher when the cost of a false negative is severe.