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Equation 5 · Futures Methods and Technological Scenarios in Practice: An Advanced Technical Guide

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log⁡(p)\log(p)

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pp

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The logarithmic score , used by Metaculus, is log⁡(p)\log(p) if the event occurs and log⁡(1−p)\log(1-p) if it does not. This is a platform claim and design note , not independent research: Metaculus documents that the log score is far more punitive of confident misses than the Brier score is rewarding of confident hits — moving from 99 percent to 99.9 percent gains almost nothing if correct but costs roughly 2.3 points if wrong [ 7 ] . That asymmetry is deliberate: it is what makes the rule “strictly proper” in Gneiting and Raftery’s sense, because it punishes the temptation to round an honest 90 percent up to a persuasive-sounding 99 percent.

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