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Equation 5 · Part 1 · Futures Methods and Technological Scenarios in Practice: An Advanced Technical Guide

Symbol p

log⁡(p)\log(p)
pp

What this part means

p is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

Its job in the formula

p is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

The passage around this formula

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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A variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.

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Sources cited in the surrounding passage

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