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Equation 3 · Part 2 · A Showdown Ladder Rating Measures the Ladder, Not the Player

superscript

d2d^2
superscript

What this part means

A raised number can be a power. When it is a label or bound, it selects a case or the upper limit of a sum; the formula’s structure distinguishes these uses.

Its job in the formula

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The passage around this formula

where d2d^2 is a variance term built from the same g(RDj\mathrm{RD}_j) and expected-score factors, sjs_j ∈\in \{0, 0.5, 1\} is the outcome of game j , and between rating periods the deviation itself grows on a fixed schedule, RDnew period\mathrm{RD}_{\text{new period}} = RDold2+c2\sqrt{\mathrm{RD}_{\text{old}}^2 + c^2} , clamped to Showdown’s own configured ceiling of 130 rather than Glickman’s generic default ceiling of 350 [ 2 , 3 ] . Substitute Showdown’s published c = 6.6775026092 and the schedule is fully determined: it is not a metaphorical “uncertainty,” it is a specific number computed the same way every 24 hours for every account on the ladder. A brand-new Showdown account starts at RD = 130 — already at the…

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Learn the underlying idea

An exponent tells how a base is used in multiplication. In x³, x is the base and 3 is the exponent: x³ = x × x × x.

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Sources cited in the article section

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