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

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d2d^2

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a variance term built from the same g(RDj\mathrm{RD}_j) and expected-score factors, sjs_j ∈\in \{0, 0. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.

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d2d^2

Symbol d^2

a variance term built from the same g(RDj\mathrm{RD}_j) and expected-score factors, sjs_j ∈\in \{0, 0.

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superscript

superscript

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.

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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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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 top of Showdown’s own configured uncertainty range, since that range tops out exactly where the starting value sits — which is the algorithm’s honest way of stating that it knows nothing about a new player yet, before either the player or their opponents log a single result.

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