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Equation 3 · Part 1 · A Showdown Ladder Rating Measures the Ladder, Not the Player

Symbol d^2

d2d^2
d2d^2

What this part means

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

Its job in the formula

d2d^2 is squared: multiply the underlying quantity by itself. The square is a mathematical operation, not a second independent variable.

Where the article explains it

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 ] .

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…

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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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See this notation across published equations →

Sources cited in the article section

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