Equation 5 · Part 1 · A Showdown Ladder Rating Measures the Ladder, Not the Player

Symbol s_j

s_j \in \{0, 0.5, 1\}

s_j

What this part means

$s_j$ 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

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

Full expressionSymbol s_jArticle meaning

The passage around this formula

where $d^2$ is a variance term built from the same g( $\mathrm{RD}_j$ ) and expected-score factors, $s_j$ $\in$ \{0, 0.5, 1\} is the outcome of game j , and between rating periods the deviation itself grows on a fixed schedule, $\mathrm{RD}_{\text{new period}}$ = $\sqrt{\mathrm{RD}_{\text{old}}^2 + c^2}$ , clamped to Showdown’s own configured ceiling of 130 rather than Glickman’s generic default ceiling…

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A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

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