Equation 4 · Part 1 · A Showdown Ladder Rating Measures the Ladder, Not the Player

Symbol g

g(\mathrm{RD}_j)

g

What this part means

g 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

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

Full expressionSymbol gArticle 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…

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A function assigns an output to each allowed input. The expression f(x) means “apply f to x”.

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