Equation 2 · Part 10 · A Showdown Ladder Rating Measures the Ladder, Not the Player

Symbol r_j

r' = r + \frac{q}{1/\mathrm{RD}^2 + 1/d^2} \sum_{j=1}^{m} g(\mathrm{RD}_j)\left(s_j - E(s \mid r, r_j, \mathrm{RD}_j)\right)

r_j

What this part means

$r_j$ is one of the signed contributions combined to compute the quantity on the left.

Its job in the formula

$r_j$ is one of the signed contributions combined to compute the quantity on the left.

Full expressionSymbol r_jArticle meaning

The passage around this formula

1 , q = 400 ln 10 ≈ 0.0057565 r' = r + $\frac{q}{1/\mathrm{RD}^2 + 1/d^2}$ $\sum_{j=1}^{m}$ g( $\mathrm{RD}_j$ ) $\left(s_j - E(s \mid r, r_j, \mathrm{RD}_j)\right)$ 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, $\mathrm{RD}_{\text{new period}}$ =…

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Learn the underlying idea

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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