Equation 2 · Part 1 · A Showdown Ladder Rating Measures the Ladder, Not the Player

Symbol r

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

What this part means

r occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.

Its job in the formula

r occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.

Full expressionSymbol rArticle 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…

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Learn the underlying idea

A variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.

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