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

Symbol q^2

g(RD)=11+3q2RD2/π2,q=ln⁡10400≈0.0057565g(\mathrm{RD}) = \frac{1}{\sqrt{1 + 3q^2 \mathrm{RD}^2 / \pi^2}}, \qquad q = \frac{\ln 10}{400} \approx 0.0057565
q2q^2

What this part means

The square of q: multiply q by itself.

Its job in the formula

q2q^2 occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.

The passage around this formula

The mechanism is two coupled numbers, not one. A player’s rating R changes only from game outcomes; the rating deviation RD changes from game outcomes and from the simple passage of time — RD shrinks as a player competes and grows as a player sits idle, because “the more games played, the more information is learned about a player’s ability… as time passes, we become more uncertain about the player’s strength” [ 3 ] . The update equations, stated with Showdown’s own configured constants substituted in, are g(RD)=11+3q2RD2/π2,q=ln⁡10400≈0.0057565g(\mathrm{RD}) = \frac{1}{\sqrt{1 + 3q^2 \mathrm{RD}^2 / \pi^2}}, \qquad q = \frac{\ln 10}{400} \approx 0.0057565. 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…

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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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Sources cited in the surrounding passage

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