Equation 25 · A Showdown Ladder Rating Measures the Ladder, Not the Player
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Symbol R
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Everything derived above about RD is a reliability result. RD tells a player, correctly, how much noise sits around their current R given how much and how recently they have played. It says nothing about whether R itself is estimating a portable trait called “skill at this game” that would produce the same number if the same player sat down against the same population under different competitive conditions. That second question is a validity question, and Cronbach and Meehl are explicit that answering it requires checking the score against a “nomological network” of related claims it should also satisfy, not just re-measuring it and finding the repeat measurement close to the first one [ 5 ]…
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Everything derived above about RD is a reliability result. RD tells a player, correctly, how much noise sits around their current R given how much and how recently they have played. It says nothing about whether R itself is estimating a portable trait called “skill at this game” that would produce the same number if the same player sat down against the same population under different competitive conditions. That second question is a validity question, and Cronbach and Meehl are explicit that answering it requires checking the score against a “nomological network” of related claims it should also satisfy, not just re-measuring it and finding the repeat measurement close to the first one [ 5 ] . Showdown’s documentation, exhaustive as it is about K-factors and system constants, makes no validity claim at all — it specifies an algorithm, not a psychological construct, and the leap from “this algorithm converges reliably” to “this algorithm measures a stable trait called skill” is a leap Showdown’s own page never asks a reader to make. Competitive players make it anyway, every time a GXE screenshot stands in for an argument about who the better player is.
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