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Equation 20 · Part 3 · A Showdown Ladder Rating Measures the Ladder, Not the Player

subscript

SDX1−reliability\mathrm{SD}_X\sqrt{1-\text{reliability}}
subscript

What this part means

The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.

Its job in the formula

A subscript distinguishes a version, component, step, or member of a quantity. It does not automatically mean multiplication.

The passage around this formula

Glickman’s RD is this same object, derived from a different starting assumption but converging on an identical use. He states the correspondence in his own words, not as an analogy this article is imposing on his work: a Glicko rating and RD together are “usually more informative to summarize a player’s strength in the form of an interval… report a 95% confidence interval. The lowest value in the interval is the player’s rating minus twice the RD, and the highest value is the player’s rating plus twice the RD” [ 3 ] . Line up the two constructions and the correspondence is not loose: SDX1−reliability\mathrm{SD}_X\sqrt{1-\text{reliability}}. This is the article’s original contribution: not the observation that a rating has…

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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.

Open the illustrated subscripts: which member of a family? guide →

Sources cited in the surrounding passage

These citations provide research context; check each source for the exact claim it supports.