Williams %R

A bounded technical-analysis oscillator locating the latest close within the recent high–low range, conventionally scaled from zero to minus one hundred.

Version

v1 · 2026-09-08 · History

Domain-specific #

7491

Origin domain

financial technical analysis

Subdomain

momentum oscillators

Core Idea

Williams %R measures how near the current close is to the highest versus lowest price observed over a selected recent window. Subtracting close from the window high and dividing by total high–low range normalizes price location, with values near zero at the high and near minus one hundred at the low. The abstraction is therefore identified by a declared carrier, a transformation or constraint over that carrier, and an invariant that tells an analyst whether the named structure is genuinely present.

Scope of Application

Williams %R belongs to financial technical analysis and is useful where the analyst can specify a price series, lookback period N, latest closing price, highest high and lowest low in the window, ratio and negative percentage scale, threshold conventions and missing or flat-range cases, then evaluate lookback, high, low, close and sign convention follow one formula and a zero-width range is handled explicitly. The scope is broad within that domain but bounded by the need for lookback, high, low, close and sign convention follow one formula and a zero-width range is handled explicitly. This is a descriptive financial indicator identity, not investment advice or a trading recommendation.

Clarity

The abstraction clarifies a crowded vocabulary by making lookback, high, low, close and sign convention follow one formula and a zero-width range is handled explicitly the center of the account. A claim should name the carrier, the governing operation or relation, the applicable assumptions, and the recognition test. A bare label is insufficient because the name Williams %R can be used for a formal identity, an implementation, or a neighboring result unless carrier and convention are stated.

Manages Complexity

Without the abstraction, an analyst must reason directly over many local details: the carrier roles, admissibility assumptions, competing conventions, derived invariants, boundary cases, and proof or validation obligations specific to Williams %R. Williams %R compresses them into the roles in the structural signature. That compression permits comparison across instances without erasing the variables that determine validity. It also exposes which details may be varied safely and which are constitutive.

Abstract Reasoning

1. Identify the carrier. State what the elements, states, objects, or observations are: a price series, lookback period N, latest closing price, highest high and lowest low in the window, ratio and negative percentage scale, threshold conventions and missing or flat-range cases. Reject examples whose alleged carrier belongs to a different problem. 2. Lock the constitutive rule. Express lookback, high, low, close and sign convention follow one formula and a zero-width range is handled explicitly independently of one notation or implementation.

Knowledge Transfer

Knowledge transfers strongly among subfields of financial technical analysis because they reuse a price series, lookback period N, latest closing price, highest high and lowest low in the window, ratio and negative percentage scale, threshold conventions and missing or flat-range cases, Subtracting close from the window high and dividing by total high–low range normalizes price location, with values near zero at the high and near minus one hundred at the low., and type the carrier, state every parameter and convention in the definition, test that lookback, high, low, close and sign convention follow one formula and a zero-width range is handled explicitly, compare the nearest accepted identity, and report counterexamples, uncertainty, and limiting cases.

Relationships to Other Abstractions

Current abstraction Williams %R Domain-specific

Parents (1) — more general patterns this builds on

• Williams %R is a kind of Measurement Prime

  The proposed strict upward parent is prime:measurement.

Hierarchy path (1) — routes to 1 parentless root

• Williams %R → Measurement

Neighborhood in Abstraction Space

Williams %R sits in a moderately populated region (55^th percentile for distinctiveness): it has near-neighbors but no dense thicket of look-alikes.

Family — Financial Risk & Market Indicators (29 abstractions)

Nearest neighbors

• Technical analysis — 0.90
• Risk return ratio — 0.89
• True strength index — 0.89
• Making-up price — 0.87
• Buffett indicator — 0.86

Computed from structural-signature embeddings · 2026-09-08