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Research draft

ratio

vr.tr.ratio · XCT.REL

Let an agent state ratios with their numerator, denominator and units, and avoid confusing ratios with rates, proportions and percentages.

Thing Registry Cross-cutting context

Research draft, second pass

A second pass drafted this model: the structure a model of this thing needs, and what is known about it in the world. The line under this one says how the second half was obtained - researched against sources, or recalled without web access, in which case nothing here was read anywhere and every claim is a lead to verify. Unreviewed either way.

written by Claude from model knowledge without web access - no source was read, every claim is a lead to verify

Researched by: Claude

Purpose and description

Let an agent state ratios with their numerator, denominator and units, and avoid confusing ratios with rates, proportions and percentages.

A relationship between two quantities expressing how many times one contains the other, written as a:b or as a quotient.

What it is for: Comparing quantities, scaling recipes and designs, and expressing financial and technical measures.

It can be compute it, from two quantities; simplify or scale it; express it as a fraction, decimal or percentage; compare ratios, provided they are defined the same way.

Distinguishing features

Compares two quantities; the order matters

Dimensionless when both quantities have the same unit

A proportion compares a part to the whole; a ratio can compare any two quantities

Named ratios have definitions that differ between sources

What it looks like

Written as 3:1, 3/1, 3 to 1 or 0.75; financial and technical ratios have names such as debt ratio or factor of safety.

How it is recognised

A colon between numbers, or a named ratio

Aspect ratios, gear ratios and odds use the same notation

Percentages are ratios with denominator 100

Related models

is a kind of - a comparison of quantities

mathematical relation

is confused with - a rate compares quantities of different kinds, often over time

rate

is expressed as - a ratio scaled to 100

percentage

is used in - many named ratios

financial analysis

In practice

Families and kinds

part-to-part and part-to-whole ratios

financial ratios: debt ratio, profit margin

technical ratios: gear ratio, factor of safety, aspect ratio

health ratios: waist-to-height ratio

Standards and regulation

ISO 80000-1 on quantities of dimension one

Accounting standards and regulator definitions for financial ratios

Failure modes and hazards

Reversing numerator and denominator

Comparing ratios with different definitions

Dividing by a small or zero denominator

Also called

factor of safetywaist-to-height ratiofinancial ratioTenörqualification ratioprofit margindebt ratioleverage ratiosolvency ratioAccounting rate of returnInvested capitalRisk return ratioHome ownership rateBejan number for entropyBejan numberisopermNet interest marginnet profit marginmolar actiontransistor densitybit rategyromagnetic ratiomolar energyrotationcloud coverbit error ratevariable bitrateconstant bitratedownload speedCommitted Information Rateupload speedaverage bitratedata signaling rateswitching fabric bandwidthmolar quantitymolar ionization energyspin countViterbi error ratepacking densityratio of two quantities of the same kind

+105

Where this came from

wikidata · CC0 1.0

Source repository Registry entry point

Also registered as vr.tr.ratio

Drafted structure

Bundle to layer to finding to question, as the second pass will find it: 4 bundles · 8 layers · 8 findings · 16 questions.

Definition What is compared to what.

A ratio without its terms is uninterpretable.

Terms

Numerator and denominator.

Ratio terms

The two quantities and their order.

  1. Which quantity is compared to which? definition
  2. Are both in the same unit? measurement

Named ratio definition

Standard definitions.

Definition source

The source of the definition.

  1. Which definition of this named ratio is used, and from which source? provenance
  2. How does it differ from other common definitions? boundary
Calculation Computing and expressing.

How a ratio is computed and presented changes how it is read.

Computation

Data and method.

Computation

The data and period used.

  1. From which data and period is it computed? provenance
  2. What happens if the denominator is near zero? boundary

Expression

Fraction, decimal, percentage or a:b.

Presentation

How it is expressed.

  1. In which form is the ratio expressed? definition
  2. Could the form mislead readers? boundary
Comparison Comparing ratios.

Comparisons are only valid between ratios defined the same way.

Benchmarks

Typical values.

Benchmark values

Reference values and their source.

  1. What value is typical, and in which population? measurement
  2. Is the benchmark defined the same way? boundary

Trends

Change over time.

Trend analysis

How the ratio changed.

  1. How has the ratio changed over time? measurement
  2. Did the definition change during the series? provenance
Use Decisions based on ratios.

Ratios drive credit, safety and design decisions.

Decision rule

Thresholds.

Threshold used

The threshold and who set it.

  1. Which threshold applies to this ratio, and who set it? provenance
  2. What decision follows from crossing it? action

Limits

What the ratio hides.

Blind spots

What the ratio does not show.

  1. What does this ratio fail to capture? boundary
  2. Which other measures should accompany it? action

What the second pass must settle

  • Should named ratios be separate entries with formal definitions?
  • How should agents report the definition used for a financial ratio?
  • How should ratios with near-zero denominators be flagged?
Draft as JSON