Adams, Ian T.

Methodological Analysis

The Denominator Problem
Why Benchmark Choice Matters

Your choice of denominator can completely change—even reverse—conclusions about racial disparities in police use of force.

Based on Tregle, Nix & Alpert (2018)

Select Year:

What's Your Denominator?

In 2015, police fatally shot 259 Black citizens and 497 White citizens.

Black citizens are ~13% of the US population but ~26% of those fatally shot. Does this prove racial bias? It depends entirely on your choice of benchmark.

The Hidden Denominator

When analyzing rates, we need both a numerator (what happened) and a denominator (the at-risk population). The denominator is like the hidden part of an iceberg—often unseen, but critical.

✓Numerator: Fatal OIS by race (known from Washington Post data)
?Denominator: Who is at risk of being shot? (debated)

The Formula

[Black Shot ÷ Black Benchmark]

[White Shot ÷ White Benchmark]

Rate Ratio: >1 means Black more likely, <1 means White more likely

Why Population is a Flawed Benchmark

Using population assumes everyone has an equal chance of encountering police. This is demonstrably false:

• Black citizens are more likely to be stopped by police
• Black citizens are more likely to be arrested
• Most people (of any race) never have police encounters that could turn lethal
• The "at-risk" population is not the general population

Using Population (2015)

3.04x

Black citizens more likely

Using Weapons Arrests (2015)

1.33x

White citizens more likely

Same numerator. Different denominators. Opposite conclusions.

Benchmark	Black Benchmark	White Benchmark	Rate Ratio	Interpretation
Total Population	39,908,095	232,943,055	3.04	Black 3.0x more likely
Police-Initiated Contacts	2,542,400	16,642,200	3.41	Black 3.4x more likely
Traffic Stops	2,001,000	13,997,700	3.65	Black 3.6x more likely
Street Stops	541,400	2,644,500	2.55	Black 2.5x more likely
Total Arrests	2,197,140	5,753,212	1.36	Black 1.4x more likely
Violent Crime Arrests	140,543	232,180	0.86	White 1.2x more likely
Weapons Offense Arrests	44,284	63,967	0.75	White 1.3x more likely

The Denominator Problem
Why Benchmark Choice Matters

What's Your Denominator?

The Hidden Denominator

The Formula

Why Population is a Flawed Benchmark

Rate Ratios by Benchmark (2015)

Detailed Comparison (2015)

Population-Based

Interaction-Based

Arrest-Based

Select a Benchmark

Total Population

Limitation

Result

Calculation:

Rate Comparison (Population)

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Input Values

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Your Result

Key Takeaways