Splitting an audience

Moonbrush research note 4

Version

1.0

Published

October 20, 2026

Checked against the product

October 19, 2026

Authors

Moonbrush

Keywordsmarket segmentation; segment criteria; small-sample variability; law of small numbers; base rates; disparate impact

Abstract

stage splits an audience into roughly three to eight mutually exclusive audience groups by the behaviors that most separate them. This note sets out the segmentation research behind that step, and the research that bears on three of the rules the engine follows.

Segmentation has been a recognized marketing strategy since the 1950s, and the standard methodological reference gives six criteria a useful segment should meet. Each maps to a card field or a product rule. The rule that a behavior is called out only when it clears both a ratio and an absolute gap against the audience is consistent with the variability of small samples: a seeded simulation in this note shows groups with no real difference clearing a twofold ratio by chance at small sizes and never at large ones. The rule that demographics describe a group but never count as evidence that it fits is consistent with research on how data-driven decisions can reproduce discrimination. The note states what the engine’s method does not publish.

1. Introduction

An audience is rarely one kind of person. Dividing it into groups that differ in what moves them, and writing to each, is one of the oldest ideas in marketing. The scientific questions are which divisions are worth making, and how to tell a real difference between groups from one produced by chance.

2. Segmentation and what makes a good segment

Segmentation was set out as an alternative to treating a market as one mass, in which a product and its marketing are adjusted to the differing wants of distinct groups (Smith, 1956). The standard methodological text gives six criteria for segments that are worth acting on: identifiability, substantiality, accessibility, stability, responsiveness and actionability (Wedel and Kamakura, 2000).

Table 1. The six criteria, and the card field or product rule each corresponds to.

Criterion	What it asks	Where it shows
Identifiable	Can the segment be recognized and measured?	Lead behavior and evidence: the departures from the audience the group was built on
Substantial	Is it large enough to be worth acting on?	Size and share of the audience
Accessible	Can it be reached?	Product rule: groups are packaged as hashed identifiers for delivery; parked groups are left out
Stable	Does it hold still?	Product rule: the framing is fixed on the run, so a re-run on the same audience gives the same groups
Responsive	Does it respond differently?	Angle and objection describe what should move it; whether it responds differently would need a held-back comparison (note 7)
Actionable	Does knowing it change what you do?	Product: a printable brief, and the creative plan

3. When is a difference real?

3.1 Two measures of difference

A group is described by the behaviors that set it apart from its audience. For a behavior with rate $p_{g}$ in the group and $p_{a}$ in the audience, two measures of difference are natural, a ratio and an absolute gap:

$$R = \frac{p_{g}}{p_{a}} \qquad\qquad D = p_{g} - p_{a}$$

The group card shows a behavior’s multiple against the audience, which is $R$. The engine calls a behavior out only when it clears both a ratio and an absolute gap. See Audience groups.

3.2 Small groups vary more

A rate measured on a small group is noisy. If a group of $n$ people is drawn at random from an audience whose rate is $p$, the group’s ratio has, approximately, a standard deviation of

$$\operatorname{sd}(R) \approx \sqrt{\frac{1-p}{n\,p}}$$

which grows as the group shrinks and as the behavior gets rarer. Small units therefore fill both ends of any ranking by rate. This has been called the most dangerous equation, because ignoring it has led to mistakes, such as reading high rates in small counties or small schools as real effects (Wainer, 2007). People, researchers included, tend to expect small samples to resemble the population more closely than they do (Tversky and Kahneman, 1971).

Figure 1 shows the consequence with groups that have no real difference at all.

• One random group
• 95% normal-approximation band
• An illustrative 2× cut

Figure 1. Small groups produce large ratios by chance. Each dot is a group drawn at random from one audience in which a behavior has a 4% rate, so every group's true ratio is 1×. Thirty groups at each of eleven sizes, generated with seed 20261020. By chance alone, 13 of 30 groups of 25 people cleared a 2× ratio, and 3 of 30 groups of 50; from 100 people up, none did. The shaded band is the 95% normal-approximation interval, 1 ± 1.96 √((1 − p) / (n p)), which is only approximate for the smallest groups.

Simulated, seeded and reproducible

Data behind figure 1

Group size	Groups at or above 2×	Highest ratio seen	95% band
25	13 of 30	3.00×	0.00× to 2.92×
50	3 of 30	2.00×	0.00× to 2.36×
100	0 of 30	1.75×	0.04× to 1.96×
200	0 of 30	1.88×	0.32× to 1.68×
400	0 of 30	1.69×	0.52× to 1.48×
800	0 of 30	1.19×	0.66× to 1.34×
1,600	0 of 30	1.31×	0.76× to 1.24×
3,200	0 of 30	1.13×	0.83× to 1.17×
6,400	0 of 30	1.12×	0.88× to 1.12×
12,800	0 of 30	1.08×	0.92× to 1.08×
25,600	0 of 30	1.04×	0.94× to 1.06×

3.3 Why both a ratio and a gap

A ratio alone rewards rare behaviors on small bases: two people out of 25 doing something that 4% of the audience does gives a ratio of 2, from two people. A gap alone ignores how large a difference is relative to how common the behavior is. Requiring both means a headline needs a difference that is large relative to the base rate and large in absolute terms. The thresholds the engine uses are not published.

4. Demographics are context, not evidence

A group card can show an age band or income range to describe a group. Those facts never count as evidence that the group fits. The rule is consistent with research on how data-driven decisions can have a disparate impact on protected groups, even without intent (Barocas and Selbst, 2016), and with audits showing that ad systems can skew who sees an ad by gender and race (Ali et al., 2019).

The rule is also a change of record: since August 2, 2026, demographic facts describe a group but no longer count as evidence that it fits. See the changelog.

5. Other rules, and how this note reads them

Table 2. Rules the grouping engine follows, and why each matters for an audit. The second column is this note’s reading; only the framing rule’s reason is stated in the product docs.

Rule	Why it matters
A missing measure is left out, never faked	A filled-in value would be read as evidence
Buying language needs a live in-market measure that separates the groups	A buying claim should rest on buying behavior (see note 2)
Group-level, not person-level	Patterns that hold for a group need not hold for each member
Operator text outranks the engine’s	What a person writes takes precedence over generated text
The framing is fixed on the run	Groups must hold still to be stable in the sense of Table 1

6. Limits

• The method is not published. How the engine chooses the behaviors that most separate groups, and its thresholds, are available to qualified reviewers under NDA.
• Responsiveness is checked afterward. Whether a group responds differently is judged by a campaign’s results, not by the grouping itself.
• Mutually exclusive groups simplify. Real people can share traits of more than one group; the engine assigns each person to exactly one.

7. Questions an auditor should ask

1. How does a re-run with the same framing reproduce the same groups, and is that tested?
2. What ratio and gap thresholds apply, and how were they chosen?
3. What is the smallest group the engine will form?

8. Conclusion

The segmentation literature supplies the criteria that a group card is built around, and elementary sampling theory supplies the reason for the engine’s caution with small groups. The rule that demographics describe but never justify a group rests on research about what behavior carries and about how proxies discriminate.

References

1. Ali, M., Sapiezynski, P., Bogen, M., Korolova, A., Mislove, A., & Rieke, A. (2019). Discrimination through optimization: How Facebook’s ad delivery can lead to biased outcomes. Proceedings of the ACM on Human-Computer Interaction, 3(CSCW), Article 199. doi.org/10.1145/3359301
2. Barocas, S., & Selbst, A. D. (2016). Big data’s disparate impact. California Law Review, 104, 671–732. doi.org/10.15779/Z38BG31
3. Smith, W. R. (1956). Product differentiation and market segmentation as alternative marketing strategies. Journal of Marketing, 21(1), 3–8. doi.org/10.1177/002224295602100102
4. Tversky, A., & Kahneman, D. (1971). Belief in the law of small numbers. Psychological Bulletin, 76(2), 105–110.
5. Wainer, H. (2007). The most dangerous equation. American Scientist, 95, 249–256.
6. Wedel, M., & Kamakura, W. A. (2000). Market segmentation: Conceptual and methodological foundations (2nd ed.). Kluwer Academic Publishers. doi.org/10.1007/978-1-4615-4651-1

How to cite this note

Moonbrush. (2026). Splitting an audience (Research note 4, version 1.0). https://docs.moonbrush.com/research/audience-groups/