---
title: "\"2.7 Times More Likely\": Relative vs Absolute Risk"
description: "Turn \"2.7 times more likely\" into people per 100: relative and absolute risk, the base rate, and a check against a real report and a made-up example."
url: "https://staging.khoi.co.uk/en/blog/rui-ro-tuong-doi-tuyet-doi"
lang: en-GB
author: "Lê Quốc Khôi"
date: 2026-11-02
updated: 2026-11-02
topics: ["Data & analytics"]
tags: ["Relative risk", "Base rate", "Natural frequencies", "Data literacy"]
---

# What does "2.7 times more likely" really mean?

## Key takeaways

- "2.7 times more likely" is a ratio of two rates, so it says nothing about how many people. The same multiple can mean 5 extra people per 100 or 38 extra people per 100, depending on the base rate of the comparison group.
- The McKinsey and LeanIn.Org report Women in the Workplace 2024 prints exactly this multiple: 60 against 22 per 100 women had considered leaving their company, comparing those who met three or more microaggressions with those who met none (McKinsey & Company and LeanIn.Org, 2024, p. 42).
- Gigerenzer and colleagues recommend absolute risks over relative risks (Gigerenzer et al., 2007, p. 53). Four steps: get the base rate, multiply by the multiple, subtract to find the extra people, scale to your own headcount.
- The retailer "Nhà Mình" is made up, and so is every figure for it. With the same 2.7, a base rate of 3 per 100 gives about 20 extra people among 400, while 30 per 100 gives about 204.

Suppose a consultancy's slide says night-shift staff are "2.7 times more likely" than day-shift staff to quit in their first six months. You run HR for a retail chain. Does that mean losing a handful of people or a few hundred? You cannot tell, because one number is missing: the day-shift quit rate.

The 2.7 is not only in the invented case. The McKinsey and LeanIn.Org report Women in the Workplace 2024 prints the same multiple on page 42 (McKinsey & Company and LeanIn.Org, 2024, p. 42). This post converts a multiple into people per 100, using that report as the exercise with real numbers.

## What does a multiple like "2.7 times more likely" tell you, and what does it leave out?

It tells you the ratio between two rates and leaves out how large either rate is. Gigerenzer and colleagues separate [relative and absolute risk](https://staging.khoi.co.uk/en/glossary#relative-vs-absolute-risk): "twice as likely" or "up 100%" is relative, "1 in 7,000" is absolute (Gigerenzer et al., 2007, p. 54). They recommend absolute risks (Gigerenzer et al., 2007, p. 53).

Their opening case is a contraceptive pill scare in Britain. In October 1995 the Committee on Safety of Medicines warned that third-generation pills doubled the risk of blood clots, an increase of 100%. The studies behind the warning showed that of every 7,000 women on second-generation pills about 1 had a thrombosis, against 2 on third-generation pills. The absolute increase was 1 in 7,000. According to the authors, many women stopped taking the pill, and an estimated 13,000 extra abortions followed in England and Wales the next year (Gigerenzer et al., 2007, p. 54). I use the case for its arithmetic and say nothing about the drugs.

Their lesson: absolute risks tend to be small numbers while relative changes look big, particularly when the base rate is low (Gigerenzer et al., 2007, p. 54). A fall from 20% to 10% and a fall from 0.0002% to 0.0001% are both a 50% relative reduction, yet they matter very differently (Gigerenzer et al., 2007, p. 66). That argument concerns reductions. The sum is identical when the multiple is an increase such as "2.7 times".

## How do you turn "2.7 times more likely" into people per 100?

In four steps, and the first is to ask for the base rate.

1. Get the [base rate](https://staging.khoi.co.uk/en/glossary#base-rate): the rate in the comparison group, such as day-shift staff. If the slide omits it, ask the author. Reporting a relative risk reduction without the base rate is bad practice, say Gigerenzer and colleagues (Gigerenzer et al., 2007, p. 66).
2. Multiply the base rate by the multiple to get the other group's rate. Check the ceiling: the result cannot exceed 100 per 100, so a multiple of 2.7 only makes sense when the base rate is below about 37 per 100. If it overshoots, the base rate or the multiple has been misquoted.
3. Subtract one rate from the other to find the extra people per 100.
4. Multiply by the headcount you actually manage to get the real number of extra people, and only then compare it with the cost.

"Per 100 people" is a frequency statement, which is the direction the authors recommend (Gigerenzer et al., 2007, p. 53). When a problem also involves test results, they use [natural frequencies](https://staging.khoi.co.uk/en/glossary#natural-frequencies): counts that add up to the whole group (Gigerenzer et al., 2007, p. 55). There is an example in the FAQ below.

## How far apart can the same 2.7 land at different base rates?

Very far. Everything in this example is invented: the retailer "Nhà Mình", its quit rates and its costs are mine, made up to show the sum.

**A hypothetical example.** Nhà Mình is a retail chain with 12 stores in Can Tho and Ho Chi Minh City and 400 night-shift staff. A consultancy's slide says night staff quit within six months 2.7 times as often as day staff. Each leaver costs VND 6m to recruit and train a replacement.

> **Figure:** (compare) Columns 1 and 3 are hypothetical figures made up by the author for illustration, not real data. Column 2 takes the two rates, 22% and 60%, from the chart on page 42 of the McKinsey and LeanIn.Org report (2024); I only restated them as people per 100.

```json
{
  "type": "compare",
  "columns": ["Base rate 3 (hypothetical)", "Base rate 22 (from the report)", "Base rate 30 (hypothetical)"],
  "rows": [
    { "label": "Comparison group, per 100 people", "cells": ["3", "22", "30"] },
    { "label": "Other group at 2.7 times, per 100 people", "cells": ["8.1", "about 60", "81"] },
    { "label": "Extra people per 100", "cells": ["5.1", "38", "51"] }
  ]
}
```

Say the day-shift quit rate is 3 per 100. Night shift is 3 × 2.7 = 8.1 per 100, about 5 extra per 100, so about 20 extra leavers among 400 and about VND 120m in replacement cost. Now say it is 30 per 100. Night shift rises to 81 per 100, 51 extra per 100, so about 204 extra leavers among 400 and about VND 1.2bn. One line on one slide, a tenfold difference.

The decision flips with it. Suppose a night allowance costs VND 300m every six months for the 400 staff and removes the gap entirely (a very strong assumption). At a base rate of 3 you pay VND 300m to avoid roughly VND 120m: it does not pay. At 30 you pay VND 300m to avoid roughly VND 1.2bn: it does, and it is worth testing whether the allowance really keeps people.

## How does the McKinsey and LeanIn.Org report use the 2.7?

The chart sits in the [Women in the Workplace 2024 case](https://staging.khoi.co.uk/en/case/mckinsey-leanin-women-in-the-workplace-2024). Page 42 compares 2024 negative outcomes for women who experienced three or more microaggressions with women who experienced none. The report describes microaggressions as everyday forms of disrespect, such as having your judgment questioned in your own area of expertise (McKinsey & Company and LeanIn.Org, 2024, p. 37). The first group is "2.7x more likely" to have considered leaving their company, and the chart prints both rates: 60% against 22% (McKinsey & Company and LeanIn.Org, 2024, p. 42). I read those two figures off the chart in the PDF, and 60 divided by 22 is about 2.7, matching the printed multiple. In people: of 100 women in the first group about 60 had considered leaving, against about 22 in the other, which is 38 more per 100. The base rate here is fairly high, so a multiple of 2.7 stands for a very large gap.

The same report states another gap in "per 100" form: for every 100 men promoted to manager in 2024, 81 women were, assuming equal numbers in each group (McKinsey & Company and LeanIn.Org, 2024, p. 8).

Gigerenzer and colleagues' four questions for any risk (Gigerenzer et al., 2007, p. 58) map onto the chart like this:

| Question | Answer from the chart on page 42 |
|:--|:--|
| Risk of what? | Having considered leaving the organisation, not having left (the report's note 66). |
| Over what period? | The survey asked about "the last year" (note 66). Employees were surveyed between March and May 2024 (McKinsey & Company and LeanIn.Org, 2024, p. 57). |
| How big? | 60 against 22 per 100, so 38 more per 100. |
| Does it apply to me? | See the next paragraph: the sample and the comparison have limits. |

On the last row: the report draws on data from 281 companies in the United States and Canada, but the 15,000-plus employees in the survey came from 27 companies. Companies joined by invitation or by expressing interest, and the employee survey was encouraged but optional (McKinsey & Company and LeanIn.Org, 2024, p. 57). Page 2 puts the two numbers side by side, which invites reading them as one sample, yet 281 counts participating companies while 15,000 counts employees from 27 companies (McKinsey & Company and LeanIn.Org, 2024, p. 2). Page 42 does not say which of the two the chart draws on, and I also found no group sizes or margins of error there. To use this for a company in Vietnam, you need the share who have considered leaving in your own two groups, not someone else's multiple.

## How can a multiple skew a decision?

Fahey and colleagues (1995) gave 140 health-authority reviewers four funding proposals that were identical except for how the benefit was written. Only 3 noticed they were equivalent. When the benefit appeared as a relative risk reduction, the programme was rated as having the greatest merit and was the most likely to be funded; Gigerenzer and colleagues retell the experiment (Gigerenzer et al., 2007, p. 70). They also describe "mismatched framing": benefits in relative numbers, harms in absolute ones (Gigerenzer et al., 2007, p. 78). With any vendor pitch, ask for benefit and cost in the same unit: people per 100, or money.

## Going deeper: what do Gigerenzer and colleagues argue, and where does it stop?

The paper appeared in 2007 in *Psychological Science in the Public Interest*; the authors are at the Max Planck Institute for Human Development in Berlin and Dartmouth Medical School (Gigerenzer et al., 2007, p. 53). Their claim: many doctors, patients, journalists and politicians do not understand health statistics, and the cause lies in how numbers are presented, sometimes by accident and sometimes to persuade, not only inside readers' heads (Gigerenzer et al., 2007, p. 53). They recommend frequency statements over single-event probabilities, absolute over relative risks, mortality over survival rates, and natural frequencies over conditional probabilities (Gigerenzer et al., 2007, p. 53). For natural frequencies the paper cites work by Gigerenzer and Hoffrage from 1995 and 1999, which I have not read.

The first limit is the field. The evidence concerns doctors, patients, journalists and health reviewers. I found no data on business managers, so applying it to staff surveys is my own inference: the arithmetic is the same, but how readers react I have not checked.

The second: the paper aims at multiples that stand alone, not at every multiple. What it calls bad practice is a relative reduction with no base rate (Gigerenzer et al., 2007, p. 66). It notes that relative risks can be derived from absolute ones but not the other way round (Gigerenzer et al., 2007, p. 78), and concedes that how transparent a format is depends on who is reading (Gigerenzer et al., 2007, p. 77).

The third is how I read. I read the paper as a full-text PDF; page numbers are the journal's printed page numbers (53–96). I read the McKinsey and LeanIn.Org report as a printed PDF without the underlying data, so I could not check its rates against the raw figures.

## Frequently asked questions

### Where do I find the base rate if a report gives only the multiple?

Look in the chart, the data table or the appendix, then ask the author for the two rates behind the multiple. If neither exists, treat the multiple as too thin to decide on. Gigerenzer and colleagues call it bad practice to report a relative risk reduction without the base rate, because readers overestimate the benefit (Gigerenzer et al., 2007, p. 66). They also report that 45% of press releases describing differences between study groups gave relative risks without base rates (Gigerenzer et al., 2007, p. 67).

### Is "2.7 times more likely" the same as 270 per cent higher?

No. It means one group's rate is 2.7 times the other's, an increase of 170 per cent. Strictly, "times more" is ambiguous, but the numbers in Women in the Workplace 2024 fit the ratio reading: 60 divided by 22 is about 2.7 (McKinsey & Company and LeanIn.Org, 2024, p. 42). For "X per cent lower" claims, Gigerenzer and colleagues point out that it is unclear whether the drop is relative or absolute; writing "percentage points" may be too subtle for many readers, so they suggest "from 20 in 100 to 10 in 100" (Gigerenzer et al., 2007, p. 66).

### What are natural frequencies, and when do I use them?

They are counts of people in a fixed group, used instead of conditional probabilities. In the authors' example, 10 in 1,000 women have a disease, 9 of those 10 test positive, and about 89 of the 990 without it also test positive. So roughly 1 in 10 who test positive really has it. After training in this format, 87% of 160 gynaecologists answered correctly, against 21% beforehand (Gigerenzer et al., 2007, p. 55).

### Does a multiple in a report prove a cause?

Not by itself. A multiple compares two groups. The chart on page 42 compares women who report three or more microaggressions with women who report none, and its title says "lead to" (McKinsey & Company and LeanIn.Org, 2024, p. 42). The methodology describes the data as point-in-time snapshots (McKinsey & Company and LeanIn.Org, 2024, p. 57). I found nothing on page 42 that separates other factors such as seniority or sector, so it does not settle cause.

## References

- Gigerenzer, G. et al. (2007) ‘Helping doctors and patients make sense of health statistics’, *Psychological Science in the Public Interest*, 8(2), pp. 53–96. https://doi.org/10.1111/j.1539-6053.2008.00033.x
- McKinsey & Company and LeanIn.Org (2024) *Women in the workplace 2024: the 10th-anniversary report*. McKinsey & Company and LeanIn.Org. Available at: https://www.mckinsey.com/featured-insights/diversity-and-inclusion/women-in-the-workplace-2024.

---

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