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Blog · Board and management reporting

Concentration ratio vs Herfindahl index: what is the difference, and which to use for customer concentration

Two ways of measuring how concentrated a customer base is. The concentration ratio adds up the revenue shares of the largest few customers: top one, top five, top ten. The Herfindahl-Hirschman index squares every customer's share and sums them, giving one number that reflects the whole distribution. This page sets out both formulas, computes them on three customer bases that share a top-ten figure and differ underneath, explains the effective number of customers, and says which to use for a board, a lender, and for tracking one book over time.

The short answerThe concentration ratio, CR-n, is the combined revenue share of the n largest customers: CR1, CR5, CR10. It is easy to explain and ignores how revenue is spread within and below the top n. The Herfindahl-Hirschman index, HHI, is the sum of the squared revenue shares of all customers, from near zero for a very fragmented base to 1, or 10,000 on the percentage scale, for a single customer. It captures the whole distribution in one number and is harder to explain. Its reciprocal, 1 ÷ HHI, is the effective number of customers: the number of equal-sized customers that would give the same concentration. Use CR1 and CR10 for boards and lenders, because those are the terms they think and write covenants in; use HHI or the effective number to track one book over time, because it moves when the top ten ratio does not.

Two measures of the same thing. One is a sentence anyone understands; the other is a single number that sees what the sentence leaves out.

The formulas

CR-n = sum of the revenue shares of the n largest customers HHI = sum over all customers of (revenue share)² Effective number of customers = 1 ÷ HHI

Shares as fractions give HHI between 0 and 1. Shares as percentages give 0 to 10,000; divide by 10,000 to convert.

Three bases with the same top ten

Each has a top-ten share of 50 percent. The remaining 50 percent is spread over 500 small customers at 0.1 percent each, contributing 500 × 0.001² = 0.0005 to HHI in every case.

Base Top ten made up of CR1 CR10 HHI Effective customers
X Ten at 5% each 5% 50% 10 × 0.05² + 0.0005 = 0.0255 39
Y One at 23%, nine at 3% each 23% 50% 0.23² + 9 × 0.03² + 0.0005 = 0.0615 16
Z One at 41%, nine at 1% each 41% 50% 0.41² + 9 × 0.01² + 0.0005 = 0.1695 6

CR10 cannot tell these apart. CR1 can, which is why it should always be reported beside CR10. HHI separates all three with one figure, and the effective number puts it in words: base Z, with 510 customers, behaves like a business with six.

What each one sees

Concentration ratio HHI
Inputs The top n customers only Every customer
Sensitive to Who is in the top n How unequal the shares are, especially the largest
Blind to Distribution inside the top n; everything below Nothing, but hard to read without the effective number
Explained in One sentence One paragraph
Used by Lenders, acquirers, auditors Economists, regulators, analysts
Moves when A customer enters or leaves the top n, or the top n's total shifts Any large share changes

A year in which CR10 did not move

Last year This year
Largest customer 12% 19%
Customers two to ten, combined 28% 21%
CR10 40% 40%
HHI 0.024 0.042
Effective customers 42 24

The board pack says concentration is unchanged at 40 percent. The largest customer grew by seven points while the next nine shrank. HHI rose by more than half, and the effective number fell from 42 to 24. This is the case for tracking both.

Which to use where

Audience or purpose Use
Board pack CR1, CR5, CR10, with last year beside each; the effective number as one extra line
Lender, covenant, due diligence CR1 and CR10; those are the terms in the documents
Tracking one book over time HHI or effective number, quarterly
Comparing reps' or partners' books Effective number; it handles books of different sizes
Supplier or carrier dependence The same two measures, on spend instead of revenue
Margin dependence Both measures, computed on gross margin or contribution

Computing them

From a ledger totalled by customer for the period: shares are each customer's total over the grand total; CR-n sums the n largest; HHI is the sum of squared shares. In a spreadsheet that is LARGE and SUMPRODUCT; the Excel guide to customer concentration gives the formulas. Two conditions matter more than the choice of measure: customers must be rolled up to their parent, or concentration is understated, and the customer totals must sum to the ledger.

Where the two get confused

CR10 alone. Bases X, Y and Z reported as the same risk.

HHI alone. A number nobody in the room can interpret; show the effective number of customers.

Antitrust thresholds borrowed. The 1,500 and 2,500 lines are for market structure, not for a company's customer list.

Subsidiaries unrolled. One group buying through six entities, each below the disclosure line.

The short version

The concentration ratio says how much the top few account for; HHI says how unequal the whole base is; one over HHI turns that into a number of customers a board can picture. Report CR1 and CR10 because people expect them, and track the effective number because it moves first. For what level is normal, see what is a good customer concentration and the concentration by industry hub. Covirage computes all of them from the ledger each month, by revenue and by margin, with customers rolled up to parents and the totals checked.

Questions people ask

What is a high HHI for a customer base?

There is no standard, and the antitrust thresholds for market concentration do not transfer. As a guide on the 0 to 1 scale: under 0.01 is very diversified, an effective hundred or more customers; 0.01 to 0.05 is moderate; above 0.10, an effective ten or fewer, means results depend on a handful of accounts. The trend in your own figure is more informative than any level.

Why can two bases with the same top-ten share have different HHI?

Because the top-ten share does not see how revenue is divided among the ten. One customer at 41 percent and nine at 1 percent is a top ten of 50 percent. So is ten customers at 5 percent each. The first has an HHI near 0.17 and depends on one account; the second is near 0.03. Squaring the shares is what makes the large ones count for more.

Should I compute these on revenue or margin?

Both. Concentration of margin is often higher than concentration of revenue, because large customers can also be the most profitable to serve, or lower, because they negotiate harder. The margin version is the one that describes what the business's profit depends on.