Blog · Board and management reporting
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.
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.
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.
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.
| 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 |
| 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.
| 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 |
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.
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 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.
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.
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.
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.