A discount ranking by salesperson is mostly a ranking of account mix. Adjust for the accounts, then test what is left against chance.
Measure each salesperson's discount against the discount their accounts should get, not against the company average. In an illustrative sales team, the representative giving the highest average discount, 11.34 per cent, is within 0.16 points of policy once account size is allowed for, while a colleague at 10.25 per cent is 3.06 points over policy, 165,500 a year of excess discount. A permutation test puts the chance of a salesperson pattern that strong arising at random at 0.0002.
Worked in full in Pricing Strategy by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
Discount reports by salesperson are standard, and they are usually read the wrong way. Large accounts earn larger discounts by policy, and accounts are not shared out at random: the senior representative holds the key accounts, the junior one the small ones. A ranking of average discount by person is therefore mostly a ranking of account mix. It punishes whoever manages the biggest customers and hides the person who gives medium-sized customers large-account terms.
The fix has two steps. First, strip out what the account explains, by comparing each discount with the policy level for that account's size band. Second, ask whether the remaining differences between people are larger than chance would produce among the same accounts.
| Input | Value |
|---|---|
| Accounts, salespeople | 20, 4 |
| Units a year, all accounts | 302,000 |
| Revenue at list | 30,200,000 |
| Policy discount, large / medium / small accounts | 12% / 8% / 4% |
| Contribution margin at list | 30% |
Each salesperson has five accounts. A holds three large ones, B only medium and small ones, C a mix, and D mostly small ones. In practice the expected discount would come from the pricing policy or from a company-wide fit of discount against volume; size bands keep the arithmetic visible.
Raw discount = Σ (units × list × discount) ÷ Σ (units × list), per salesperson
Expected discount = the same, with each account's policy discount for its band
Excess = raw − expected, in points and in money
In Excel: =SUMPRODUCT(Units,Disc)/SUM(Units) and =SUMPRODUCT(Units,Policy)/SUM(Units) per person, with SUMIFS or a pivot table to split by salesperson.
| Salesperson | List revenue | Raw discount | Expected for mix | Excess, points | Excess, money |
|---|---|---|---|---|---|
| A, key accounts | 13,200,000 | 11.34% | 11.18% | 0.16 | 21,500 |
| B | 5,400,000 | 10.25% | 7.19% | 3.06 | 165,500 |
| C | 7,500,000 | 9.45% | 9.44% | 0.01 | 500 |
| D | 4,100,000 | 6.41% | 6.15% | 0.27 | 11,000 |
| Company | 30,200,000 | 10.01% | 9.35% | 0.66 | 198,500 |
On the raw figures A looks like the problem and D like the model. Once the accounts are allowed for, A, C and D are all within about a quarter of a point of policy, and 165,500 of the company's 198,500 of excess discount sits with B, on 5,400,000 of list revenue. Every one of B's five accounts is 2.5 to 4.0 points over its band; B is giving medium accounts the large-account rate.
Four people and twenty accounts will always show some spread. The test is how much of the variation in the account-level excess sits between salespeople rather than within each person's book, compared with what a random allocation of the same accounts would give.
Between-salesperson share = Σ nk (meank − grand mean)² ÷ Σ (excess − grand mean)²
Chance level ≈ (salespeople − 1) ÷ (accounts − 1) = 3 ÷ 19 = 15.8%
Permutation test: shuffle the salesperson labels across accounts 20,000 times and count how often the share is at least as high as observed.
On the raw discounts the between-salesperson share is 35.7 per cent, but most of that is account size: the size bands alone explain 78.2 per cent of the raw variance. On the mix-adjusted excess the between-salesperson share is 80.8 per cent, 5.1 times the chance level. In 20,000 shuffles only 4 matched it, a p-value of 0.0002. With twenty accounts that is about as clear as this test gets.
B's 165,500 of excess discount comes straight out of contribution. B's accounts earn 1,066,500 of contribution after discount, so the excess is 15.5 per cent of it. Recovering half, 82,750, by bringing B's renewals back towards policy would survive a volume loss of up to 7.2 per cent on B's book, the usual break-even of a price rise on its own contribution margin.
| Salesperson | Raw rank, most discount first | Excess, money | Share of excess |
|---|---|---|---|
| A | 1 | 21,500 | 10.8% |
| B | 2 | 165,500 | 83.4% |
| C | 3 | 500 | 0.3% |
| D | 4 | 11,000 | 5.5% |
Acting on the raw ranking. Here it would have put pressure on A, whose 11.34 per cent is the policy result of holding the three largest accounts, and praised D, whose low average is simply a small-account book. The opposite mistake is just as costly: concluding from a spread of averages that "salespeople differ" without checking it against chance. With a handful of accounts each, one big customer can move a person's average by a point. Adjust for mix first, then compare the between-person share with the chance level, then put a number on the excess. The same band logic, applied to accounts instead of people, sets a price floor from a pocket price band, and the authority each person should have is set in discount approval levels for a sales team.
The book splits its own direct industrial accounts by salesperson, and its working documents print the chance level beside the salesperson test; both are in the free workbook for this case.
Adjust for account mix first. Compute each rep's volume-weighted discount and the discount their accounts would get under policy, and compare the two. In the illustration the rep with the highest average, 11.34 per cent, holds the large accounts and is 0.16 points over policy; another rep at 10.25 per cent is 3.06 points over.
Compare the share of the account-level variation that sits between salespeople with the share chance would give, roughly (reps minus 1) divided by (accounts minus 1). With 4 reps and 20 accounts chance is 15.8 per cent; an observed 80.8 per cent was matched by only 4 of 20,000 random shuffles of the labels.
It comes straight out of contribution. In the illustration one rep's 165,500 of excess discount is 15.5 per cent of the 1,066,500 of contribution their accounts earn after discount. Recovering half of it would survive a volume loss of up to 7.2 per cent on that book.
Chapter 6 of Pricing Strategy turns on the salesperson variance split; the companion workbook reproduces it on the book's direct industrial accounts. The book takes the same case from first principles to the decision, chapter by chapter, and every figure it prints is a live formula in the free companion workbooks.
Get the book on Amazon →Free companion files
Also on Amazon UK · Amazon Germany · Amazon France · Amazon Canada
Reading guide: business operations: cost, contracts, pricing and supply chain → · All 1523 articles →
If this book helped, or didn’t, a few lines on Amazon are worth more than they look: they are what the next reader goes on. Write a review. The workbook stays free either way.