Level 6 · Metric trap: the average discount rate

Two ways to get “the rate”

A rate is a numerator over a denominator: discounts over gross sales, conversions over sessions, refunds over net sales. When you need it for a whole year, there are two tempting ways to compute it:

• Ratio of totals: add up all the discounts, add up all the gross sales, divide once.
• Average of ratios: compute the rate for each month (or each order, or each customer), then take the plain average of those rates.

They only agree when every group has the same denominator. At a store with a Black Friday and a holiday season, they never do.

Why the monthly average is low

month    gross sales   discount rate
Feb        101,430.63       0.42%
Oct        184,532.84       0.16%
Nov        316,329.72       3.53%
Dec        307,041.00       4.46%
year     2,410,185.52       1.99%
mean of 12 monthly rates:   1.68%

The plain average gives February, the smallest month, the same say as November, three times its size. Worse, the big months are exactly the discounted ones (BFCM25 and HOLIDAY20 run then), so down-weighting them pulls the average down. The ratio of totals weights every dollar of sales equally, which is what “discount rate of the year” means.

Other groupings, other wrong answers

The same trap exists for any group. Averaging each customer’s own discount rate gives 2.46% for 2025: small customers who used one welcome coupon count as much as business accounts with dozens of full-price orders. Averaging each order’s rate gives 2.01%, close to the truth only by luck. Three averages of ratios, three answers; one ratio of totals.

When the average of ratios is right

Sometimes you do want each group to count once: “in how many months did the discount rate exceed 3%?” or “what is the typical customer’s discount rate?” are questions about months or customers, not about dollars. Name the unit in the label: “average monthly rate” is a different metric from “discount rate”.

Common mistakes

• AVERAGE on a column of percentages in a spreadsheet subtotal row.
• Averaging conversion rates across days or sources with very different traffic.
• Comparing the two numbers across periods. If the mix of months shifts, the average of ratios moves even when nothing changed.

Interview note

“Ratio of averages or average of ratios?” is a classic. Answer: for an overall rate, sum the numerator and the denominator separately and divide once; average the ratios only when each group should count equally, and say so.