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The mathematical trap of averaging ROAS and CPA across platforms
An authority article demonstrating why averaging ratios generates false data and how weighted Macro-ROAS is calculated.
Quick answer
ROAS and CPA are ratios. They cannot be averaged across platforms because each ratio has a different denominator. The correct method is to first add the raw magnitudes (spend, revenue, conversions) and calculate the ratio on those totals. That is weighted Macro-ROAS.
Key takeaways
- Averaging ratios ignores the weight of spend.
- Macro-ROAS = total revenue / total spend.
- Real CPA = total spend / total conversions.
In this guide
Simpson’s paradox in marketing
Simpson’s paradox occurs when a trend appears in each group separately but disappears or reverses when they are combined. In marketing, the classic case is ROAS: two channels can improve individually while the consolidated result worsens if the spend mix changed.
Averaging ratios is a way to introduce that paradox without noticing. The simple average treats every platform as if it had the same weight, even when one spends ten times more than the other.
A worked example
Google Ads: US$1,000 spend, US$4,000 revenue, 4.0x ROAS. Meta Ads: US$9,000 spend, US$9,000 revenue, 1.0x ROAS. The simple average is 2.5x. The real consolidated figure is (4,000 + 9,000) / (1,000 + 9,000) = 13,000 / 10,000 = 1.3x.
The difference is enormous because Meta holds 90% of spend. A report showing 2.5x is hiding that most of the budget is returning below 1.5x. The business decision changes completely.
| Channel | Spend | Revenue | ROAS |
|---|---|---|---|
| Google Ads | US$1,000 | US$4,000 | 4.0x |
| Meta Ads | US$9,000 | US$9,000 | 1.0x |
| Simple average | — | — | 2.5x (wrong) |
| Real consolidated | US$10,000 | US$13,000 | 1.3x |
The correct formulas
Macro-ROAS = sum of revenue / sum of spend. Macro-CPA = sum of spend / sum of conversions. With more than two channels, add all of them before dividing. With different currencies, convert before adding.
For variations against the previous period, the same rule applies: calculate the totals for each period and then the variation. Never average the percentage variations of each platform.
- Macro-ROAS = Σ revenue / Σ spend.
- Macro-CPA = Σ spend / Σ conversions.
- Variation = (current ratio − previous ratio) / previous ratio.
The lead generation client case
If an agency consolidates e-commerce and lead generation clients, including spend from clients without revenue in the ROAS denominator dilutes the result. The spend exists, but it has no associated revenue.
A reasonable practice is to calculate ROAS only on clients that have revenue and report lead generation spend separately. The important thing is that the numerator and denominator measure the same universe.
Checklist to audit a consolidated report
Before trusting a consolidated ROAS, verify that it was calculated on totals, that currencies were normalized and that the client universe is consistent. If the report shows an average of ratios, the number is decorative.
A quick way to detect it: multiply ROAS by spend. If the result does not match total revenue, the calculation is wrong.
- Were revenue and spend added before dividing?
- Were currencies converted before adding?
- Does the denominator include clients without revenue?
- Was the variation calculated on totals?
Frequently asked questions
Why can’t ROAS be averaged?
Because ROAS is a quotient and each platform has a different denominator. The simple average gives the same weight to a US$100 account and a US$10,000 account. The result does not represent the business return.
What is Macro-ROAS?
It is the return calculated on consolidated totals: total revenue divided by total spend. It is used to measure the overall performance of a portfolio or a client with multiple platforms.
Does Clarika calculate it this way?
Yes. Clarika adds the raw metrics first and calculates ratios on the totals. It does not average percentages across platforms.
Stop reporting averages that mislead
Calculate real ROAS and CPA on consolidated totals.
Keep reading
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