Growth Bridge
Your dashboard says revenue is down. It does not say why. Enter two periods and get a driver-by-driver bridge whose bars sum exactly to the change.
Change in revenue
–
vs period 1
- Period 1
- –
- Period 2
- –
Change in ROAS
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vs period 1
- Period 1
- –
- Period 2
- –
Change in blended CVR
–
vs period 1
- Period 1
- –
- Period 2
- –
Simpson's paradox
Why growth decomposition matters
"Revenue is down 4%" is not an insight. It's a headline. The board doesn't want the number; they want to know which lever moved, by how much, and whose problem it is. Decomposition turns a vague miss into an assignable one.
The math here is not a model and not a guess. Log-mean (LMDI) and midpoint decomposition split a metric's change exactly across its drivers. The bars always sum to the total, so there is no "unexplained" bucket for wishful thinking to hide in.
The mix-shift check matters most. A blended conversion rate can fall while every single channel improves. That is Simpson's paradox, and teams routinely "fix" funnels that were never broken. Separate rate from mix before you reorganize anything. Your analytics team, and your board, will thank you.
Formulas
- Revenue
- = Sessions × CVR × AOV
- ROAS
- = (CVR × AOV) ÷ CPC
- CPC
- = CPM ÷ (1,000 × CTR)
- Contribution of a driver
- = L(Y₂, Y₁) × ln(x₂ ÷ x₁), where L is the logarithmic mean
- Mix
- = Δ(w·r) = w̄·Δr + r̄·Δw
Frequently asked questions
What is a revenue bridge?
A revenue bridge is a waterfall that starts at last period's revenue, adds or subtracts one bar per driver (traffic, conversion rate, order value), and lands on this period's revenue. It answers "why did revenue move" with numbers you can assign to a team, instead of a single headline percentage.
Why do the bars sum exactly to the change?
The tool uses the logarithmic mean Divisia index (LMDI) for multiplicative metrics and a midpoint identity for weighted averages. Both are exact decompositions: every unit of the change is attributed to a driver, so there is no residual or interaction bucket. If you re-add the bars you get the total change to the cent.
What is Simpson's paradox in marketing data?
Simpson's paradox is when every segment moves one way but the blended total moves the other. A blended conversion rate can fall while every channel converts better, because traffic shifted toward channels that convert at a lower rate. The Mix Shift mode flags this when it happens so you do not rebuild a funnel that was never broken.
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