BakingAdsFast start, steady slowdown
For series that grow quickly at first and decelerate progressively.
Forecast & ARPU
A campaign’s value doesn’t stop at the first revenue.
When customers keep buying after the first conversion, early returns can understate a campaign’s potential. BakingAds estimates what an acquired cohort will be worth at day 365, and tells you how far to trust the estimate.
Built on established statistics: growth-curve modelling, non-parametric trend testing and forecast combination.
The principle
Simple, transparent reasoning. Automated at scale.
If history says similar cohorts typically reach 70% of their final value by day 14, and your cohort is worth €0.90 per user at day 14, the estimate at maturity is about €1.29 per user.
€0.90ARPU observed at day 14
÷
70%Share of value reached by day 14
≈
€1.29Estimated ARPU at maturity
Worked example for illustration. BakingAds learns the maturation curve from the historical cohorts of the same segment.
The science behind the forecast
Four well-studied growth models compete. The data picks the winner.
Cumulative revenue per user rarely grows in a straight line: it rises fast, then decelerates and settles. BakingAds fits four established families of growth curves to the cumulative ARPU of each segment and selects the one that describes the real data best.
Constant deceleration
For sub-linear growth that keeps slowing at a regular pace.
Asymmetric S-curve
For growth that accelerates early, then saturates towards a ceiling.
Symmetric S-curve
For a central acceleration followed by a symmetric saturation.
Model selection follows standard goodness-of-fit measures, applied in order:
1 · Scatter IndexError relative to the mean level2 · R²Share of variance explained3 · RMSEAbsolute fitting error
A forecast that learns as data arrives
Three checkpoints. Each one corrects the last.
A single curve fitted on day one is not enough. The forecast is refined in cascade at day 7, 14 and 21: every new week of real data corrects both the level and the trajectory of the projection, while corrections stay within the ranges observed in historical cohorts.
Day 7
First estimate
The first real week anchors the selected curve to the cohort’s actual level.
Day 14
Trajectory correction
The change from week one to week two reveals whether the cohort is growing faster or slower than its benchmark.
Day 21
Stabilised forecast
A third week confirms the momentum and settles the long-horizon estimate.
Designed for real-world data
Shape and level, handled separately.
The engine learns how value grows relative to itself separately from how much it is worth today. That separation gives the forecast four properties that matter in day-to-day business.
Scale invariance
A currency change or a price-plan rescaling moves the forecast proportionally, without being mistaken for a change in growth pattern.
Seasonality-aware
A cohort acquired in a strong or weak season is judged on its growth structure, not only on its absolute level.
Consistent over time
Long-horizon estimates change when new evidence arrives, not simply because the observation day moved.
Shape-agnostic
The same logic applies whichever curve family best describes the segment.
What each analysis returns
One request. The forecast and its context.
Choose an acquisition period, the event that brings a user into the cohort and the traffic dimensions that define the segment.
| Value | What it tells you | The decision it enables |
|---|---|---|
| ARPU Forecast | Estimated value per user at maturity, projecting observed ARPU onto the historical maturation curve. | Compare cohorts and segments on expected value, not only on value already realized. |
| Dynamic forecast | The projection across the cohort’s life at checkpoints from day 7 to day 365. | Read how value should mature, not just the final result. |
| Gross estimate | A combination of short-term, observed and near-term projected values. | Have a single, lower-variance reference number for quick evaluations. |
| Traffic trend | Whether first-week value of new cohorts is growing, declining or stable, with statistical significance. | Spot improving or deteriorating sources before it shows in historical averages. |
| Scatter Index | How closely the curve fits real historical data: High, Medium or Low, plus the numeric value. | Know how much to trust the forecast for that segment. |
| Confidence-adjusted forecast | A reliability factor combining curve fit, cohort maturity and sample size, with 80/90/95% intervals at day 365. | Judge a sustainable acquisition cost with a margin of prudence. |
| Cohort status | ARPU observed so far, days of maturity and the share of potential already reached. | Know where the cohort you are judging stands on its journey. |
Trend-aware
Where is the traffic heading this week?
Two sources with the same historical ARPU can be moving in opposite directions. BakingAds tracks the first-week value of each new cohort and tests for a monotonic trend with the Mann–Kendall test, estimating its speed with Sen’s slope.
Both are non-parametric, rank-based methods: they make no normality assumption and are robust to the outliers that holidays, promotions or platform changes inject into marketing data.
GrowthStatistically significant upward trend (5% level).
DeclineStatistically significant downward trend.
StableNo significant trend, or a series too noisy to trust.
InsufficientToo few weeks for a meaningful test.
Incomplete recent weeks are excluded, and the trend adjusts the estimate only when it is significant.
Source AGrowth · +€0.18 / week
WEEK 1WEEK 9
The robust slope ignores the single outlier that would skew an ordinary regression line.
Forecast combination
Three horizons are better than one.
Each estimate carries its own systematic bias: early checkpoints run hot, the latest observation depends on how long you have watched, a projection depends on the model. Combining independent estimates reduces overall variance, a principle established in forecasting research since the late 1960s.
Short termCheckpoint historyWhat cohorts are worth in their first weeks
+
ObservedLatest real valueARPU on the last observed day
+
Near-term projectionForecast aheadProjected just beyond the observed data
→
Gross estimateOne reference valueThen adjusted for significant traffic trends
How it works
Six steps from cohort to decision.
Define the cohort
Pick the acquisition period, the event that brings a user in (registration, email confirmation, signup) and up to 20 combinable traffic dimensions: campaign, country, network, source, custom parameters.
Rebuild the cohort’s history
Each acquired user is linked through the click identifier to the revenue they generated over time, and cumulative ARPU is computed day by day.
Learn the maturation curve
Four growth-model families are fitted on the segment’s history and ranked by Scatter Index, R² and RMSE.
Refine in cascade
Checkpoints at day 7, 14 and 21 correct the projection’s level and trajectory with each new week of real data.
Combine and read the trend
Short-term, observed and projected values are combined; a statistically significant traffic trend adjusts the estimate.
Measure and declare reliability
Every answer carries the Scatter Index, a confidence factor and confidence intervals. When data is not enough, you get an explicit message instead of a misleading number.
Reliability is part of the result
A forecast is never shown as an isolated number.Signals of fit, maturity and sample size travel with every estimate, together with confidence intervals at the 80%, 90% and 95% levels. Combined, they produce a prudent reference to compare expected value with acquisition cost.
80%
90%
95%
Scatter Index
< 10% HighDistance between the curve and real historical data. 10–20% is Medium, above is Low. Beyond 25% the forecast is refused.
Cohort maturity
Days observedA cohort observed for 3 days inspires less confidence than one observed for 28.
Sample size & dispersion
UsersFew users or highly dispersed early revenue widen the intervals and reduce the confidence factor.
Price suggestion
Turn expected value into a spending limit.
The ARPU panel places users, cost, revenue and acquisition metrics next to the forecast. The trend-adjusted, confidence-aware estimate feeds a Price suggestion: a reference for the maximum sustainable cost per lead, net of the margin you apply.
- Current ARPU and ARPU at day 365 in the same row.
- Context by network, country and other dimensions.
- Refreshed as data arrives: new observations and new trends update the reference.
ARPU now
€1.10
Day 21
Adjusted D365
€4.80
Confidence applied
Price suggestion
€2.40
Per lead, after margin
Current CPL €4.45. Above the suggested price: review bids or wait for more maturity before scaling.
When the answer is “not yet”
Weak numbers are worse than no numbers.
BakingAds flags the situations where an estimate is not possible or not meaningful, and keeps observed data visible.
Too young
A cohort that coincides with the observation day has no useful maturation data yet.
Short history
Without enough history for the segment, only observed ARPU is returned.
No data
If the segment has no leads or revenue in the period, the response says so.
Unreliable curve
Above the scatter threshold the forecast is refused, and the reason is reported.
Where it applies
Any product where value builds up over time.
The approach fits digital products with subscription or freemium monetization, where revenue per user accumulates along a curve. It was built and validated on subscription apps, and self-calibrates on each market’s own history.
DatingFitness & wellnessStreamingSaaSMobile gaming
What the model needs
- A lead and a revenue event linked by the same click identifier.
- Historical cohorts for the segment: as a guideline, around 90 days of observations on cohorts of a few hundred users.
- Consistent event definitions over time, so that cohorts stay comparable.
Use case
Same week-one result. Different future.
Two campaigns show the same revenue per lead today. The first has a higher projected value at day 365, the second a lower acquisition cost. Putting real results, projection and suggested price in one frame shows which one deserves more budget, and with what spending limit.
The final decision stays anchored to observed data and to the reliability of the projection.
Explore the ARPU forecastScientific references
- Gompertz, B. (1825). On the nature of the function expressive of the law of human mortality. Philosophical Transactions of the Royal Society.
- Verhulst, P.-F. (1838). Notice sur la loi que la population suit dans son accroissement. Correspondance mathématique et physique.
- Mann, H. B. (1945). Nonparametric tests against trend. Econometrica, 13(3).
- Kendall, M. G. (1975). Rank Correlation Methods (4th ed.). Griffin.
- Sen, P. K. (1968). Estimates of the regression coefficient based on Kendall’s tau. Journal of the American Statistical Association, 63(324).
- Bates, J. M. & Granger, C. W. J. (1969). The combination of forecasts. Operational Research Quarterly, 20(4).
Projections are estimates, not guaranteed revenue. Methods are described at a general level; implementation details are proprietary.
The next decision starts here
Know what a cohort is worth, before it matures.
Choose the segment, read ARPU and forecast, check reliability and trend, compare with acquisition cost, decide where to invest.