From analysis to a testable simulation
Three stages build on each other. The fourth step does not happen in the browser.
The fourth step happens inside the publishing house: after a measure is introduced, the simulated trajectory is compared with measured reality. If reality deviates, the assumptions were wrong, and the measured deviation is not a flaw of the method but its yield.
What a tenth of a point of churn is worth
The churn rate works like an interest rate: small monthly changes compound over time into sizeable shifts in subscriber base and customer value. Baseline and measure use the identical formula. Only the rate differs.
Every slider is an assumption, not a fact. All initial values are fictional examples: no customer data, no industry benchmarks.
Calculation: base(t+1) = base(t) × (1 − rate) + new subscriptions. Customer value = ARPU × (1 − (1 − rate)^horizon) / rate. Equilibrium base = new subscriptions / rate. Both curves start at the equilibrium base of the baseline. Assumption: constant monthly churn rate per scenario, no ageing and no cohort effect.
After a measure is introduced, the survival curves of real starting cohorts are compared month by month with the simulated survival.
Subscriber forecast with an uncertainty band
A forecast that shows its uncertainty can be measured against reality once a measure is introduced. Here, 2,000 simulated trajectories run per scenario; the random generator starts from a fixed seed, so every visit shows the same result.
Calculation: for each path and month the churn rate is lognormally distributed around the set median, new subscriptions are normally distributed and truncated at zero; months are independent. 2,000 paths, fixed random seed. Reproducibility is part of the method.
The actual base is placed into the band month by month. If it repeatedly falls outside, that speaks against the assumptions, and the deviation itself is the finding.
Price increase and introductory offer
Two pricing questions, one tool: Can the base carry an increase? And what does an introductory discount cost on the day of the switch to full price?
Calculation, part A: quantity response = elasticity × price change. Revenue factor = (1 + price change) × (1 + elasticity × price change). Linear elasticity only holds for small price changes. Part B: full price and churn rate come from simulation 01; at the switch to full price the set share cancels additionally. The share who would have subscribed without the discount cannot be observed without a control group, so here it remains a pure assumption.
Price test staggered or per segment: the realised churn rate after the increase yields the actual elasticity; the measured switch cancellation replaces the assumption.
Paywall: scenario A versus scenario B
This simulation claims no relationship between meter height and conversion rate, because such a curve only emerges from your data. You set both scenarios yourself; only the consequences of your assumptions are calculated.
Calculation: new subscriptions per month = users × share at the limit × conversion rate. Subscription revenue = 12 monthly cohorts of one year, each calculated over its first 12 months, with survival, ARPU and churn rate from simulation 01. Advertising revenue = page views × eCPM / 1,000 × 12; page views = 8 per user and month (assumption), reduced under scenario B by the set decline.
Meter test on a random segment: the measured conversion rate and the measured reach loss replace the sliders.
What this page assumes, fully disclosed
Every number on this page follows arithmetically from the slider values. In addition:
- Constant churn rate: constant over time per scenario, no ageing and no cohort effect.
- Linear elasticity: only holds for small price changes; the value is your input, not an industry figure.
- Monte Carlo: churn rate lognormally distributed, new subscriptions normally distributed and truncated at zero, independent months, 2,000 paths, fixed random seed.
- Paywall: no relationship between meter height and conversion rate is claimed. Both scenarios are your assumptions; only their consequences are calculated.
- Example values: all initial values are fictional, with no customer data, no measurements and no industry benchmarks.
- Nominal revenue: without costs, without discounting, without VAT, before payment defaults.
- Unobservable quantities: the share who would have subscribed without the discount cannot be observed in the individual case; without a control group it remains an assumption.
This page is a basis for conversation, not an offer. All values are model calculations based on freely adjustable assumptions; no number is a commitment, a forecast for a specific publishing house or an industry figure.
In a real project your data replaces the sliders: your cohorts provide the churn rates, your price tests the elasticity, your meter test the conversion rates. The calculation paths stay the same.