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 held against 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 held monthly against 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 - 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 - 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 - 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 - 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 - no customer data, no measurements, 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.