A mobile freemium funnel is a chain of conditional probabilities. Starting from 10,000 installs, each stage keeps only the fraction that converts:
Paywall views = Installs · p_paywall
Trial starts = Paywall views · p_trial
Paid subs = Trial starts · p_paid
Overall conv. = p_paywall · p_trial · p_paid
Every dot falling through the 2D funnel is assigned that fate the moment it spawns — a single random draw against the three cumulative thresholds — so the stream visibly thins at each of the three gates in proportion to the sliders above, exactly matching the aggregate percentages in the readouts.
Subscribers who convert don't stay forever — each month a fixed fraction (the churn rate c) cancels. For a cohort of N₀ paying users, the number still subscribed after t months follows geometric decay:
N(t) = N₀ · (1 − c)^t (bar chart, 24 months)
LTV = price / c (perpetuity: Σ price·(1−c)^t for t=0..∞)
Payback (months) = CAC / price
- Paywall exposure / trial start / trial→paid — the three funnel gates; raising any one thins fewer dots at that ring and grows the paid-subscriber count downstream.
- Price & churn — churn alone sets subscriber lifetime; a lower churn rate stretches the retention bars and raises LTV directly (LTV ∝ 1/c), independent of price except as a multiplier.
- CAC — compared against monthly price to get the payback period: how many months of a single subscriber's revenue it takes to recoup the cost of acquiring them.
- Reseed — respawns a fresh 10,000-install cohort with the current rates so you can watch a whole batch flow through from the top.
- Drag / scroll on the funnel — pans and zooms the flow view; it doesn't change the math, only how closely you're looking at the gates.
This is the same funnel + retention-decay model behind ARPU, ARPPU and LTV:CAC dashboards used across the freemium, subscription and hybrid monetization strategies mobile apps actually ship with.