How much of your engagement is feeding itself?

What the dials do

Outside drive is life: the flow of sessions that would happen with no loop at all. Loop strength is the number this whole page exists to introduce — the branching ratio: how many further sessions one session causes, on average. At 0, every session is an independent visit; the game is something the player picks up. As it rises toward 1, each session recruits the next — bursts stretch, quiet gaps thin, and an ever-larger share of the activity is the system’s own echo. At 1 the process crosses into a cascade regime that no longer needs the outside world at all. Watch the third statistic as you push the slider: total sessions grow as 1/(1 − n) — the loop’s multiplier on every hour life happens to supply.

This way of reading activity — split it into an exogenous stream and a self-excited echo, and measure the echo’s share — comes from the mathematics of self-exciting point processes (Hawkes, 1971), and the echo-share reading was developed for financial markets, where it is called reflexivity (Filimonov & Sornette, 2012). Applied to a live-service game, it asks a question a retention dashboard cannot: of all this engagement, how much is the game being loved, and how much is the loop echoing?

Now turn on the calendar

Flip the content calendar toggle. Amber bands appear — seasons, patches, double-XP weekends — and each one drives a surge of outside sessions. Here is the trap: to the eye, and to a naïve fitted model, those surges are indistinguishable from self-excitation. A moving baseline wears the loop’s costume. The bursts look endogenous; the true loop strength has stayed exactly where your slider left it — the first statistic doesn’t move, because we know the ground truth. On real telemetry nobody knows the ground truth, and a model fitted with a flat baseline will book the whole calendar as loop (Wheatley, Filimonov & Sornette, 2016).

A live-service platform runs the loudest exogenous calendar in consumer software — which is precisely what makes the problem tractable there. Unlike a financial market, the game’s outside shocks are observed, timestamped, and the studio’s own: the calendar can enter the model as measured covariates. The confound that sinks the naïve read elsewhere is, on a game, a thing you already have in a spreadsheet.

Why the number matters

Two games with identical daily actives can sit in opposite regimes. In a schedule-driven world (low loop strength), engagement is governed by the calendar and the baseline: players come when life and the season bring them, and the lever that holds them is the quality of what they find. In a loop-driven world (high loop strength), engagement increasingly manufactures itself — and readings you’d trust in the first regime, a green dashboard above all, mean something different in the second. Which regime each mode of your game sits in is measurable. It is also, for most games, unmeasured.