Estimating Daily Active Users (DAU) Using New Users and Retention Modeling

Introduction

New users, retention, and daily active users (DAU) are common product metrics. The article poses two typical forecasting questions: (1) How many DAU can we expect next quarter based on current trends? (2) Is a proposed daily new‑user target realistic for achieving a specific quarterly DAU goal?

DAU as an Accumulation Process

Stacking Concept

Any day's active users are the sum of historical daily new users that have survived through retention decay. New users start to decay from the second day after acquisition; the earlier the acquisition, the smaller the remaining proportion.

The accompanying diagram (not shown) illustrates how each day's new users contribute to the current DAU as vertical slices.

Notation

To avoid verbosity, the following symbols are defined (images represent the symbols):

t – current day in the product’s history.

T – future day whose DAU we want to estimate.

N(t) – new users on day t.

R(t, d) – retention rate of users acquired on day t after d days.

The target estimation equation is then expressed using these symbols (image).

Required Input Data

Daily new‑user count (historical values are known; future planned values are input directly).

Retention rate for each cohort after a given number of days (unknown and needs to be modeled).

The core problem reduces to determining the retention‑decay function.

Challenges with Historical Retention

Two issues arise:

Retention rates have changed over the product’s three‑year history, making simple averages unreliable.

Long‑term forecasts (e.g., six months ahead) require retention data beyond the observed history.

Short‑Term vs. Long‑Term Retention

Short‑Term Variation

Caused by channel expansion or operational campaigns; can be approximated with recent averages.

Long‑Term Variation

Driven by product iterations and evolving user habits; maintaining a full cohort‑by‑cohort retention matrix is computationally heavy and may not reflect future trends.

Proposed Solution

Separate the retention contribution into two parts using the current day as a split point. The first part uses recent (e.g., one‑year) average retention, while the second part models the decay beyond the stable period.

For the stable period, the retention‑decay ratio (R i /R i+1 ) becomes approximately constant, suggesting an exponential decay. Before the stable period, a power‑law function fits better.

Both segments are fitted to historical samples:

Apply a logarithmic transformation to obtain linear relationships.

Estimate parameters via least‑squares regression.

Optimize using Adjusted R‑squared and grid search.

The resulting piecewise function (image) captures both early‑stage and stable‑stage decay.

Final Model

The model outputs the estimated DAU for any future day T as a function of:

Current day’s DAU decomposition (image).

Planned daily new‑user numbers for the forecast horizon.

Recent retention‑rate series (e.g., one‑year sample).

Compared with the simple heuristic “DAU / New Users”, the model provides controlled inputs and reduces sensitivity to historical fluctuations.

Conclusion

The presented methodology enables more reliable DAU forecasting by explicitly modeling new‑user accumulation and retention decay, handling both short‑term variations and long‑term trends through a combination of recent averages and curve‑fitted decay functions.