Formula
Remaining players = Starting cohort × (Retention rate)Periods
Cumulative retained player-periods sum the expected retained cohort after each modeled period.
What the result means
The forecast gives an expected cohort size if the same retention factor repeats every period. A retained player-period represents one player retained for one modeled interval.
Actual retention usually changes with cohort age. Replace the constant-rate assumption with observed period-by-period rates for operational forecasting.