[MUD-Dev] Predictive models for churn in subscription based games

[Scott A. Farley]

In a previous incarnation (incarceration?) of my career I created
churn models for a wireless phone carrier. I was working with
pre-paid wireless products, where the customer had no contract or
obligation to continue service other then the USD$50 or so as a sunk
cost in the phone handset.  The average customer spent between $25
and $40 per month to purchase their airtime, usually on phone cards
in convenience stores, or via phone using a credit card.

I occurred to me that this is a roughly similar model to a retail
box MMO with a subscription so I thought I would share some
observations regarding churn models.

  - Definition of churn

    Churn is the percentage of total subscribers that discontinue
    service divided into the total population.  Usually it is
    expressed as a percent based on the population change from month
    to month.  An average monthly churn rate for wireless phones is
    around 5%.

    Churn should be calculated on the existing subscriber base and
    not include new subscriptions within the time period measured.
    The purpose of this metric is to understand the retention rate.
    How many existing customers at the end of January are customers
    at the end of February?

As a measure of retention, management would like to see a steady,
predictable rate of churn.  This allows for long term planning and
validates business assumptions regarding fixed costs like equipment.
My experience is that churn is rarely steady and that predicting the
spikes in churn before they occur goes a long way toward helping
planning and the viability of the specific subscription model.

  - Predictive models for churn

    My most successful predictive model for churn was based on two
    major factors, the size of the monthly 'add' population and that
    population's length of stay.  The easiest way to predict a
    future churn rate was to view the total population of
    subscribers as many discrete populations based on the service
    start month.  Each monthly population goes through a retention
    curve, where subscribers churn at an expected rate based on
    their length of service.

So if you add 10,000 subs in December, and you expect that 20% will
not pay past the first month, (your historical month one retention)
then you will have 2,000 subs leaving in January.  In February, the
expected churn for the December population drops to 8%, so you need
to predict a loss of 8,000 *.08 = 640 subs leaving 7,360 in the
December population.  The retention rate curve usually declines over
the length of service for wireless phones, so for this fictitious
population, March might be 6%, then every month for next 4 might be
5%, then 4% for the next 6 months, etc.  The December population can
only decline over time as more and more of it's members drop their
subscriptions.  For MMOs, I expect there is a serious spike in churn
after some period of time as players simply grow tired of the game.

The basic tenet of this model is that churn spikes for the entire
subscriber population are driven by churn spikes for specific
populations, based on subscription start, aged along an expected
retention curve.  By creating individual populations based on month
of initiation and aging those populations over time, very accurate
models of future retention can be made.

Measuring the effects of market changes or promotions to the
retention curves of each specific population is the true value of
churn analysis.  For MMOs, I would guess that developing age-based
retention projections is also the hardest part of predicting future
churn.

FWIW, always discount February churn numbers, since it has 10% less
days in the numerator of the churn calculation!

SAF


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