Lieke
Neijens
Customer
Analytics,
Summary
Papers
1-‐8
!
PAPER
9
IS
MISSING:
COULD
NOT
FIND
THE
RIGHT
VERSION…
Paper
1
Fader
&
Hardie
2007a:
How
to
Project
Customer
Retention
Abstract
–
at
the
heart
of
any
contractual
or
subscription-‐oriented
business
model
is
the
notion
of
the
retention
rate.
An
important
managerial
task
is
to
take
a
series
of
past
retention
numbers
for
a
given
group
of
customers
and
project
them
into
the
future
to
make
more
accurate
predictions
about
customer
tenure,
lifetime
value,
and
so
on.
As
an
alternative
to
common
“curve-‐fitting”
regression
models,
we
develop
and
demonstrate
a
probability
model
with
a
well-‐
grounded
“story”
for
the
churn
process.
We
show
that
our
basic
model
(known
as
a
‘shifted-‐
beta-‐geometric’)
can
be
implemented
in
a
simple
Microsoft
Excel
spreadsheet
and
provides
remarkably
accurate
forecasts
and
other
useful
diagnostics
about
customer
retention.
We
provide
a
detailed
appendix
covering
the
implementation
details
and
offer
additional
pointers
to
other
related
models.
The
retention
rate
for
period
t
(rt)
is
defined
as
the
proportion
of
customers
active
at
the
end
of
period
t
–
1
who
are
still
active
at
the
end
of
period
t.
it
is
the
ratio
of
sequential
values
of
the
survivor
function.
The
churn
rate
for
a
given
period
is
defined
as
the
proportion
of
customers
active
at
the
end
of
period
t
–
1
who
dropped
out
in
period
t.
The
survivor
function,
denoted
by
S(t),
is
the
probability
that
a
customer
has
‘survived’
to
time
t
(i.e.
is
still
active
at
t).
The
expected
(or
average)
tenure
of
a
customer
is
simply
the
area
under
the
survivor
function.
Recalling
the
definition
of
a
retention
rate,
it
follows
that:
In
a
contractual
setting,
the
empirical
survivor
function
S(t)
is
simply
the
proportion
of
customers
acquired
at
Time
0
who
are
still
active
at
Time
t.
A
major
problem
in
using
the
empirical
survivor
function
to
compute
expected
tenure
or
lifetime
value
is
that
the
observed
time
horizon
is
often
quite
limited
The
standard
textbook
expression
for
(expected)
customer
lifetime
value
(CLV)
in
a
contractual
setting
that
(correctly)
reflects
the
phenomenon
of
non-‐constant
retention
rates,
can
be
written
as:
.
The
objective
of
this
article
is
to
present
an
alternative
approach
to
the
problem
of
projecting
the
survivor
function;
one
that
does
‘work’.
We
formulate
a
probabilistic
model
of
contract
duration
that
is
based
on
a
simple
story
of
customer
behavior.
The
resulting
model
offers
useful
diagnostic
insights
and
is
very
easy
to
implement
using
Microsoft
Excel.
1
Neijens
Customer
Analytics,
Summary
Papers
1-‐8
!
PAPER
9
IS
MISSING:
COULD
NOT
FIND
THE
RIGHT
VERSION…
Paper
1
Fader
&
Hardie
2007a:
How
to
Project
Customer
Retention
Abstract
–
at
the
heart
of
any
contractual
or
subscription-‐oriented
business
model
is
the
notion
of
the
retention
rate.
An
important
managerial
task
is
to
take
a
series
of
past
retention
numbers
for
a
given
group
of
customers
and
project
them
into
the
future
to
make
more
accurate
predictions
about
customer
tenure,
lifetime
value,
and
so
on.
As
an
alternative
to
common
“curve-‐fitting”
regression
models,
we
develop
and
demonstrate
a
probability
model
with
a
well-‐
grounded
“story”
for
the
churn
process.
We
show
that
our
basic
model
(known
as
a
‘shifted-‐
beta-‐geometric’)
can
be
implemented
in
a
simple
Microsoft
Excel
spreadsheet
and
provides
remarkably
accurate
forecasts
and
other
useful
diagnostics
about
customer
retention.
We
provide
a
detailed
appendix
covering
the
implementation
details
and
offer
additional
pointers
to
other
related
models.
The
retention
rate
for
period
t
(rt)
is
defined
as
the
proportion
of
customers
active
at
the
end
of
period
t
–
1
who
are
still
active
at
the
end
of
period
t.
it
is
the
ratio
of
sequential
values
of
the
survivor
function.
The
churn
rate
for
a
given
period
is
defined
as
the
proportion
of
customers
active
at
the
end
of
period
t
–
1
who
dropped
out
in
period
t.
The
survivor
function,
denoted
by
S(t),
is
the
probability
that
a
customer
has
‘survived’
to
time
t
(i.e.
is
still
active
at
t).
The
expected
(or
average)
tenure
of
a
customer
is
simply
the
area
under
the
survivor
function.
Recalling
the
definition
of
a
retention
rate,
it
follows
that:
In
a
contractual
setting,
the
empirical
survivor
function
S(t)
is
simply
the
proportion
of
customers
acquired
at
Time
0
who
are
still
active
at
Time
t.
A
major
problem
in
using
the
empirical
survivor
function
to
compute
expected
tenure
or
lifetime
value
is
that
the
observed
time
horizon
is
often
quite
limited
The
standard
textbook
expression
for
(expected)
customer
lifetime
value
(CLV)
in
a
contractual
setting
that
(correctly)
reflects
the
phenomenon
of
non-‐constant
retention
rates,
can
be
written
as:
.
The
objective
of
this
article
is
to
present
an
alternative
approach
to
the
problem
of
projecting
the
survivor
function;
one
that
does
‘work’.
We
formulate
a
probabilistic
model
of
contract
duration
that
is
based
on
a
simple
story
of
customer
behavior.
The
resulting
model
offers
useful
diagnostic
insights
and
is
very
easy
to
implement
using
Microsoft
Excel.
1
