Unlike the player patience data, session times can not be fitted
with a simple negative exponential distribution.
However, the data can be closely matched to a Weibull distribution, a more
general
distribution that is often used to model lifetime distributions in reliability
engineering [22].
Since quitting the game can be viewed as an attention ``failure'' on
the part of the player, the Weibull distribution is well-suited for
this application.
The generalized Weibull
distribution has three parameters ,
, and
and is shown
below.
In this form, is a shape parameter or slope of the distribution,
is a scale parameter, and
is a location parameter.
As the location of the distribution is at the origin,
is set
to zero, giving us the two-parameter form for the Weibull PDF.
Using a probability plotting method [22], we estimated
the shape () and scale
(
) parameters of the session time PDF.
As Figure 2(a) shows, a Weibull distribution
with
,
, and
closely fits the PDF of
measured session times for the trace.
This result is in contrast to previous studies that have
fitted a negative exponential distribution to session-times of multiplayer
games [23]. Unlike the Weibull distribution
which has independent scale and shape parameters, the shape of the
negative exponential distribution is completely determined by , the
failure rate. Due to the memory-less property of the negative exponential
distribution, this rate is assumed to be constant.
Figure 3 shows the failure rate for individual
session durations over the trace. As the figure shows, the failure rate
is
for flows of shorter duration, thus making it difficult to
accurately fit it to a negative exponential distribution.
While it is difficult to
pinpoint the exact reason for this, it could be attributed to the fact
that Counter-Strike servers are notoriously heterogeneous. Counter-Strike
happens to be one of the most heavily modified on-line games with
support for a myriad of add-on features [24,25].
Short flows could correspond to
players browsing the server's features, a characteristic not predominantly
found in other games. As with player patience, it may be possible to
fit a negative exponential for longer session times.
As part of future work,
we hope examine this as well as characterize session duration
distributions across a larger cross-section of games
to see how distributions vary
between games and game genres.