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Gamers have short attention spans

Using the same trace, we extracted the total session time of each player session contained in the trace. Figure 2 plots the session time distributions of the trace in unit increments of a minute % latex2html id marker 1471
{\thefootnote}. The figure shows, quite surprisingly, that a significant number of players play only for a short time before disconnecting and that the number of players that play for longer periods of time drops sharply as time increases. Note that in contrast to heavy-tailed distributions reported for most source models for Internet traffic; the session ON times for game players is not heavy-tailed. To further illustrate this, Figure 2(b) shows the cumulative density function for the session times of the trace. As the figure shows, more than 99% of all sessions last less than 2 hours.

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 $\beta$, $\eta$, and $\gamma$ and is shown below.

$f(T)=\frac{\beta}{\eta} ({\frac{T-\gamma}{\eta}})^{\beta-1} e^{-(\frac{T-\gamma}{\eta})^{\beta}}$

In this form, $\beta$ is a shape parameter or slope of the distribution, $\eta$ is a scale parameter, and $\gamma$ is a location parameter. As the location of the distribution is at the origin, $\gamma$ is set to zero, giving us the two-parameter form for the Weibull PDF.

$f(T)=\frac{\beta}{\eta} ({\frac{T}{\eta}})^{\beta-1} e^{-(\frac{T}{\eta})^{\beta}}$

Using a probability plotting method [22], we estimated the shape ($\beta$) and scale ($\eta$) parameters of the session time PDF. As Figure 2(a) shows, a Weibull distribution with $\beta=0.5$, $\eta=20$, and $\gamma=0$ 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 $\lambda$, 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 {\em higher} 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.

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