An Analysis of WoW Players’
Game Hours
Matt Ross, Christian Ebinger,
Anthony Morgan
What problem is the paper trying to solve?
• Predicting how long players will stay once they join a
game by predicting players online gamers’
subscription time (length of time since he/she first
joined the game to the time of his/her last login).
Why is it important?
• Predict gamers’ gaming hours and unsubscription
decisions.
• With this companies can predict future revenue
generated from game subscriptions and can also
predict what are the main usage time of the servers.
Previous Research – Rocky MUD
• Medieval Fantasy MMOG (massive multiplayer online
game) developed in 1993
• Players advance their character, their way
• No arbitrary classes or levels, and unlimited power
• Built-in/live quests, hundreds of mini-quests
• Advanced tactical interface
• Massively unique, destinies and fighting styles
http://www.topmudsites.com/forums/mudinfo-rockymud.html
Previous Research – Rocky MUD cont.
• Measured by four variables:
– inter-arrival times
– avatars’ transition between different regions
– region stay times
– session lengths
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Inter-arrival times – time between the arrival of one gamer and the arrival of
the next gamer
Avatars’ transition between different regions – movement from one regional
location to another
Region stay times – time a gamer spent in a particular regional location
Session lengths – time a gamer played in one sitting
Terms Defined
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Inter-arrival times of game sessions follow an exponential distribution
Transition of avatars between different regions modeled by a
first-order Markov chain
Region stay time best modeled by Pearson distribution
Session length described by Pareto distribution
Exponential distribution - a process in which events occur continuously and
independently at a constant average rate.
First-order Markov chain - the next step only depends on the current state of
the system, and not additionally on the state of the system at previous steps.
Pearson distribution – is a family of continuous probability distributions.
Pareto distribution - the Pareto principle or the "80-20 rule" says that 20% of
the population controls 80% of the wealth; (20% of players have longest 80%
session times)
Behavior Study of Counter-Strike
• Two issues:
– users’ satisfaction with a game
– predictability of the game server’s work load
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Found that it is extremely difficult to satisfy users
Users have short attention spans, session times are usually < 1 hour
Number of users on different servers follows a power-law distribution
Server workloads exhibits predictable patterns in terms of day and week
scales, but the predictability diminishes with larger time scales.
World of Warcraft traces
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Conjectured that at least four types of information are required to establish a
prediction model:
– server’s population changes over time
– arrival rate and session duration of players
– spatial distribution of avatars in the virtual world
– movements of avatars over time (how many distinct regions the avatars visit
and how long they stay in a region)
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Number of players fluctuated in a diurnal pattern; 5x increase in the number of
players between 4am and 6pm.
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Session times appeared to follow a power-law distribution where approximately
50% of the gamers remain online for 10 minutes or less.
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Number of players versus the rank of each zone, from the most populated to the
least populated, exhibited a power-law relationship.
Power-law distribution
• Session times followed a power-law distribution where
approximately 50% of the gamers remain online for 10
minutes or less.
Gamers online
7043
gamers
10mins
1 hour
Session time
5 hours
How does this paper solve the problem?
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Collected their traces by using the who command with different races, professions,
and levels. Automated process that happened every 10 minutes with a character
that remained connected at all times (ran for 2 years).
Monitored 664 days, 34521 accounts were observed. Only 7,043 remained active
for more than 30 days (Indicates that most accounts were never used after the
free trial period expired)
Only going to focus only on the 7043 accounts who subscriptions periods are
longer than 30 days.
Analyze Four Categories:
– Subscription Time
– Consecutive Game Play
– Daily Activities
– When Do Gamers Play
Subscription Time:
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Used the Kaplan-Meier estimator
which takes account of the
censored status (started playing
before and after measurements) of
each subscription periods, to
estimate the distribution of
players’ subscription times.
– Kaplan-Meier estimator’s output
is called the survival function
(reduces to the cumulative
distribution function if none of the
subscription periods are
censored).
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50% of users will subscribe for
longer than 500 days.
Consecutive Game Play:
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Consider the distribution of consecutive
game play days in order to understand the
extent of addiction of WoW gamers.
ON period defined as a group of
consecutive days during which a player
joins the game everyday.
OFF period as the interval between two
ON periods.
OFF periods slightly longer than ON
periods on average, but the difference is
insignificant.
Probabilistically around 80% of gamers’
ON OFF periods are shorter than 5 days.
3% of OFF Periods are longer than 1
month
1% longer than 3 months.
Forces another look at sessions (ON
PERIODS) and vacations (OFF Periods
longer than 30 days) [Chart b]
•Vacations generally longer then sessions
difference is not significant.
•50% of sessions are longer than 60 days.
Less than 20% of vacations are longer
than 180 days, only 20% of people
returned to the game after a vacation that
long.
•20% of the seasons are shorter than 10
days.
When Do Gamers Play?:
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Occurred during the night, day
weekday or weekend.
Thought game play would be
higher on weekend then on
weekday. Slightly true but
difference is not significant.
Obvious difference between the
number of gamers during night
hours and morning hours.
– Rapid increase around
6:00pm, start to play right
after work. Peek at 10:00pm to
midday, lowest from 5am to
7am.
Number of gamers increase
between 6am – 10 pm.
Predictability Analysis: short term
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Summary of players’ short-term behavior:
– Average session time
– Average daily session count
– Average daily playtime
Possible correlation with players’ long-tem behavior:
– Average length of ON periods
– the Average season length
– the overall subscription time
Fig. 5 shows the plots of the correlations between the three short-term behavioral
factors and the three long-term behavioral factors.
Predictability Analysis: short term
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We observe that the lengths of the average ON periods are moderately correlated with all
the short term behavioral factors, and the average daily play time has the strongest
predictability.
– Fig. 5(c) shows that, if players’ average daily game time is shorter than 1 hour, then their
average ON periods will probably be less than 2 days.
– On the other hand, the average daily playtime of highly addicted players can be as high
as 10 hours, and they may play the game for more than 20 days without interruption.
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However, it is clear that the average length of seasons and the overall subscription
time do not correlate with all the short-term behavioral factors.
Since this indicates that players’ interests may change significantly over time, we
cannot simply use an overall average of players’ short-term behavior to predict
their long-term game play behavior.
Instead monitor the evolution of players’ game hours over time and keep track of
their interest in the game in order to accurately predict when unsubscription will
occur.
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Figure 5
Predictability Analysis: Long Term
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Examine whether players’ game play behavior in one time period will be carried
over to the following period.
As shown in Fig. 6, five types of time periods are considered:
– session
– day
– Week
– ON period
– season.
Not surprisingly, the overall playtime between consecutive weeks exhibits the
strongest autocorrelations among all the time scales we consider.
Session time and daily playtime are also strongly auto-correlated; however, the
magnitude is not as strong as that of weekly playtime.
Figure 6
Authors Solution
• Short Term:
– Prediction is feasible
• Long Term:
– Much more difficult
– Players’ interest in the game may increase or
decrease over time.