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

Previous Research – Rocky MUD cont. Measured by four variables: – inter-arrival times – avatars’ transition between different regions – region stay times – session lengths 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 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 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 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) Number of players fluctuated in a diurnal pattern; 5x increase in the number of players between 4am and 6pm. Session times appeared to follow a power-law distribution where approximately 50% of the gamers remain online for 10 minutes or less. 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 Session time 10mins 1 hour5 hours 7043 gamers

How does this paper solve the problem? 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, 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: 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). 50% of users will subscribe for longer than 500 days.

Consecutive Game Play: 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?: 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 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 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. 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.

Figure 5

Predictability Analysis: Long Term 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.