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October 31, 2005

Guilds: Densities

Server Sample: RP (High), PvE (Medium), PvE (High), PvP (High), PvP (High)
Sampling Period: 8/01/2005 12:00 am - 8/30/2005 12:00 am
Sampling Resolution: ~12 minutes
Parsing Method: The sample unit is each unique guild. See also entry on how we derived these social network measures.
Data Filter: None
Sample Size: 5569 guilds

As another measure of guild cohesiveness, we implemented a measure of density - that is to say, given the matrix of all characters in a guild, how many of those cells are filled. For example, a percentage of 25% (using the co-presence metric) means that on average over the month of August, each guild member has been online at the same time with 25% of other guild members at least once. But this also means that on average, each character was never online at the same time as 75% of other guild members over the period of the month.

We ran our analyses for both the co-presence and the co-location metric. Furthermore, we analyzed the data either: 1) with all observed connections, 2) excluding connections with a weight of one (observed only once over a month - approximately 12 minutes), and 3) excluding connections with a weight less than 3 (observed only once or twice over a month - approximately 24 minutes).

There are several weaknesses we'd like to mention up front. First, alts of the same player who are in the same guild can by definition never be co-present or co-located. So presumably, this has an effect on our results as the guild size increases when alts are more frequent. Secondly, characters who switch guilds are counted on the rosters of both guilds for the analysis. So this too may artificially deflate our results.

Still, the overall guild densities were lower than we would have expected. The result indicates that in an average guild in WoW - the average guild has a mean size of 26 and a median size of 10 - over a period of a month, every guild member is co-present with only 30% of his/her guild. In other words, the average guild member is never co-present with 70% of his/her guild members over the period of one month. But if we choose a more conservative co-presence filter (only counting those members who have been co-present for more than 20 mins over the period of a month), the percentage drops by one-third. The average guild member in WoW, over a period of one month, is never online for more than 20 minutes at the same time as 80% of other members of his/her guild.

As a proxy for collaboration, the co-location metric lets us get a sense of how often guild members work together. The analysis shows that over a period of a month, the average guild member collaborates with 11% of his/her guild members for at least 10 minutes. In the table below, "Co-Loc > 1" means counting those members who were co-located for more than 1 time sample (~12 mins).

Here are the two tables for the guild densities analyzed by guild size.

We also calculated whether guild densities correlate with guild size. The co-presence metric does correlate around .21 - .25, but this measure must correlate with guild size - after all, the more dice you roll, the more likely that two will be the same number. The correlation with the co-location metric is more interesting. It does not significantly correlate with guild size. In other words, guild members in large and small guilds are just as likely to work with other members. This raw measure doesn't give a sense of true frequency though. However, this is congruent with our finding that members of large guilds do not spend more time together than members in smaller guilds. Although, again, this may simply be confounded with increase in alts in larger guilds who by definition can never be co-present or co-located.

Posted by nickyee at 05:45 PM | Comments (0) | TrackBack

October 24, 2005

Guilds: Max Subgraph Size

Server Sample: RP (High), PvE (Medium), PvE (High), PvP (High), PvP (High)
Sampling Period: 8/01/2005 12:00 am - 8/30/2005 12:00 am
Sampling Resolution: ~12 minutes
Parsing Method: The sample unit is each unique guild. See also entry on how we derived these social network measures.
Data Filter: None
Sample Size: 5569 guilds

A subgraph in a social network is a self-contained group of individuals who are interconnected. For example, in the example social network below (using the co-location metric), there are 5 subgraphs - 4 of which are dyads and 1 subgraph containing 6 members. The max subgraph in a social network is the subgraph with the most members. Thus, the max subgraph size in the example is 6.

The max subgraph size of each guild gives a rough sense of cohesiveness. If most members of a guild often do group and work together, they would have a large max subgraph size. In the example shown above, the low max subgraph size relative to the guild size (6 vs. 37) implies that the guild is fairly fragmented and not cohesive.

Unsurprisingly, larger guilds have larger max subgraph sizes. The correlation is r = .63.

But as a function of the guild size, the ratio itself is only weakly correlated with guild size, r = -.08. To a certain extent, this is partly due to the presence of alts who by definition cannot be co-located with the mains.

Plotting this out allows us to see more clearly that there is a steady rise in max subgraph size that essentially starts fluctuating past a guild size of 50. We could almost argue that maximum guild cohesiveness occurs at a guild size of around 50. After that point, it starts getting hard for a guild to remain cohesive.

Plotting this out by subgraph ratio (max subgraph size / guild size) shows a more dramatic trend. The subgraph ratio peaks at around 10 at .50 and drops steadily to below .10. The plot also shows that the correlation between guild size and subgraph ratio is strong only after a guild size of 10. Re-running the correlation after excluding guilds with less than 10 members, we find a correlation of -.36. Again, the larger the guild, the harder it is to remain cohesive.

Posted by nickyee at 01:29 PM | Comments (4) | TrackBack

October 18, 2005

Guild Members: Time Spent Together

Server Sample: RP (High), PvE (Medium), PvE (High), PvP (High), PvP (High)
Sampling Period: 8/01/2005 12:00 am - 8/30/2005 12:00 am
Sampling Resolution: ~12 minutes
Parsing Method: The sample unit is each unique character. Each character was tracked across the server logs. Total playing time, lowest observed level, highest observed level, guild affiliation, and zones seen in were parsed.
Data Filter: None
Sample Size: 241,378 characters

From the social network analyses, we had connection frequencies between any two members in all observed guilds. This data allowed us to explore the average amount of time any two members from the same guild are observed together (co-location metric) over a period of a month. In other words, how much time do guild members actually spend working with each other?

We looked at the data in two ways. In our first pass, we looked at the data for every member of the same guild. In other words, the question we were asking was - over a period of a month, what's the average amount of time any two members of the same guild spend together? We also analyzed this data for guilds of different sizes. Interestingly, the result was largely constant across guilds with more than 5 members - with a median between 6 and 9 minutes over a period of a month. The amount of time members in a guild spend together doesn't appear to change as a function of guild size (r = -.02).

We then redid the analysis but only included those dyads in each guild that did spend time together. In other words, the question we were asking was - over a period of a month, for those members of the same guild that spend time together, what is the average amount of time they spend together? Again, we see the same pattern, the result was largely consistent across different guild sizes - the median hovering around 80-87. The correlation between guild size and time spent together was again very weak (r = .04).

While the results seem low, remember that this is the average for all possible dyads within a guild. It's the average amount of time any 2 members of the same guild will spend together in a month. In a guild with 5 people, member A is thus expected to spend about 15 minutes each month with each of the other 4 members.

Posted by nickyee at 02:22 PM | Comments (5) | TrackBack

October 07, 2005

Mapping Social Networks

Server Sample: RP (High), PvE (Medium), PvE (High), PvP (High), PvP (High)
Sampling Period: 8/01/2005 12:00 am - 8/30/2005 12:00 am
Sampling Resolution: ~12 minutes
Parsing Method: The sample unit is each unique character. Each character was tracked across the server logs. Total playing time, lowest observed level, highest observed level, guild affiliation, and zones seen in were parsed.
Data Filter: None
Sample Size: 241,378 characters

We've been working on social network data at the guild level and would like to give an overview of our approach before getting into the gory details of what we've found. As many of you already know, there are only a few variables that we are able to get at from the client-side, so actual character interaction is something we must approximate via proxy metrics. We'd like to describe the metrics that we have used, but please do not hesitate to suggest others that would be possible with the set of variables the client-side currently has access to.

Guild Roster: Over the sampling period, we generated a list of all guilds we observed. Then we generated a roster for every guild consisting of every character who has been observed to have that guild tag.

Co-Presence Metric: In each snapshot, find all members of each guild that are online. For each observed pair, increment the connection weight between these two characters by 1. In other words, this metric tabulates overall guild co-presence - the frequency at which members of a guild are online at the same time.

Co-Location Metric: In each snapshot, find all members of each guild that are online and in the same zone (and only if the zone is not a main city zone). For each observed pair, increment the connection weight between these two characters by 1. In other words, this metric serves as a proxy for collaboration - the frequency at which members are working together at the same time.

We've found that the co-location metric provides more readable and comprehensible graphs and have used this metric for most of our analyses. Below, we present some social networks of guilds constructed using the co-location metric. We have removed the names of characters but left in their class and level information.

In the following social network graphs, connection weights are based on the co-location metric (with a minor threshold applied to exclude very weak ties). The weight of each line implies the collaboration frequency over the sampling period. Each node is marked by the character's class and level progression over the sampling period. The more connections a node has, the more central it is placed in the graph itself. Characters who were never co-located with others during the sampling period are depicted as free-floating nodes. All 4 guilds depicted had between 40-50 members. Therefore, the connection weights themselves are directly comparable between the guilds.

The social network in these 4 guilds are somewhat different. In the top-left example is a fairly low-level guild. Most of the members are in the mid 20's. It appears that most guild members do not play with each other. In the top-right example is a mostly high-level guild where most members do work together. It is easy to pick out the pairs that seem to work together the most (such as the mid-level druid and mage).

In the bottom-left example, we have a guild where we see more distinct cliques. There's a somewhat hard-core 4 character cluster on the left-hand side, a mid-level triad on the bottom left, a mid 20's clique that's held together by the druid in the middle, and finally a more casual low-level clique on the top right.

Posted by nickyee at 11:36 AM | Comments (16) | TrackBack

October 03, 2005

Grouping and Guild Recruitment

Server Sample: RP (High), PvE (Medium), PvE (High), PvP (High), PvP (High)
Sampling Period: 8/07/2005 12:00 am - 8/14/2005 12:00 am
Sampling Resolution: ~12 minutes
Parsing Method: The sample unit is each unique character. Each character was tracked across the server logs. Total playing time, lowest observed level, highest observed level, guild affiliation, and zones seen in were parsed.
Data Filter: None
Sample Size: 148,846 characters

There was another aspect of guild recruitment that we were interested in exploring. We wondered whether most guild recruitment events could be attributed to grouping. In other words, do unguilded characters get recruited into guilds primarily because they group up with someone who is in a guild? Or do most guild recruitment events occur outside of a grouping situation?

To address this question, we built upon the guild recruitment location data:

Grouping Status During Guild Recruitment Event: For each guild recruitment location, check whether the character is in a group or not when they are observed to be in a new guild.

Here are the raw percentages for each zone type. Given that most guild recruitment occurs in main cities and outdoor zones, this implies that most characters are recruited into a guild when they are not grouped.

To get a more direct number, we took the guild recruitment location data and multiplied it by the percentage grouped data. Of all guild recruitment events, about 39% occur when a character is grouped, and 61% occur when a character is ungrouped.

Posted by nickyee at 10:42 AM | Comments (3) | TrackBack