For a measure of advancement, we used the following:

Standardized Character Advancement Score: A character's raw advancement is simply the number of levels the character has advanced. In this case, we subtracted the starting level from the ending level (end of month - beginning of month). The problem is that over a two week period, a 10 level advancement by a level 1 character is much less significant than a 10 level advancement by a level 50 character. In other words, the advancement needs to be qualified by the starting level somehow. The method we used to standardize character advancement was to calculate the average (and standard deviation) of advancement for every starting level. In other words, compared with other characters who also started at level 10, were you above, below, or right on the curve? Mathematically, we did this by calculating the z-score of advancement for every character. Characters who were already level 60 at the beginning of the sampling period were excluded. See this article for more details.

Standardized Guild Advancement Score: As a measure of guild performance and achievement, we averaged the standardized advancement scores of every member in that guild. This guild score was thus how much the guild as a whole advanced during the sampling period. Again, characters who were already level 60 at the beginning of the sampling period were excluded.

A multiple regression showed that the guild metrics from the first 10 days of the month were better predictors than guild metrics from the last 10 days of the month (r-squared = .18 vs. r-squared = .08).

Using only the guild metrics from the first 10 days of the month, we find that the size of the guild is negatively correlated with guild advancement. The bigger a guild is, the slower the members level. Intriguingly, the best positive predictor of guild advancement was not max subgraph size or density but the number of subgraphs with size greater than 3 (referred to in table below as masscount). And the total number of subgraphs was far weaker of a predictor. In other words, dyads don't help and it's really the number of subgraphs with 3 or more members in a guild that helps.

So the numbers are saying that how interconnected a guild is helps but it's got to be interconnected in the right way. The crucial thing seems to be having separate subgraphs that cater to different level bands within your guild that facilitate teaming and leveling throughout your guild. This seems like a reasonable explanation for what the masscount correlation is showing. Our analysis with guild metrics from different times of the month also show how dynamic this influence is. The guild metrics at the beginning of the month were better predictors than those at the end of the month.

The bottom-line seems to be that large guilds do not facilitate character advancement unless they are well-connected and have clusters of guild members for different level ranges.

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; 3,335 guilds