Exploring Guilds

Introduction

The report uses the World of Warcraft Avatar History dataset available at Kaggle and was intended to be published as a kernel on Kaggle. However, unfortunately Kaggle upholds a runtime limit of 20 minutes for kernels, which was not enough to run the report.

Codes are available at https://github.com/posfaig/wow.

The report focuses on guilds, especially on the dynamics of guilds, that is how guilds change over time, how avatars enter or leave guilds in the game.

Many of the ideas, used R packages, code snipets came from other analyses, like the analysis of Thiago Balbo, 33Vito and others. Their contributions were a huge help in making this report. So many thanks.

Initial Setup, Data Import, Auxiliary Variables

library(lubridate)
library(stringr)
library(data.table)
library(dplyr)
library(ggplot2)
library(plotly)
library(visNetwork)
library(scales)
library(lazyeval)
library(dygraphs)
library(tidyr)

set.seed(0)
data_dir <- "../../../data/raw/"

#wow <- tbl_df(fread("../input/wowah_data.csv"))  # For Kaggle kernel
wow <- tbl_df(fread(paste(data_dir, "wowah_data.csv", sep = "")))

## 
Read 20.3% of 10826734 rows
Read 32.2% of 10826734 rows
Read 43.9% of 10826734 rows
Read 52.6% of 10826734 rows
Read 69.4% of 10826734 rows
Read 86.7% of 10826734 rows
Read 10826734 rows and 7 (of 7) columns from 0.599 GB file in 00:00:09

names(wow) <- trimws(names(wow))
wow$race <- gsub(" ", "", wow$race, fixed = TRUE)
wow$charclass <- gsub(" ", "", wow$charclass, fixed = TRUE)

# Create a new column for identifying avatars
wow$avatar <- with(wow, paste(char, race, charclass, sep = "."))

# Other columns
wow$timestamp <- mdy_hms(wow$timestamp)
wow <- arrange(wow, timestamp)
wow$current_date <- as.Date(wow$timestamp)
#wow$hour <- hour(wow$timestamp)
#wow$month <- format(wow$current_date, "%b")
# Create a new column with the activation date of each avatar
wow <- wow %>% group_by(avatar) %>% mutate(activation_date = min(current_date)) %>% group_by()

# Create new column for identifying avatars that were created during the observed period (i.e. avatars who were seen at level 1, or level 55 for Death Knight avatars)
wow <- wow %>% group_by(avatar) %>% mutate(new_avatar = (min(level) == 1 | (min(level) == 55 & charclass[1] == "DeathKnight"))) %>% group_by

min_date <- min(wow$current_date)
max_date <- max(wow$current_date)
race_names <- unique(wow$race)
charclass_names <- unique(wow$charclass)

Basic Characteristics

How many different guilds were observed?

wow %>% filter(guild >= 0) %>% summarise("Number of guilds" = n_distinct(guild))

## Source: local data frame [1 x 1]
## 
##   Number of guilds
##              (int)
## 1              419

Number of avatars who were member of at least one guild:

avatar_count_guilds <- nrow(wow %>% filter(guild >= 0) %>% distinct(avatar))
avatar_count_no_guilds <- length(unique(wow$avatar)) - avatar_count_guilds
c("Was member" = avatar_count_guilds, "Never joined" = avatar_count_no_guilds)

##   Was member Never joined 
##        12127        26204

Percentage of avatars who were in a guild at least once on a certain level by levels:

ggplotly(wow %>% group_by(level, avatar) %>%
    summarise(in_guild = max(guild) >= 0) %>%
    summarise(in_guild_percent = sum(in_guild) / length(unique(avatar))) %>%
    ggplot(aes(x = level)) +
    geom_line(aes(y = in_guild_percent), color = 'steelblue') +
    scale_y_continuous(labels = percent_format()) + 
    theme_bw() + labs(title = "Percentage of Avatars in Guilds by Levels", x = "Level", y = "Percentage of Avatars in Guilds"))

There is a significant drop at level 55, which is presumably caused by the Death Knight class (introduced in WotLK, Nov 13, 2008), which starts at level 55.

Distribution of the number of different guilds avatars were part of:

wow %>% 
    group_by(avatar) %>%
    summarise(number_of_guilds = n_distinct(guild)-1) %>% 
    arrange(desc(number_of_guilds)) %>%
    ggplot(aes(x = number_of_guilds)) + geom_density(color = "steelblue", fill = "steelblue", alpha = 0.6) + 
    theme_bw() + 
    labs(title = "Distribution of the Number of Different Guilds Avatars Were Member of", x = "Number of Different Guilds", y = "Density")

At what level avatars enter their first guild (only for new avatars):

wow %>% filter(new_avatar & guild >= 0) %>% group_by(avatar) %>%
    summarise(lvl_at_first_guild = min(level)) %>% 
    ggplot(aes(x=lvl_at_first_guild)) + 
    geom_density(color = "steelblue", fill = "steelblue", alpha = 0.6) + 
    theme_bw() + 
    labs(title = "Distribution of Levels When Avatars Enter Their First Guild", x = "Level When Entering First Guild", y = "Density")

Distribution of the number of members of guilds. More precisely, for each guild the number of avatars who were a member of the guild at least once:

guild_members_count <- wow %>% 
    filter(guild >= 0) %>% 
    group_by(guild) %>% 
    summarise(members_count = n_distinct(avatar))
summary(guild_members_count$members_count)

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##    1.00    3.00    7.00   38.46   16.50 1803.00

ggplot(guild_members_count, aes(x = members_count)) + 
    geom_density(color = "steelblue", fill = "steelblue", alpha = 0.6) + 
    xlim(1, 50) +
    theme_bw() + 
    labs(title = "Distribution of the Number of Guild Members by Guilds", x = "Number of Guild Members", y = "Density")

Note: in the density plot above only guilds with less than or equal to 50 members are shown in order to make the slope of the density’s drop more visible.

Introducing Guild Events

We create a new column indicating the events of entering and leaving guilds. The new column can take one of four values:

• No Event: no event.
• Guild Left: the avatar left his/her guild and did not enter a new one.
• Guild Entered: the avatar entered a guild without leaving one.
• Guild Changed: the avatar changed his/her guild, i.e. left his/her current guild and entered a new one immediately.

To do this, first we create a prev_guild column which indicates the last observed guild of the current avatar. If there is no previous observation for the avatar, then the value is -2.

wow <- wow %>% group_by(avatar) %>% mutate(prev_guild = lag(guild)) %>% group_by
wow$prev_guild[is.na(wow$prev_guild)] <- -2

Now create the event column:

wow <- wow %>%
    mutate(event = ifelse(guild == prev_guild, "No Event", "Guild Changed")) %>%
    mutate(event = ifelse(event == "Guild Changed" & prev_guild == -1, "Guild Entered", event)) %>%
    mutate(event = ifelse(event == "Guild Changed" & guild == -1, "Guild Left", event)) %>%
    mutate(event = ifelse(prev_guild == -2, ifelse((guild != -1 & new_avatar), "Guild Entered", "No Event"), event))
summary(factor(wow$event))

## Guild Changed Guild Entered    Guild Left      No Event 
##          1839         31827         26422      10766646

Guild Members Over Time

In order to examine the dynamics of guilds, we are going to look at how certain attributes of guilds change over time. To make computations feasible, we are going to compute these attributes only for midnight at each day in the observed period. The computed attributes include the number of guild members, the average level of guild members, the number of members in each race and class and a few other variables.

# Auxiliary data frame variable
guild_members <- wow %>% group_by(avatar) %>% slice(1) %>% group_by() %>% filter(current_date == min_date | !new_avatar)

time_step <- 60*24  # minutes
snap_times <- seq(as.POSIXlt(as.Date("2008-01-02")), as.POSIXlt(as.Date("2009-01-01")), time_step * 60)

compute_guild_features <- function(current_time) {
    feature_names <- c("guild_members_count", "avg_level", "median_level", "sd_level", "min_level", "max_level", race_names, charclass_names)
    values_for_mising_guilds <- c(0, 0, 0, 0, 0, 0, rep(0, length(race_names) + length(charclass_names)))

    if (!is.null(guild_members) && nrow(guild_members) > 0) {
        stats_df <- guild_members %>% group_by(guild) %>% summarise(
            guild_members_count = length(level),
            avg_level = mean(level),
            median_level = median(level),
            sd_level = ifelse(guild_members_count == 1, 0, sd(level)),
            min_level = min(level),
            max_level = max(level),
            Orc = sum(race == "Orc"),
            Tauren = sum(race == "Tauren"),
            Troll = sum(race == "Troll"),
            Undead = sum(race == "Undead"),
            BloodElf = sum(race == "BloodElf"),
            Rogue = sum(charclass == "Rogue"),
            Hunter = sum(charclass == "Hunter"),
            Warrior = sum(charclass == "Warrior"),
            Shaman = sum(charclass == "Shaman"),
            Warlock = sum(charclass == "Warlock"),
            Druid = sum(charclass == "Druid"),
            Priest = sum(charclass == "Priest"),
            Mage = sum(charclass == "Mage"),
            Paladin = sum(charclass == "Paladin"),
            DeathKnight = sum(charclass == "DeathKnight")
        )
        missing_guilds <- setdiff(unique(wow$guild), stats_df$guild)
    } else {
        missing_guilds <- unique(wow$guild)
    }

    if (!is.null(missing_guilds) && length(missing_guilds)>0) {
        sapply(missing_guilds, 
               function(missing_guild) {
                    stats_df <<- rbind(stats_df, c(missing_guild, values_for_mising_guilds))
                    }
               )
    }

    stats_df$time <- current_time
    stats_df
}

temporal_guild_stats <- data.frame()
row_index <- 1
for (current_time in snap_times) {   # ~20 min on my machine

    # Getting the next block of records containing data up to the time of the next snap
    new_records <- wow[(row_index:nrow(wow)), ] %>% filter(timestamp <= current_time)
    row_index <- row_index + nrow(new_records)

    if (!is.null(new_records) && nrow(new_records) > 0) {
        # Keeping only the last record of each avatar in the current time interval
        guild_members <- rbind(guild_members, new_records)
        guild_members <- guild_members %>% group_by(avatar) %>% slice(n()) %>% group_by()
    }
    #print(paste(row_index, nrow(wow), sep="/"))

    # Compute guild stats for the time of the snap
    if (is.null(temporal_guild_stats) || nrow(temporal_guild_stats) == 0) {
        temporal_guild_stats <- compute_guild_features(current_time)
    } else {
        temporal_guild_stats <- rbind(temporal_guild_stats, compute_guild_features(current_time))
    }
}
rm(guild_members, new_records)

temporal_guild_stats$time <- as.POSIXct(temporal_guild_stats$time, origin = '1970-01-01')  # Not sure why the time column lost its class
temporal_guild_stats$date <- as.Date(temporal_guild_stats$time)
temporal_guild_stats$guild <- as.character(temporal_guild_stats$guild)

Number of Members By Guilds Over Time

get_avg_lvl_by_time_plot <- function(min_guild_id, max_guild_id, y_column, y_axis_title, title) {
    data <- temporal_guild_stats %>% 
        filter(as.numeric(guild) >= min_guild_id & as.numeric(guild) <= max_guild_id) %>%
        select_("date", "guild", y_column) %>%
        spread_("guild", y_column)
    
    dygraph(
        ts(data[, -1], min_date + 1, max_date + 1), xlab = "Date", ylab = y_axis_title, main = title) %>% 
        dyRangeSelector(dateWindow = c(as.Date("2008-09-01"), as.Date("2008-12-01"))) %>%
        dyEvent("2008-11-13", "WoTLK release", labelLoc = "bottom") %>%
        dyLegend(show = "onmouseover")
}

Guild ID [0,90]

get_avg_lvl_by_time_plot(0, 90, "guild_members_count", "Number of Members", "Number of Guild Members Over Time By Guilds")

[91,180]

get_avg_lvl_by_time_plot(91, 180, "guild_members_count", "Number of Members", "Number of Guild Members Over Time By Guilds")

[181,270]

get_avg_lvl_by_time_plot(181, 270, "guild_members_count", "Number of Members", "Number of Guild Members Over Time By Guilds")

[271,360]

get_avg_lvl_by_time_plot(271, 360, "guild_members_count", "Number of Members", "Number of Guild Members Over Time By Guilds")

[361,450]

get_avg_lvl_by_time_plot(361, 450, "guild_members_count", "Number of Members", "Number of Guild Members Over Time By Guilds")

[451,540]

get_avg_lvl_by_time_plot(451, 540, "guild_members_count", "Number of Members", "Number of Guild Members Over Time By Guilds")

-1 (Avatars with No Guild)

get_avg_lvl_by_time_plot(-1, -1, "guild_members_count", "Number of Members", "Number of Guild Members Over Time By Guilds")

Transient Drops in the Number of Guild Members

In some guilds there can be seen transient fluctuations in the number of members quite frequently. Take a closer look on one of these guilds, e.g. guild 273.

guild_id <- 273
ggplotly(temporal_guild_stats %>% 
    filter(guild == guild_id) %>% 
    ggplot(aes(x=date)) +
        geom_line(aes(y = guild_members_count), color="steelblue") +
        theme_bw() + 
        labs(title = paste("Number of Members of Guild", guild_id), x = "Date", y="Number of Members"))

The suspicion was right, the fluctuation is much more apparent in this plot. Let’s take a look on the records where avatars left this guild, and also the previous and subsequent records of those avatars:

leaving_avatars <- wow %>% filter(prev_guild == guild_id & guild != guild_id) %>% select(avatar) %>% group_by(avatar) %>% summarise(records_count = n()) %>% arrange(desc(records_count))

invisible(wow %>%
    filter(avatar %in% leaving_avatars$avatar[1:3]) %>%
    select(avatar, guild, prev_guild, timestamp) %>%
    group_by(avatar) %>% do(
        {
            rows <- which(.$prev_guild == guild_id & .$guild != guild_id)
            if (length(rows) > 0) {
                rows <- c(rows, rows - 1, rows + 1)
                rows <- sort(rows[rows > 0 & rows <= nrow(.)])
                print("------------------------")
                print(cbind(row = rows, .[rows,]))
            }
            data.frame()
        }
    ))

## [1] "------------------------"
##     row           avatar guild prev_guild           timestamp
## 1   313 65943.Orc.Hunter   273        273 2008-05-20 07:33:19
## 2   314 65943.Orc.Hunter    -1        273 2008-05-20 07:43:49
## 3   315 65943.Orc.Hunter   273         -1 2008-05-20 20:53:23
## 4  1178 65943.Orc.Hunter   273        273 2008-09-24 23:16:39
## 5  1179 65943.Orc.Hunter    -1        273 2008-09-24 23:26:36
## 6  1180 65943.Orc.Hunter   273         -1 2008-09-24 23:46:58
## 7  1610 65943.Orc.Hunter   273        273 2008-11-11 00:23:34
## 8  1611 65943.Orc.Hunter    -1        273 2008-11-11 00:40:36
## 9  1612 65943.Orc.Hunter   273         -1 2008-11-11 23:55:20
## 10 1649 65943.Orc.Hunter   273        273 2008-11-23 23:16:54
## 11 1650 65943.Orc.Hunter    -1        273 2008-11-23 23:39:07
## 12 1651 65943.Orc.Hunter   273         -1 2008-11-23 23:49:24
## 13 1787 65943.Orc.Hunter   273        273 2008-12-21 23:11:07
## 14 1788 65943.Orc.Hunter    -1        273 2008-12-21 23:21:23
## 15 1789 65943.Orc.Hunter   273         -1 2008-12-21 23:32:22
## 16 1790 65943.Orc.Hunter   273        273 2008-12-21 23:52:10
## 17 1791 65943.Orc.Hunter    -1        273 2008-12-22 23:03:44
## 18 1792 65943.Orc.Hunter   273         -1 2008-12-22 23:16:19
## [1] "------------------------"
##     row                 avatar guild prev_guild           timestamp
## 1   677 71303.BloodElf.Paladin   273        273 2008-05-11 18:38:01
## 2   678 71303.BloodElf.Paladin    -1        273 2008-05-11 18:47:46
## 3   679 71303.BloodElf.Paladin   273         -1 2008-05-11 18:58:45
## 4  2181 71303.BloodElf.Paladin   273        273 2008-07-02 18:59:56
## 5  2182 71303.BloodElf.Paladin    -1        273 2008-07-02 21:40:50
## 6  2183 71303.BloodElf.Paladin   273         -1 2008-07-02 21:50:28
## 7  2320 71303.BloodElf.Paladin   273        273 2008-07-06 11:18:10
## 8  2321 71303.BloodElf.Paladin    -1        273 2008-07-06 11:28:44
## 9  2322 71303.BloodElf.Paladin   273         -1 2008-07-06 21:49:45
## 10 2471 71303.BloodElf.Paladin   273        273 2008-07-11 02:16:33
## 11 2472 71303.BloodElf.Paladin    -1        273 2008-07-11 02:26:18
## 12 2473 71303.BloodElf.Paladin   273         -1 2008-07-11 20:34:55
## 13 2509 71303.BloodElf.Paladin   273        273 2008-07-12 13:16:04
## 14 2510 71303.BloodElf.Paladin    -1        273 2008-07-12 13:25:48
## 15 2511 71303.BloodElf.Paladin   273         -1 2008-07-12 13:36:40
## 16 2566 71303.BloodElf.Paladin   273        273 2008-07-13 00:06:31
## 17 2567 71303.BloodElf.Paladin    -1        273 2008-07-13 00:16:17
## 18 2568 71303.BloodElf.Paladin   273         -1 2008-07-13 00:36:35
## 19 2745 71303.BloodElf.Paladin   273        273 2008-07-18 23:45:33
## 20 2746 71303.BloodElf.Paladin    -1        273 2008-07-18 23:56:08
## 21 2747 71303.BloodElf.Paladin   273         -1 2008-07-19 13:33:04
## 22 2923 71303.BloodElf.Paladin   273        273 2008-07-25 03:12:08
## 23 2924 71303.BloodElf.Paladin    -1        273 2008-07-25 03:22:33
## 24 2925 71303.BloodElf.Paladin   273         -1 2008-07-25 07:36:59
## 25 3465 71303.BloodElf.Paladin   273        273 2008-08-15 20:12:36
## 26 3466 71303.BloodElf.Paladin    -1        273 2008-08-16 00:53:51
## 27 3467 71303.BloodElf.Paladin    -1         -1 2008-08-16 01:02:35
## [1] "------------------------"
##    row               avatar guild prev_guild           timestamp
## 1   60 71943.Tauren.Warrior   273        273 2008-05-24 02:54:28
## 2   61 71943.Tauren.Warrior    -1        273 2008-05-24 03:04:14
## 3   62 71943.Tauren.Warrior   273         -1 2008-05-25 01:05:17
## 4  139 71943.Tauren.Warrior   273        273 2008-06-11 02:25:57
## 5  140 71943.Tauren.Warrior    -1        273 2008-06-11 02:36:28
## 6  141 71943.Tauren.Warrior   273         -1 2008-06-11 09:06:27
## 7  167 71943.Tauren.Warrior   273        273 2008-06-22 02:55:29
## 8  168 71943.Tauren.Warrior    -1        273 2008-06-22 03:05:13
## 9  169 71943.Tauren.Warrior   273         -1 2008-06-24 01:38:03
## 10 189 71943.Tauren.Warrior   273        273 2008-06-27 09:25:01
## 11 190 71943.Tauren.Warrior    -1        273 2008-06-27 09:35:27
## 12 191 71943.Tauren.Warrior   273         -1 2008-06-28 02:33:34
## 13 284 71943.Tauren.Warrior   273        273 2008-07-14 03:03:13
## 14 285 71943.Tauren.Warrior    -1        273 2008-07-14 03:12:57
## 15 286 71943.Tauren.Warrior   273         -1 2008-07-21 00:09:15
## 16 321 71943.Tauren.Warrior   273        273 2008-08-17 13:42:50
## 17 322 71943.Tauren.Warrior    -1        273 2008-08-17 13:49:28
## 18 323 71943.Tauren.Warrior   273         -1 2008-08-31 11:08:25

It can be seen there are temporal exits, when an avatar leaves his/her guild, but in the next record the avatar is already a member of it again. (So these temporal guild exits go through even within days, moreover within a few successive records of avatars.) I do not know what is the reason behind this phenomena. Maybe these records could be just incorrect data, or there might be some kind of peculiarity in the game causing this. Anyway, later on – depending on the task – it might be necessary to filter out such temporal exits.

Number of Guild Events by Date

transitions_by_date <- tbl_df(data.frame(current_date = seq.Date(min_date, max_date, "days")))
transitions_by_date <- inner_join(transitions_by_date, wow %>% filter(event != "No Event" & !is.na(event))) %>% mutate(Event = factor(event))
ggplotly(ggplot(data = transitions_by_date, aes(x = current_date)) + geom_bar(aes(fill = Event)) + 
        theme_bw() + 
        labs(title = "Number of Guild Events by Date", x = "Count", y = "Number of Events"))

There is a huge peak in October, more specifically:

transitions_by_date <- transitions_by_date %>% group_by(current_date) %>% summarise(transitions = n())
transitions_by_date[which(transitions_by_date$transitions > 400), "current_date"]

## Source: local data frame [2 x 1]
## 
##   current_date
##         (date)
## 1   2008-10-08
## 2   2008-10-09

Even though it is quite strange, it coincides with the plot of the number of guild members over time for guild ids [451,540], where it can be seen that one guild (guild 460) had a huge growth in the number of members. So probably only a single guild is responsible for the observed peak in October. We can look at the guild entering events on the corresponding dates for that guild:

nrow(wow %>% filter(event != "No Event" & (current_date == "2008-10-08" | current_date == "2008-10-09") & guild == 460))

## [1] 1067

If we would ignore the events of this guild for these dates, the number of the remaining events would not be extraordinary anymore.

Additionally, in Thiago Balbo’s analysis, there was a plot of character activations, where a significant peak was shown around these dates, as noted by 33Vito in the comments. By looking at the avatars entering guild 460 on 08-10-2008 and 09-10-2008, it can be seen, that most of these avatars were activated on these days indeed, and also most of these avatars were actually newly created ones, (so not just their first observed record pertains to these dates, but they were also created at that time, i.e. their level is 1):

# Activation date is either 08-10-2008 or 09-10-2008
summary(wow %>% filter(guild == 460 & event == "Guild Entered" & (current_date == "2008-10-08" | current_date == "2008-10-09")) %>% mutate(activated_at_entering_surge = (activation_date == "2008-10-08" | activation_date == "2008-10-09")) %>% select(activated_at_entering_surge))

##  activated_at_entering_surge
##  Mode :logical              
##  FALSE:38                   
##  TRUE :1029                 
##  NA's :0

# How many are newly created avatars between them?
summary(wow %>% filter(guild == 460 & event == "Guild Entered" & (current_date == "2008-10-08" | current_date == "2008-10-09")) %>% select(new_avatar))

##  new_avatar     
##  Mode :logical  
##  FALSE:24       
##  TRUE :1043     
##  NA's :0

So to sum up this strange observation, we saw, that a lot of new avatars were created on two days in mid October (most of them are warriors), and these avatars immediately joined guild 460 resulting in a huge growth in the number of its guild members.

Relation Between Levels and Guild Event Frequency

Number of guild events by levels:

ggplotly(wow %>%
    filter(event != "No Event") %>%
    ggplot(aes(x = level)) + geom_bar(aes(fill = event)) +
        theme_bw() + 
        labs(title = "Number of Guild Events by Level", x = "Count", y = "Level"))

As can be seen most of the events belong to avatars at maximum level (i.e. level 70 before WotLK and level 80 after WotLK), however, this does not necessarily mean that maximum-level avatars change guilds more frequently than others, it can be simply the result of that most of the records belong to maximum-level avatars (as they probably play a lot). So let’s take a look at the distribution of levels across all records:

ggplot(data = wow, aes(x = level)) + 
    geom_density(color = "steelblue", fill = "steelblue", alpha = 0.6) +
    theme_bw() + 
    labs(title = "Distribution of Levels", x = "Level", y = "Density")

It can be seen that the distribution of levels coincides very well with the number of events at each level. So in order to find out if the frequency of guild events is independent of levels, we do a chi-squared test of independence. First we cut the level variable into groups and create a contingency table containing the number of guild events and the number records without guild event for all level groups. Finally we perform the chi-squared test of independence on the table, where the null hypothesis asserts that the variables are independent:

level_breaks <- c(0, 2, 8, 15, 30, 45, 60, 69, 71, 78, 80)
wow$level_group <- cut(wow$level, breaks = level_breaks)
tbl <- table((wow$event != "No Event"), wow$level_group)
# Test for significant disproportions
chisq.test(tbl)

## 
##  Pearson's Chi-squared test
## 
## data:  tbl
## X-squared = 6513.2, df = 9, p-value < 2.2e-16

Since the p-value is very low (e.g. <0.05), we can reject the null hypothesis. That tells us that somewhere across the contingency table there is a disproportionate number of guild events across the level groups. To find out which level groups stick out, we do post-hoc tests comparing the ratio within level groups to the total ratio of guild-event records (guild entered/left/changed) and No Event records. We are going to use Bonferroni-corrected p-values to account for the number of tests, and are going to test with significance level 0.05.

number_of_tests <- length(unique(wow$level_group))
t_test_results <- list()
for (current_group in unique(wow$level_group)) {
    tbl <- table((wow$event != "No Event"), factor(wow$level_group == current_group))
    t_test_results[[current_group]] <- chisq.test(tbl)
}
tTestCorrectedPValues <- lapply(t_test_results, 
                                function(x) {
                                    x$p.value * number_of_tests
                                    }
                                )
lapply(tTestCorrectedPValues, 
       function(x) {
           paste("Null hypothesis rejected:", x < 0.05, "(Bonferroni-corrected p-value:", x, ")")
           }
       )

## $`(0,2]`
## [1] "Null hypothesis rejected: TRUE (Bonferroni-corrected p-value: 0 )"
## 
## $`(8,15]`
## [1] "Null hypothesis rejected: TRUE (Bonferroni-corrected p-value: 0.0037237771997027 )"
## 
## $`(15,30]`
## [1] "Null hypothesis rejected: TRUE (Bonferroni-corrected p-value: 1.23027321073315e-38 )"
## 
## $`(45,60]`
## [1] "Null hypothesis rejected: FALSE (Bonferroni-corrected p-value: 6.09364025621775 )"
## 
## $`(60,69]`
## [1] "Null hypothesis rejected: TRUE (Bonferroni-corrected p-value: 3.25812469153734e-06 )"
## 
## $`(69,71]`
## [1] "Null hypothesis rejected: TRUE (Bonferroni-corrected p-value: 3.43079105311725e-68 )"
## 
## $`(30,45]`
## [1] "Null hypothesis rejected: FALSE (Bonferroni-corrected p-value: 9.0201585162032 )"
## 
## $`(2,8]`
## [1] "Null hypothesis rejected: TRUE (Bonferroni-corrected p-value: 0.0498472146510742 )"
## 
## $`(71,78]`
## [1] "Null hypothesis rejected: TRUE (Bonferroni-corrected p-value: 1.54011988727995e-05 )"
## 
## $`(78,80]`
## [1] "Null hypothesis rejected: TRUE (Bonferroni-corrected p-value: 4.57243642646283e-14 )"

The null hypothesis was retained for only 2 level group(s), so probably there is a strong relationship between the level of avatars and the frequency of guild events.

Distribution of Event Types Within Races and Character Classes

get_distr_within_factor <- function(group_by_col) {
    wow %>%
        filter(event != "No Event") %>%
        group_by_(group_by_col, "event") %>%
        summarise(count = n()) %>%
        mutate(Percentage = count / sum(count), Event = factor(event)) %>%
        group_by() %>%
        ggplot(aes_string(x = group_by_col, y = "Percentage")) +
        scale_y_continuous(labels = percent_format()) + 
        geom_bar(aes(fill = Event), stat = "identity", position = "dodge") +
        theme_bw()
}

Races

ggplotly(get_distr_within_factor("race") + labs(title = "Distribution of Guild Events Within Races", x = "Race"))

Character Classes

ggplotly(get_distr_within_factor("charclass") + labs(title = "Distribution of Guild Events Within Character Classes", x = "Character Class"))

Lifetime of Guilds

Distribution Guild Lifetimes

We compute the lifetime of a guild as the time between the last and the first date when the guild had more than 0 members.

guild_lifetime <- temporal_guild_stats %>%
    group_by(guild) %>%
    summarise(start_date = min(date[guild_members_count != 0]), end_date = max(date[guild_members_count != 0])) %>%
    mutate(lifetime = as.numeric(end_date - start_date))
ggplot(guild_lifetime, aes(x = lifetime)) + 
    geom_density(color = "steelblue", fill = "steelblue", alpha = 0.6) +
    theme_bw() + 
    labs(title = "Distribution of Guild Lifetimes", x = "Lifetime in Days", y = "Density")

Subsistence of Guilds by Dates

guild_lifetime %>% 
    mutate(lifetime = end_date - start_date) %>%
    gather(type, date, start_date:end_date) %>%
    mutate(guild = factor(guild)) %>%
    ggplot(aes(x = date, y = guild)) + 
    geom_line(aes(color = guild)) +
    theme_bw() + 
    theme(axis.text.y = element_blank(), legend.position = "none") +
    labs(title = "Guild Lifetimes", x = "Date", y = "Guild ID")

Newly Created Guilds

Let’s find out how many of the guilds were created during the observed period and how many of them had already been existed. We consider a guild newly created if all its observed members are either newly created avatars or avatars that had been a member of a different guild before joining this one.

# First, create a column indicating whether the current guild is the first guild of the avatar
wow <- wow %>%
    group_by(avatar) %>%
    mutate(this.is.first.guild = sapply(1:length(guild), 
                                        function(x,y) {
                                            length(unique(y[1:x])) == 1
                                            }, 
                                        guild)) %>% group_by()

# Create a data frame for guilds, with a column indicating whether it is a new guild or not
new_guilds <- wow %>%
    group_by(guild, avatar) %>%
    slice(1) %>%
    group_by(guild) %>%
    summarise(new_guild = (sum(new_avatar | !this.is.first.guild) == length(new_avatar)))

# Number of already existing guilds and new guilds
summary(new_guilds$new_guild)

##    Mode   FALSE    TRUE    NA's 
## logical     268     152       0

Most of the guilds had been created before the beginning of the observed period, however more than one third of the guilds were cerated afterwards.

Creation of new guilds by dates:

# First we create a logical column indicating if the current record corresponds to the creation of a new guild
wow <- left_join(wow, new_guilds, by = "guild")
wow <- wow %>% 
    group_by(guild) %>% 
    mutate(guild_creation = c(new_guild[1], rep(FALSE, length(new_guild)-1))) %>% 
    group_by()

# Count and plot the number of new guilds for each date
tbl_df(data.frame(current_date = seq.Date(min_date, max_date, "days"))) %>%
    full_join(wow %>% filter(guild_creation) %>% group_by(current_date) %>% summarise(n = n())) %>%
    mutate(n = ifelse(is.na(n), 0, n)) %>%
    ggplot(aes(x = current_date, y = n)) + 
    geom_bar(stat = "identity", fill = "darkorange", color = "darkorange") + 
    theme_bw() + 
    labs(title = "Number of Created Guilds by Date", x = "Date", y = "Number of Created Guilds")

Graph of Guild Transitions

We can visualize the transitions between guilds. The following plots are divided by the level of the transitioning avatars. The color of the nodes indicate the sign of the difference between joining and leaving avatars: green indicates more joining than leaving avatars, red represents the opposite, and yellow corresponds for equal number of joining and leaving avatars. The size of nodes and thickness of edges correspond to the number of transitions. Also the color of edges represent the type of events. Green edges represent avatars entering a guild, red edges represent avatars leaving a guild and blue represents direct changes between two guilds. For better visibility only nodes and edges with enough number of transitions are shown. The thresholds vary across the plots and are defined as arguments to the plot_lvl_group function.

nodes <- data.frame(id = unique(wow$guild))
edges <- ungroup(wow) %>% filter(event != "No Event") %>% select(avatar, level, level_group, prev_guild, guild)
names(edges) <- c("avatar", "level", "level_group", "from", "to")

plot_lvl_group <- function(min_level = 0, max_level = 5, transition_threshold_for_nodes = 5, transition_threshold_for_edges = 5, node_size_metric = c("entered", "left", "entered+left", "entered-left"), log_node_size = TRUE) {
    edges <- edges %>% filter(level >= min_level, level <= max_level)

    # Compute nodes' size
    entered_avatars <- edges %>% group_by(to) %>% summarise(entered = n())
    left_avatars <- edges %>% group_by(from) %>% summarise(left = n())
    nodes <- left_join(nodes, entered_avatars, by = c("id" = "to"))
    nodes <- left_join(nodes, left_avatars, by = c("id" = "from"))

    nodes$entered[is.na(nodes$entered)] <- 0
    nodes$left[is.na(nodes$left)] <- 0

    if (node_size_metric == "entered") {
        nodes$value <- nodes$entered
    } else if (node_size_metric == "left") {
        nodes$value <- nodes$left
    } else if (node_size_metric == "entered+left") {
        nodes$value <- nodes$entered + nodes$left
    } else if (node_size_metric == "entered-left") {
        nodes$value <- nodes$entered - nodes$left
    } else {
        stop("Unknown node size metric")
    }
    nodes$value <- abs(nodes$value)

    # Compute edges' size
    edges <- edges %>% group_by(from, to) %>% summarise(transitions = n())
    edges$value <- edges$transitions

    # Node attributes
    nodes$label <- nodes$id
    nodes$title <- str_c("Entered: <b>", nodes$entered, "</b><br>Left: <b>", nodes$left, "</b>")
    nodes$color <- "#D41313"
    nodes$color[nodes$entered == nodes$left] <- "#E4E63F"
    nodes$color[nodes$entered > nodes$left] <- "#17A019"

    # Edge attributes
    edges$title <- paste(paste(edges$from, edges$to, sep=" -> "), edges$transitions, sep=" : ")
    edges$color <- "#618CC1"
    edges$color[edges$to == -1] <- "#DD5A5A"
    edges$color[edges$from == -1] <- "#61C163"

    # Filter nodes and edges
    print(paste("All transitions:", sum(edges$transitions)))
    nodes <- nodes %>% filter(entered + left >= transition_threshold_for_nodes)
    edges <- edges %>% filter(from %in% nodes$id & to %in% nodes$id)
    edges <- edges %>% filter(value >= transition_threshold_for_edges)

    if (log_node_size) {
        if (min(nodes$value == 0)) {
            nodes$value <- nodes$value + 1
        }
        nodes$value <- log(nodes$value)
    }
    print(paste("Shown edges:", nrow(edges)))
    print(paste("Shown nodes:", nrow(nodes)))

    visNetwork(nodes, edges, width = "100%") %>%
        visEdges(arrows = "to")
}

Level [1,5]

plot_lvl_group(min_level = 1, max_level = 5,
    transition_threshold_for_nodes = 10,
    transition_threshold_for_edges = 0,
    node_size_metric = "entered+left",
    log_node_size = TRUE)

## [1] "All transitions: 3185"
## [1] "Shown edges: 71"
## [1] "Shown nodes: 38"

[6,15]

plot_lvl_group(min_level = 6, max_level = 15,
    transition_threshold_for_nodes = 10,
    transition_threshold_for_edges = 0,
    node_size_metric = "entered+left",
    log_node_size = TRUE)

## [1] "All transitions: 2107"
## [1] "Shown edges: 115"
## [1] "Shown nodes: 46"

[16,30]

plot_lvl_group(min_level = 16, max_level = 30,
    transition_threshold_for_nodes = 15,
    transition_threshold_for_edges = 0,
    node_size_metric = "entered+left",
    log_node_size = TRUE)

## [1] "All transitions: 4179"
## [1] "Shown edges: 174"
## [1] "Shown nodes: 54"

[31,50]

plot_lvl_group(min_level = 31, max_level = 50,
    transition_threshold_for_nodes = 15,
    transition_threshold_for_edges = 0,
    node_size_metric = "entered+left",
    log_node_size = TRUE)

## [1] "All transitions: 4467"
## [1] "Shown edges: 169"
## [1] "Shown nodes: 51"

[51,65]

plot_lvl_group(min_level = 51, max_level = 65,
    transition_threshold_for_nodes = 20,
    transition_threshold_for_edges = 2,
    node_size_metric = "entered+left",
    log_node_size = TRUE)

## [1] "All transitions: 6137"
## [1] "Shown edges: 126"
## [1] "Shown nodes: 50"

[66,70]

plot_lvl_group(min_level = 66, max_level = 70,
    transition_threshold_for_nodes = 50,
    transition_threshold_for_edges = 5,
    node_size_metric = "entered+left",
    log_node_size = TRUE)

## [1] "All transitions: 36575"
## [1] "Shown edges: 162"
## [1] "Shown nodes: 51"

[71,75]

plot_lvl_group(min_level = 71, max_level = 75,
    transition_threshold_for_nodes = 5,
    transition_threshold_for_edges = 0,
    node_size_metric = "entered+left",
    log_node_size = TRUE)

## [1] "All transitions: 1251"
## [1] "Shown edges: 90"
## [1] "Shown nodes: 36"

[76,80]

plot_lvl_group(min_level = 76, max_level = 80,
    transition_threshold_for_nodes = 5,
    transition_threshold_for_edges = 0,
    node_size_metric = "entered+left",
    log_node_size = TRUE)

## [1] "All transitions: 2187"
## [1] "Shown edges: 115"
## [1] "Shown nodes: 36"

A few things can be seen on the transition graphs. E.g. for levels [1,5] the node of guild 460 is apparently bigger than others, that is, it had many low-level avatars joining, however, if we switch to higher levels, guild 460 is not noticable anymore. Also, as we go to higher levels more and more red nodes and blue edges appear. Also, the number of all transitions is remarkably higher for level group [66,70] than for any other level group. (Note, that levels above 70 only came into to game in November.)

Impacts on Guild Events

Impact of Previous Guilds

We examine whether avatars are more easily join guilds if they had been already a guild member previously or not. To do this we examine how long does it take for an avatar after leaving a guild to join a new one.

We only take into consideration avatars who have been recorded at least 365 times.

We compute the intervals in two units: days passed, and the number the avatar’s observed records during that time.

# First, create a column indicating how many different guilds the avatars had been member of till the current time
# ~ 15 min
wow <- wow %>%
    group_by(avatar) %>%
    mutate(joined_guilds_count =
               sapply(1:length(guild),
                      function(x, y) {
                          tmp <- y[1:x]
                          tmp <- tmp[tmp != -1]
                          length(unique(tmp))},
                      guild)) %>%
    group_by()

# If the avatar is a new avatar, then we can assess how much time did it take for him/her to join his/her first guild. Here, we only consider avatars that joined at least one guild at some point.
# Additionally, for each avatar with at least 2 observed guilds, we compute the length of intervals the avatar spent between his/her guilds. That is, how much time passed from leaving a guild until entering the next guild.

min_records <- 365
wow <- wow %>% group_by(avatar) %>% mutate(records = n()) %>% group_by()
# ~20 minutes
intervals <- wow %>% 
    filter(records >= min_records) %>% 
    group_by(avatar) %>% 
    do({
        result <- data.frame()
        if (.$new_avatar[1]) {
            tmp_ind <- which(.$joined_guilds_count == 1)[1]  # First guild joined.
            if (!is.na(tmp_ind) && length(tmp_ind) > 0) {
                result <- rbind(result, data.frame(
                    Interval = (.$timestamp[tmp_ind] - .$timestamp[1]), 
                    unit = "Interval Units: Days", 
                    Type = "Before Joining First Guild"))
                result <- rbind(result, data.frame(
                    Interval = (tmp_ind - 1), 
                    unit = "Interval Units: Records", 
                    Type = "Before Joining First Guild"))
            }
        }
        last_record_in_guild <- which(.$guild != -1)
        if (length(which(.$guild != -1)) > 0) {
            last_record_in_guild <- max(last_record_in_guild)
            tmp_df <- .[1:last_record_in_guild, c("guild", "joined_guilds_count", "timestamp")]
            tmp_df <- tmp_df %>% filter(guild == -1 & joined_guilds_count >= 1)
            tmp <- tmp_df %>% group_by(joined_guilds_count) %>% summarise(interval = max(timestamp) - min(timestamp))
            if (nrow(tmp_df) > 0) {
                result <- rbind(result, data.frame(
                    Interval = tmp$interval, 
                    unit = "Interval Units: Days", 
                    Type = "Before Joining Subsequent Guilds"))
                result <- rbind(result, data.frame(
                    Interval = as.vector(table(tmp_df$joined_guilds_count)), 
                    unit = "Interval Units: Records", 
                    Type = "Before Joining Subsequent Guilds"))
            }
        }
        result
    })

ggplot(intervals, aes(Type, Interval)) + facet_wrap( ~ unit, scales="free") +
    geom_boxplot(aes(fill = Type)) +
    theme_bw() +
    theme(legend.position = "top", axis.text.x = element_text(angle = 45, hjust = 1)) +
    ggtitle("Time Spent Outside of Guilds Until Joining First and Subsequent Guilds") +
    ylab("Length of Intervals Spent Outside of Guilds")

Interestingly, if we look at the time of intervals (~days), it can be seen that it takes less time to join the first guild than joining subsequent guilds after leaving the previous one. Even more interestingly, if we measure the length of intervals in the number of observed records the relation turns around, which can be interpreted as it takes less playtime joining guilds after leaving the previous one, than joining the very first guild.

So my not too elaborate interpretation would be that new avatars are probably quite enthusiastic so they play a lot in the beginning, but they might not know many things about guilds so it takes some time for them to join one. On the other hand, avatars who have already left a guild are less enthusiastic on average, so they play less frequently, therefore it takes even more (real) time for them to join another guild. But they are also more familiar with guilds, so they more easily join a new one, thus it takes less playtime (observed records) for them to join a new guild.

Impact of the Number of Guild Members on Guild Events

We plot the distribution of the number of members of corresponding guilds at guild entering/leaving events. To do this, we join the original data frame of observed records with the guild statistics over time by date.

Note that we computed the number of guild members only on a daily basis earlier, so this plot (and many of the following ones) are not totally accurate, but still might be useful.

wow <- left_join(wow,
            temporal_guild_stats %>%
                mutate(current_date = date, guild = as.numeric(guild)) %>%
                select(guild, current_date, guild_members_count, avg_level, Orc, Tauren, Troll, Undead, BloodElf, Rogue, Hunter, Warrior, Shaman, Warlock, Druid, Priest, Mage, Paladin, DeathKnight),
            by = c("current_date", "guild"))

wow <- left_join(wow,
                  temporal_guild_stats %>%
                      mutate(current_date = date,
                             prev_guild = as.numeric(guild),
                             prev_guild_members_count = guild_members_count,
                             prev_guild_avg_lvl = avg_level) %>%
                      select(prev_guild, current_date, prev_guild_members_count, prev_guild_avg_lvl),
                  by = c("current_date", "prev_guild"))

Guild Entering Events

wow %>% 
    filter(!is.na(guild_members_count) & (event == "Guild Entered" | event == "Guild Changed")) %>% 
    select(guild_members_count) %>% 
    ggplot() + 
    geom_density(aes(x = guild_members_count), 
                 color = "steelblue", fill = "steelblue", alpha = 0.6) + 
    theme_bw() + 
    labs(title = "Distribution of the Number of Guild Members at Guild Entering Events", x = "Number of Guild Members", y = "Density") +
    xlim(1, 1750) + ylim(0, 0.0028)

Guild Leaving Events

wow %>% 
    filter(!is.na(prev_guild_members_count) & (event == "Guild Left" | event == "Guild Changed")) %>% 
    select(prev_guild_members_count) %>% 
    ggplot() + 
    geom_density(aes(x = prev_guild_members_count), 
                 color = "steelblue", fill = "steelblue", alpha = 0.6) + 
    theme_bw() + 
    labs(title = "Distribution of the Number of Guild Members at Guild Leaving Events", x = "Number of Guild Members", y = "Density") + 
    xlim(1, 1750) + ylim(0, 0.0028)

As can be seen the number of entering events – after a short increase at the beginning – starts to quickly decrease by increasing guild members, so probably most of the guilds do not grow beyond a certain size, however, there are a few peaks at bigger guilds, which probably pertain to individual guilds that grew to a big size.

The distribution pertaining to guild leaving events shows a similar shape but is slightly flatter at the beginning and the area under the curve is somewhat ,,shifted’’ to the right. That is, at bigger guild sizes it is more likely that members will leave, than that new members will join. Of course eventually this distribution also diminishes to zero, as guilds do not grow forever.

Distribution of Maximum Guild Sizes

The histogram of the maximal sizes that guilds have reached.

wow %>%
    group_by(guild) %>%
    summarise(max_guild_members_count = max(guild_members_count, na.rm = TRUE)) %>%
    filter(guild != -1) %>% 
    ggplot() +
    geom_histogram(aes(x = max_guild_members_count, y = (..count..) / sum(..count..)), size = 1.0, alpha = 0.6, bins = 40) +
    geom_vline(xintercept = 500, color = "red", size = 1.0, alpha = 0.6) +
    scale_y_continuous(labels = percent) +
    theme_bw() +
    labs(title = "Histogram of the Maximal Number of Guild Members for each Guild", x = "Maximal Number of Members", y = "Percentage of Guilds")

wow %>% filter(guild != -1 & guild_members_count > 500) %>% 
    distinct(guild) %>% select(guild, guild_members_count)

## Source: local data frame [3 x 2]
## 
##   guild guild_members_count
##   (dbl)               (dbl)
## 1   103                 501
## 2   282                 506
## 3   460                 765

As shown, only a few guilds had more than 500 members. We can check out which guilds are these exactly and how many of them are there:

wow %>% filter(guild != -1 & guild_members_count > 500) %>% 
    distinct(guild) %>% select(guild, guild_members_count)

## Source: local data frame [3 x 2]
## 
##   guild guild_members_count
##   (dbl)               (dbl)
## 1   103                 501
## 2   282                 506
## 3   460                 765

As it was kind of suspectable, only very few (3) guilds were responsible for all the guild entering/leaving events pertaining to remarkably large guilds.

Impact of the Guilds’ Average Level

Distribution of the Average Level of Guild Members at Guild Events

First we plot the distribution of the average level of guild members at guild events for the events’ corresponding guilds.

Guild Entering Events

wow %>% 
    filter(!is.na(avg_level) & (event == "Guild Entered" | event == "Guild Changed")) %>% 
    select(avg_level) %>% 
    ggplot() +
    geom_density(aes(x = avg_level), color = "steelblue", fill = "steelblue", alpha = 0.6) + 
    theme_bw() + 
    labs(title = "Density of Guild Entering Events", x = "Average Level of Guild Members", y = "Density")

Guild Leaving Events

wow %>% 
    filter(!is.na(prev_guild_avg_lvl) & (event == "Guild Left" | event == "Guild Changed")) %>% 
    select(prev_guild_avg_lvl) %>% 
    ggplot() +
    geom_density(aes(x = prev_guild_avg_lvl), color = "steelblue", fill = "steelblue", alpha = 0.6) +
    theme_bw() + 
    labs(title = "Density of Guild Leaving Events", x = "Average Level of Guild Members", y = "Density")

The two plots are very similar. Guild events mostly belong to strong guilds, where the average level of members is close to the maximal level, but there is also a slight prominence for very low-level guilds.

2D Density Plot of Guild Events by the Level of Avatars and the Average Level of Guilds

We can also plot the 2D density plot of guild events by the members’ average level in the corresponding guilds and the level of the avatars taking part in the events.

Guild Entering Events

wow %>% 
    filter(!is.na(avg_level) & (event == "Guild Entered" | event == "Guild Changed")) %>% 
    ggplot(aes(x = avg_level, y = level)) + 
    stat_density2d(aes(alpha = ..level..), geom = "polygon") +
    scale_alpha_continuous(limits = c(0,0.2), breaks = seq(0,0.2, by = 0.025))+
    geom_point(colour = "red", alpha = 0.02)+
    theme_bw() + 
    labs(title = "2D Density Plot of Guild Entering Events", x = "Average Level of Guild Members", y = "Level of the Entering Avatar", alpha = "Density Level")

Guild Leaving Events

wow %>% 
    filter(!is.na(prev_guild_avg_lvl) & (event == "Guild Left" | event == "Guild Changed")) %>% 
    ggplot(aes(x = prev_guild_avg_lvl, y = level)) + 
    stat_density2d(aes(alpha = ..level..), geom = "polygon") +
    scale_alpha_continuous(limits = c(0,0.2), breaks = seq(0, 0.2, by = 0.025)) +
    geom_point(colour = "red", alpha = 0.02)+
    theme_bw() + 
    labs(title = "2D Density Plot of Guild Leaving Events", x = "Average Level of Guild Members", y = "Level of the Leaving Avatar", alpha = "Density Level")

As with guilds, most of the avatars involved in guild events are high-level avatars, and there is also a more dense region for avatars with very low level. Additionally, it seems that there is a positive correlation between the level of the avatar and the average level of the guild members.

Impact of Races and Character Classes on Guild Entering Events

We examine the distribution of guild entering events by the ratio of the entering avatar’s race/class between the old members of the guild for each race and class. That is we want to examine whether the race and class of guild members affect the race and class of future members.

We filter out guild 460, as it seems kind of an extreme guild based on the previous findings and it might distort findings on other guilds significantly.

get_avatar_group_plot_data <- function(current_col_value, col_name = c("race", "charclass")) {
    col_name_2 <- gsub(" ", "", current_col_value, fixed = TRUE)
    tmp <- wow %>%
        filter(guild != 460 &
                   guild != -1 &
                   !is.na(guild_members_count) &
                   guild_members_count > 0 &
                   (event == "Guild Entered" | event == "Guild Changed") &
                   ((col_name == "charclass" & charclass == current_col_value) | (col_name == "race" & race == current_col_value)))

    if (col_name == "charclass") {
        tmp <- tmp %>% group_by_(same_charclass_ratio_in_guild = interp(~ round(var / guild_members_count, 2), var = as.name(col_name_2)))
    } else {
        tmp <- tmp %>% group_by_(same_race_ratio_in_guild = interp(~ round(var / guild_members_count, 2), var = as.name(col_name_2)))
    }
    tmp <- tmp %>%
        summarise("entered_avatars_count" = n(),
                  "different_guilds_count" = length(unique(guild)),
                  "top_1_guild" = max(table(guild)),
                  "other_guilds_count" = entered_avatars_count - top_1_guild) %>% ungroup
    tmp[, col_name] <- col_name_2
    tmp
}

plot_by_race_ratio <- function(data = race_plot_data, 
                               x_col = "same_race_ratio_in_guild", 
                               y_col = "entered_avatars_count", color_col = "race", 
                               x_axis_title = "", 
                               main_title = "") {
    ggplot(data, aes_string(x = x_col)) + 
        geom_line(aes_string(y = y_col, color = color_col, group = color_col), size = 1.3, alpha = 0.5) + 
        theme_bw() + 
        scale_x_continuous(labels = percent) + 
        labs(
            title = main_title, 
            x = x_axis_title, 
            y = "Number of Joining Avatars")
            
}

Impact of Races

race_plot_data <- c()
for (race_name in race_names) {
    race_plot_data <- rbind(race_plot_data, get_avatar_group_plot_data(race_name, "race"))
}
ggplotly(plot_by_race_ratio(
    x_axis_title = "Percent of the Entering Avatar's Race Between the Members of the Event's Corresponding Guild", 
    main_title = "Impact of the Existing Guild Members' Race on the Race of Joining Avatars"))

Impact of Character Classes

charclass_plot_data <- c()
for (charclass_name in charclass_names) {
    charclass_plot_data <- rbind(charclass_plot_data, get_avatar_group_plot_data(charclass_name, "charclass"))
}
ggplotly(plot_by_race_ratio(
    charclass_plot_data, 
    "same_charclass_ratio_in_guild", 
    color_col = "charclass", 
    x_axis_title = "Percent of the Entering Avatar's Charclass Between the Members of the Corresponding Guild", 
    main_title = "Impact of the Existing Guild Members' Charclass on the Charclass of Joining Avatars"))

As can be seen, the most prominent peaks of races are somewhat at different positions and – except for Blood Elf – the curves drop very quickly after the peak, which could mean, that there is a certain unique ratio for each race representing the ideal or average proportion of the race within guilds. However, the Blood Elf guild kind of stands out of the others, it has multiple peaks and there are an apparent number of entering events even in guilds with very high ratio (including 100%) of Blood Elf members.

This finding is not valid for character classes, as the lines of different character classes are jumbled, and the peaks are overlapping.

Impact of Guild and Avatar Activity on Guild Events

Take a look at the relation between the activity of a guild and the activity of avatars entering those guilds. So we want to find out what is the correlation between the activity of avatars entering guilds and the average activity of the members of the corresponding guild.

We are going to compute activity for an avatar as the average number of daily records in the last N days, and for guilds as the average of the daily averages of the members’ number of records for the last N days. We are going to try out multiple values for N.

We are going create 2D density plots and compute (Pearson) correlation strength and significance. To test the significance of the correlations we use the cor.test function, which performs a t-test internally for the Pearson correlation coefficient.

# Create a data.frame containg the average activity of the members of guilds for each day, when the guild existed
# Get daily sum of activities for each guild
guild_daily_activities <- wow %>%
    mutate(guild_creation_date = ifelse(guild_creation, current_date, NA)) %>%
    group_by(guild, current_date) %>%
    summarise(activity = n(), new_guild = new_guild[1], guild_creation_date = guild_creation_date[1]) %>%
    group_by() %>%
    mutate(date = current_date)
guild_daily_activities$current_date <- NULL

# Join with data frame that contains daily guild statistics including number of members
guild_daily_activities <- left_join(guild_daily_activities,
                                    temporal_guild_stats %>%
                                        select(guild, date, guild_members_count) %>%
                                        mutate(date = date - 1, guild = as.numeric(guild)),
                                    by = c("guild", "date"))

# Although only those days were kept for every guild for which there was observed activity, it is still possible to have 0 guild_members_count value, because this value represent the number of members at the end of the corresponding day. Let's simply remove them and then get the daily averages.

guild_daily_activities <- guild_daily_activities %>%
    filter(guild != -1 & guild_members_count != 0) %>%
    mutate(avg_daily_activity_of_members = activity / guild_members_count)

# Create rows for every date when the guild existed, regardless having any activity on that day or not
guild_daily_activities <- left_join(
    tbl_df(data.frame(date = seq.Date(min_date, max_date, "days"))), 
    guild_daily_activities,
    by = "date") %>%
    filter(!new_guild | guild_creation_date <= date) %>%
    mutate(avg_daily_activity_of_members = ifelse(is.na(avg_daily_activity_of_members), 0, avg_daily_activity_of_members))

# Create a similar DF for avatars, i.e. containing the average daily activity of the last N days by dates
avatar_daily_activities <- wow %>%
    group_by(avatar, current_date) %>%
    summarise(daily_activity = n(), new_avatar = new_avatar[1], avatar_creation_date = activation_date[1]) %>%
    group_by() %>%
    mutate(date = current_date)
avatar_daily_activities$current_date <- NULL

# Create rows for every date when the avatar existed, regardless having any activity on that day or not
avatar_daily_activities <- left_join(
    tbl_df(data.frame(date = seq.Date(min_date, max_date, "days"))),
    avatar_daily_activities,
    by = "date") %>%
    filter(!new_avatar | avatar_creation_date <= date)

# Get the average of daily averages for the last N days
aggregate_means <- function(daily_means, group_by_col, daily_mean_col, N) {
    daily_means <- arrange(daily_means, date)
    result <- daily_means %>%
        group_by_(group_by_col) %>%
        do({
            current_df <- .
            avg_last_N_day <- c()
            if (N < length(.$date)) {
                avg_last_N_day <- sapply((1 + N):nrow(current_df), 
                                         function(index) { 
                                             mean((current_df[[daily_mean_col]])[(index - N - 1):(index - 1)])
                                             }
                                         )
                data.frame(date = .$date[-(1:N)], avg_last_N_day = avg_last_N_day)
            } else {
                data.frame(date = c(), avg_last_N_day = c())
            }
        })
    ungroup(result)
}

get_activity_stats <- function(days_n, guild_daily_activities, avatars_daily_activities) {
    # Get averages for last days_n days
    
    # For guilds
    guild_daily_activities <- aggregate_means(
        guild_daily_activities, "guild", "avg_daily_activity_of_members", days_n)
    
    # For avatars
    avatar_daily_activities <- aggregate_means(
        avatars_daily_activities, "avatar", "daily_activity", days_n)

    # Combine stats into one DF together guild entering events
    activities_combined <- left_join(
        wow %>% filter(event == "Guild Entered") %>%
            select(current_date, avatar, guild, level, guild_members_count) %>%
            mutate(date = current_date),
        guild_daily_activities,
        by = c("date", "guild")
    )

    activities_combined$avg_last_N_day_guild <- activities_combined$avg_last_N_day
    activities_combined$avg_last_N_day <- NULL

    activities_combined <- left_join(activities_combined, avatar_daily_activities, by = c("date", "avatar"))
    activities_combined$avg_last_N_day_avatar <- activities_combined$avg_last_N_day
    activities_combined$avg_last_N_day <- NULL
    activities_combined$current_date <- NULL
    
    activities_combined_filtered <- activities_combined %>%
        filter(!is.na(avg_last_N_day_guild) &
                   (date > (min_date + days_n)) &
                   !is.na(activities_combined$avg_last_N_day_avatar))
    plot <- ggplot(activities_combined_filtered, aes(x = avg_last_N_day_avatar, y = avg_last_N_day_guild)) +
        stat_density2d(aes(alpha = ..level..), geom = "polygon") +
        scale_alpha_continuous(limits = c(0,0.1), breaks = seq(0,0.1, by = 0.01))+
        geom_point(colour = "red",alpha = 0.02) +
        xlim(0, 100) +
        ylim(0, 25) +
        theme_bw() + 
        labs(
            title = paste("Density of Guild Entering Events By the Avatar's and Guild's Activities in the Last", days_n, "day(s)"), 
            x = "Average Daily Activity of the Members of the Event's Corresponding Guild", 
            y = "Average Daily Activity of the Entering Avatar", 
            alpha = "Density Level")
    correlation <- cor(activities_combined_filtered$avg_last_N_day_avatar, activities_combined_filtered$avg_last_N_day_guild)
    cor_test <- cor.test(activities_combined_filtered$avg_last_N_day_avatar, activities_combined_filtered$avg_last_N_day_guild)
    list(plot = plot, correlation = correlation, cor_test = cor_test, df = activities_combined_filtered)
}

number_of_N_values <- 5

N = 1

N <- 1
activities_at_entering_events <- get_activity_stats(N, guild_daily_activities, avatar_daily_activities)
activities_at_entering_events[["plot"]]

paste("Correlation =", activities_at_entering_events[["correlation"]])

## [1] "Correlation = 0.240838425710198"

paste("Bonferroni-corrected p-value for correlation test =", activities_at_entering_events[["cor_test"]]$p.value * number_of_N_values)

## [1] "Bonferroni-corrected p-value for correlation test = 0"

N = 2

N <- 2
activities_at_entering_events <- get_activity_stats(N, guild_daily_activities, avatar_daily_activities)
activities_at_entering_events[["plot"]]

paste("Correlation =", activities_at_entering_events[["correlation"]])

## [1] "Correlation = 0.239881498758409"

paste("Bonferroni-corrected p-value for correlation test =", activities_at_entering_events[["cor_test"]]$p.value * number_of_N_values)

## [1] "Bonferroni-corrected p-value for correlation test = 0"

N = 3

N <- 3
activities_at_entering_events <- get_activity_stats(N, guild_daily_activities, avatar_daily_activities)
activities_at_entering_events[["plot"]]

paste("Correlation =", activities_at_entering_events[["correlation"]])

## [1] "Correlation = 0.242129019270479"

paste("Bonferroni-corrected p-value for correlation test =", activities_at_entering_events[["cor_test"]]$p.value * number_of_N_values)

## [1] "Bonferroni-corrected p-value for correlation test = 0"

N = 4

N <- 4
activities_at_entering_events <- get_activity_stats(N, guild_daily_activities, avatar_daily_activities)
activities_at_entering_events[["plot"]]

paste("Correlation =", activities_at_entering_events[["correlation"]])

## [1] "Correlation = 0.240239034775643"

paste("Bonferroni-corrected p-value for correlation test =", activities_at_entering_events[["cor_test"]]$p.value * number_of_N_values)

## [1] "Bonferroni-corrected p-value for correlation test = 1.28457067918724e-321"

N = 5

N <- 5
activities_at_entering_events <- get_activity_stats(N, guild_daily_activities, avatar_daily_activities)
activities_at_entering_events[["plot"]]

paste("Correlation =", activities_at_entering_events[["correlation"]])

## [1] "Correlation = 0.239355586210549"

paste("Bonferroni-corrected p-value for correlation test =", activities_at_entering_events[["cor_test"]]$p.value * number_of_N_values)

## [1] "Bonferroni-corrected p-value for correlation test = 4.23585650313031e-312"

It can be seen that there is a correlation between the activity of guilds and the activity of entering avatars, and the correlation is significant at significance level 0.05 since the Bonferroni-corrected p-values of the t-tests for correlation were below 0.05 for all tests. (I.e. the null hypotheses asserting there is no correlation can be rejected.) The correlation was highest for N=3.

Conclusions

Many of the computations presented in this analysis are not totally accurate, as we made some approximations in order to make computations more feasible. However, the presented observations still might be sufficient to grasp some of the peculiarities and characteristics of the data.

There are still many things to investigate regarding guild dynamics. E.g. I am planning to do some experiments on how these dynamics (guild events) can be predicted based on the available data.

I would be more than happy to have your feedback and suggestions to improve the current analysis or any ideas to move on to in the future.