Leagues analysed

• REBBL - Seasons 5, 6 and 7 (PC league - 3896 games)
• OCC - All seasons (PC league - 3611 games)
• MML - Seasons 9, 10 and 11 (PS4 league - 4525 games)
• Champion Ladder - Season 12 (PC matchmaking league - sample of 4119 games)

These four leagues provide a good spread across platforms, league types and experience levels so should be a good test of the robustness of our findings.

league_data <- c("REBBL" = "REBBL_S567.rds", "OCC" = "OCC_All.rds", "MML" = "MML_S91011.rds", "CCL XII" = "CCL_XII.rds")

read_and_clean <- function(path) {
  readRDS(str_c(data_dir, path)) %>% 
    map_dfr(
      ~.x$teams %>% # .x$teams stores the statistics for the match
        map_dfr(
          ~purrr::flatten(.x) %>% 
            purrr::modify_if(is.null, ~NA) %>% 
            as_data_frame()
        )
    ) %>% 
    filter(mvp == 1) # only want completed games
}

data_tables <- map(league_data, read_and_clean)

Selecting data

Since this analysis is limited by the data that goes into it, it’s worth considering precicely what data will be used. A lot of data is collected for a team each match including information about the state of the team (TV, Fan Factor, #rerolls, etc.) as well as the match performance (score, #blocks, #kills, etc.). Taking the usable¹ performance statistics gives us the following to work with:

select_stats <- function(df) {
  df %>% 
    mutate(race = id_to_race(idraces)) %>% # race names rather than idcodes
    select(
      race,
      occupationown:sustaineddead, 
      -mvp, 
      -inflictedpushouts, # always zero, so uninformative
      -inflictedcatches # passes/catches are duplicates so only keep one
      ) 
}

data_tables <- map(data_tables, select_stats)

data_tables$REBBL %>% colnames()

##  [1] "race"                   "occupationown"         
##  [3] "occupationtheir"        "inflictedpasses"       
##  [5] "inflictedinterceptions" "inflictedtouchdowns"   
##  [7] "inflictedcasualties"    "inflictedtackles"      
##  [9] "inflictedko"            "inflictedinjuries"     
## [11] "inflicteddead"          "inflictedmetersrunning"
## [13] "inflictedmeterspassing" "sustainedexpulsions"   
## [15] "sustainedcasualties"    "sustainedko"           
## [17] "sustainedinjuries"      "sustaineddead"

Obviously these don’t cover the full spectrum of things that occur during a match, but do provide a good mix to look at.

Analysis

We will be using Principal Component Analysis to take a basic look at how the data break down. An excellent visual introduction to PCA con be found here, but essentially we transform the 17 statistics for each match into a coordinate system that explains most of the variation in values.

run_pca <- function(df) {
  df %>% 
    select(-race) %>% 
    as.matrix() %>% 
    prcomp(scale = T)
}

PCAs <- map(data_tables, run_pca)

The first two principal components for each league explain around 37% of the variation in match statistics. Not an overly impressive amount, however there will be a lot of noise in the data due to the large reliance on random dice rolls in a match. Taking a look at how the matches can be plotted across these two components for an individual league, we see that it is a little bit of a mess:

cbind(as_data_frame(PCAs$REBBL$x), race = data_tables$REBBL$race) %>% 
  ggplot(aes(x = PC1, y = PC2, colour = factor(race) %>% fct_reorder2(PC1, PC2, sum))) +
  geom_point(alpha = 0.5) +
  theme(legend.position = "none") +
  ggtitle("PCA", "REBBL S5, S6 & S7")

Each point on this plot is a single team’s statistics for a match (3896 games - 7792 points) coloured by the race of the team. While there is clearly a lot of variation in how individual matches finish up, there does seem to be a clear trend in certain races clustering to certain parts of the graph. We can summarise this by just taking the median coordinates for each race.

plot_pca <- function(pca, data, flip_x = 1, league) { 
  cbind(data.frame(pca$x), race = data$race) %>% 
    group_by(race) %>% 
    summarise(PC1 = median(PC1)*flip_x, PC2 = median(PC2), count = n()) %>% 
    ggplot(aes(PC1, PC2, label = race, colour = factor(race) %>% forcats::fct_reorder2(PC1,PC2,sum))) +
    geom_point(aes(size = count), alpha = 0.4) +
    ggrepel::geom_text_repel(size = 3, point.padding = unit(0.05,"lines")) + 
    theme(legend.position = "none") +
    ggtitle(league) +
    scale_x_continuous(expand = c(0.2,0))+
    scale_y_continuous(expand = c(0.2,0))
}

plots = pmap(list(PCAs, data_tables, flip_x = c(1,-1,-1,1), names(league_data)), plot_pca)
plot_grid(plotlist = plots)

In this case we have also scaled the size of the points to be proportional to the number of games a race has played in each league, to get some idea of the popularity of each race as well.

Some initial impressions from looking at these results:

• REBBL, MML and CCL all have relatively similar patterns while I have no idea what they’re putting in the water over at OCC to get such a weird relationship (stunty teams mixed in with the regular ones?).
• The distribution of teams maps pretty well onto the usual bash/dash/hybrid definition, with a few interesting differences.
• The races exist along a spectrum, rather than in distinct clusters, which explains why there might be disagreements about how some of the trickier teams could be classified.

Despite this spectrum making an hard classification essentially arbitrary, how would you group races based on this analysis? My attempt to do so would be as follows:

Final thoughts

Even though this analysis is pretty basic, we have been able to create a data-driven classification of Blood Bowl races based on team performance. This classification is generally consistent with those created based on other characteristics, with the added benefit of being able to identify races that play differently from expectations within a specific league environment. This could be due to unique team builds or playstyles adopted by coaches within the league.

If anyone has any insights from within these leagues as to why specific races might look out of the ordinary I’d be glad to hear them. Or if you think there’s a better grouping of teams based on the above graphs let me know below.