State of the Crusade


Metrics in Warhammer 40,000: Eternal Crusade

You, the players, are agents of chaos (even the Space Marines).
You are free electrons in the neatly designed world that the designers create, and you rarely behave as expected. By giving you guys more freedom, they enhance the portion of the game design process that they cannot control.  Although it makes the game more fun, it makes their jobs way harder. Each new feature introduces more complexity in the game.

But they are smart. They don’t go in blind! Like Tzeentch, they monitor your puny conflicts, using what they call metrics.

A metric can be anything measurable. Metrics include scores like numbers of kills, deaths or rescues, and it can be specific behaviours like classes and weapons choice, communication, or experience progression. There is no need to say that all those metrics adds up to create huge and bloated databases.

Here is where I come in. I am a PHD student in evolutionary biology (some sort of Magos Biologis) with a speciality on social animal behaviour (soon to be the leading expert on the Tyranids taxon). Evolutionary sciences offer centuries of scientific findings on interactions among individuals and their environment. My statistical background and scientific conceptualisation will squeeze the most out of the highly diverse metrics that the Eternal Crusade team monitor. My goal is to come up with predictions on player behaviour to give the necessary information to enlighten the design decisions from patch to patch.  
 
Here are a couple of miscellaneous descriptive statistics in Eternal Crusade.

As of now, more than 25,000 matches have been played. One player played 1,977 matches. On average, a player kills 12.8 opponents, dies 10.8 times per match (see figure 1). 1.5% of players fail to kill any opponents and only 0.5% manage to stay alive the entire match.  On average, a player rescues 1.05 teammates and executes 1.4 opponents per match.

Figure 1: Histogram of kills per match (left-hand side)
and deaths per match (right-hand side)


The Bolter is by far the most used weapon, followed by the Power Sword and the Chain Sword (see figure 2).  The Quad Gun had a spike in popularity since its accuracy was increased during April 14th patch. Note that Psychic Power kills are underestimated since the poison lasted a certain time and the kills can be attributed to another weapons. Around 34 % of kills are done with melee weapons.

Figure 2: Frequency of weapons (%) used to fight


Any multiplayer game can be approached as an ever-changing ecosystem. Nothing is really fixed. In my point of view, classes or factions are “species”, maps are “habitat” and fighting to capture a control point is only a struggle between individuals to secure a resource of interest. Being in constant evolution, some changes (tweaks) create unexpected outcomes in the game. 
 
For example, the Mark of Nurgle sure did his part in breaking the balance. The “mutation” of the Mark Of Nurgle overpowered the Traitor Assault (see k/d ratio; top part of figure 3) and the class invaded the population i.e. became more frequent at the expense of the Traitor class (middle part of figure 3). Traitor Assault stayed popular long after the nerf of the Mark Of Nurgle on the April 14th patch, even though our monitoring of the Kill/death ratio clearly indicates a drop in his over-poweredness. It even correlated with a largely tilted winning frequency in favour to the Chaos Space Marine faction (bottom part of figure 3).  I’ll draw your attention on the fact that the most common classes – Traitor and Tactical – are generalists with a wider range of options. Specialist classes like support classes have a smaller niche in the current systems and it will be very interesting to see what will happen with a specialist-oriented faction (Eldar).

Figure 3: Kill/Death ratio (up), class frequency (middle) and frequency of winning (bottom) from March 18th to April 21th


As you know, Marines have a short lifespan and we estimate that they die on average 1 minute 28 seconds after spawning (way shorter than a mayfly). Survival chances are better in the Fortress Harkus map (see figure 4). We did not see any difference in lifespan for the classes or faction. My prediction is that future stealth classes will survive longer. They will move slower and it is known that slower-paced organisms have longer lifespan! The oldest marine that has ever “lived” lasted a little more than 21 minutes while playing a havoc class. Beware, like in many species, Marines are often victim of teammates. 4.9% of kills is from friendly fire, and 65.2% of players killed at least one teammate. One player killed a grand total of 1 opponent and 13 teammates in one match.

Figure 4: Survival odds through time of Marines for different maps.


Beyond descriptive figures, a statistical analysis of in-game metrics can have a predictive power.

As with species, we expect factions to respond differently to their environment. The winning odds are different depending on your factions or on whether you are the attacker of the defender of the territories (see figure 5). A logistic regression (binomial generalized linear model) emphasizes a higher effect of kills on the winning odds when defending (GLM, estimate= 3.065, p<0.001) than in attacking (GLM, estimate= 1.229, p<0.001). It makes sense because attackers must capture control points to win, while defenders fend off attackers by killing them. Rescues, on the other hand, are an attacker strategy because it is more significantly correlated with winning for attackers (GLM, estimate= 1.383, p<0.001) than for defenders (GLM, estimate= 0.068, p<0.661), maybe because the latters usually spawn closer to the action. There is also a significant correlation between the amount of executions and the odds of winning only for the defender team (GLM, estimate= 1.603, p<0.001). The strategic advantage of executions is unclear, and that correlation may only mean that winning defender teams have more occasions (more free time) to execute opponents. Finally, teams that communicate more win more often (GLM, estimate= 0.258, p=0.002). The Black Bolt Defense map is the easiest to attack on, and our hypothesis is that the higher number of control points (4) makes it easier to capture and hold many points (see figure 5).

Figure 5: Proportion of matches won by Space Marines and Chaos Space Marines in different maps. 


Teams that win capture points sooner in the match than teams that lose (see figure 6; boxplots show the four quartiles – 25% of data − distribution). Timing and strategies are therefore capital for attackers and there is no time to lose. In the Thug of war game mode, don’t expect to win if you don’t capture the first control point in the first 15 minutes or so. In the domination game mode, conclusions are harder to find since any control point can be captured at any time, and since criteria for winning is different. Interestingly, we observe that some teams are able to capture all the four points very quickly (less than 5 minutes). In the Fortress mode, half of the matches last longer than the regular 25 minutes (see figure 7) because the second point (the one that determines the win) is often captured during the time extension (see figure 6).

Figure 6: Distribution of the moments the attacker team captures a new control point.


Figure 7: Distribution of durations of match based on game mode.


We also monitor predation (kills) and cooperation (rescues) events, and where they take place. Both are unevenly distributed in space and further analysis should point out to map elements and structure that actually promote kills and/or rescues, or that favour a specific class and/or weapon. Can you guess the map by looking at where players die?

Figure 8: Spatial distribution of kills in different maps.


Social interactions are common to all multiplayer games, and Eternal Crusade displays many interesting layers of social interactions. Such social interactions can be mapped in networks to study the resulting social structure. Each node is a player and each arrow is an interaction (rescues or kills) between two players. Some teams are more tightly connected than others (see the Space Marine rescues network; left-hand side of figure 9) and some players are key in uniting teammates (see the player CSM11 in Chaos Space Marine rescues network; right-hand side of figure 9). I hypothesize that the social structure of a team drives its success and that a player in a center position should progress faster.

Figure 9: Network of social interactions in a match. The space marines defended and won.


In conclusion, since my whole PHD thesis will be on the evolution of group behaviour, I will strongly suggest you to keep on fighting and stay close to your friends.

Finally, as an evolutionary biologist, I put my money on the Tyranids. The Hive Mind and their reproductive system allowing the selection of morphs enable the whole race to respond to natural selection way faster than any other factions or races.

Julien Céré
PHD Student / Stats Guy
Warhammer 40,000: Eternal Crusade
www.eternalcrusade.com

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