Beyond Stasis Graphs

On November 10th, 2020 Bungie launched an expansion for their game Destiny 2 entitled Beyond Light. In addition to new story content, the large yearly expansions often come with dramatic tuning of the game world via changes to the weapon systems, abilities, and/or new game modes. Beyond Light follows that trend by not only introducing a new element — Stasis — into Destiny (a first for the game since it launched in 2012), but also making drastic changes to the weapon system.

Given that Bungie had some plan in mind (e.g. slowing down the game so that players have to be more tactical, cautious, and increasing the tools players have to counteract aggressive enemies (e.g. putting up an ice wall to protect you from a shotgun user running at you)) when making these changes (weapon changes, ice abilities, etc.), being able to identify if they met their goal would be a useful analysis from the game studio’s point of view since AAA games cost tens to hundreds of millions of dollars to make today.

Statis is a new damage type in Destiny that freezes enemies and provides crowd-control tools for players. For example, a new stasis grenade available in the game creates a wall of ice wherever the person throws it thereby blocking off entire corridors (an advantageous ability in Player vs Player arenas) and freezing people the wall touches (thereby making them more vulnerable to one-hit kill abilities).

Regarding weapon system changes, Bungie has: nerfed (e.g. made worse) Hand Cannons (by removing an entire sub-category), nerfed Sniper Rifles (by increasing zoom), and nerfed auto rifles to name just a few of the weapon system changes. Another change is that Bungie is sunsetting old gear (making it so that old gear is obsolete after a period of time) to force players to change up their weapon loadouts and to ensure they have space to design new cool weapons without worrying about breaking the game forever.

As a reminder, this work has been analyzing player-weapon graphs created in the Competitive Player vs Player environment of Destiny. These graphs are created by pulling PostGameCarnageReports from Bungie’s open-facing API. I collect the data using Snowball sampling where I start with a single individual (myself), and pull down the k most recent matches played (k=50). Since matches are team-based, I also get IDs for m more players (m changes depending on the game mode, in this case m=7). Using their IDs, I pull k more matches from their history. And so on and so forth repeating this process until I decide to kill the script (It ran for about 13 hours pulling data for about 22k unique players.).

The graphs created using the player and weapons/abilities they use are bipartite graphs. Specifically, you can see the pre Beyond Light graph below:

Pre Beyond Light: Bipartite Player-Weapon graph from previous posts + Degree Distribution + Eigenvector Centrality.

We would like to see how this graph changes over time. Since Beyond Light came out a few days ago, we only have a few days worth of data we can pull, but given that the player population for this game is in the hundreds of millions of players, there shouldn’t be an issue of too little data. The only change in how the data was pulled was that rather than going deep into a player’s Competitive PvP history to pull matches, we can only pull matches from the past 4 days (as of writing this). At a practical level, this means the amount of time the snowball sampling is running will be higher and that the number of games pulled from each person will be smaller. That being said, the game’s population is high enough that we shouldn’t run out of people to sample data from.

The first thing we can check is: does the degree distribution change for the player-weapon graphs in Beyond Light. If so, this would signal a massive change in how players are playing the game.

Degree Distribution Graphs split by date.

In this case, the degree distribution graphs have not meaningfully changed. And this makes sense here as when someone goes into a PvP match, they have a loadout of 3 guns and 3 unique abilities. The guns can be swapped on the fly, but clearly, most people don’t do that as the median degree of a given playerNode is 4 indicating that the median person uses 4 unique weapons/abilities. This was true both pre and post Beyond Light.

The next natural question, and one that is likely to be more meaningful, is: how does the centrality of the weaponNodes change after Bungie’s patch? Pre Beyond Light sees the four most central nodes as Grenade Launcher, Hand Cannon, Pulse Rifle, and Rocket Launcher (top 4 because that’s the median number of guns used according to the degree distributions). Two of these nodes (Grenade and Rocket Launchers) are heavy-weapons (guaranteed one-hit kills), but with rare ammo. On the other hand, the primary weapons of Hand Cannons and Pulse Rifles are the preferred weapon choices in the community (from what I’ve seen and from influential streamers).

Weapon Centrality using Eigenvector Centrality split by date.

Each day here has something interesting to note, so we’re going to take them in order.

Nov 10th: hand cannons have been replaced by machine guns as the most central weaponNode. Furthermore, bows and sniper rifles have become in the top-4 most central nodes. Bows and sniper rifles are long-range weapons which would be fitting in a slowed-down cautious game.

Nov 11th: machine guns and pulse rifles are still holding over from the 10th, but shotguns have increased in usage dramatically. This is likely because the new ice-based abilities can freeze enemies. This means that if a shotgun user were to freeze an enemy in place (say with a freezing grenade), they could then close the distance easily and kill the enemy with ease.

Nov 12th: Hand cannons and rocket launchers have returned to their pre Beyond Light usages. But the interesting thing here is that Super abilities (the most powerful class defining abilities in the game) have joined the top-4 central nodes. This is likely people experimenting with the new Stasis subclasses after they finished earning the new subclasses.

Nov 13th: LinearFusionRifleKills is the interesting node here. This is a very difficult weapon type to use where all of the damage goes into a single shot, where if that is a critical hit, it kills the enemy. But, given how fast the game is normally, it’s often quite hard to use this weapon type effectively. This is more supporting evidence that Bungie’s design goal of slowing down the pace of the game is working as intended.

As we discussed last time, we can use Modularity to partition latent clusters in the graph. So, we use the same method again, but on the temporal graph slicing it by day as above but coloring the graph according to the modularity classification.

We can note that each day sees a new modularity class color defining the graph from slightly blue to blue to pink to green (with a darker green class not taking a prominent role in the visualization). Furthermore, the clusters grow in size indicating that either I just have more data from those days and modularity split the graph in parallel to time or strategies are becoming more pronounced as the player-base solidifies into the new systems put in place.

Limitations and Ethical Concerns:

1. It is possible that this analysis is too soon after the launch of Beyond Light. One of the fundamental changes Bungie made to Destiny with this expansion is that they are sunsetting old weapons. This means that everyone has to leave their old gear behind. Since people will still be grinding to reach the new max power (a stat in the game) for a little while still and they had to leave their old gear behind, they could be using whatever gear they happened to have at the moment while in the PvP arena. This would mean that their weapon choices are not the specific meaningful choice as I assume them to be (and would be later on the expansion’s lifecycle).
2. As before, I am undoubtably missing contextual data that would allow me to create a more nuanced analysis. In this case, since we’re looking at whether or not Bungie slowed down the game rather than playstyles, other useful metrics would be averageKillDistance, averageDeathDistance, matchLength, percentCriticalHits. While there are proxies for some of these in the graphs I did create (e.g. shotgunKills being a proxy for averageKillDistance being low), it would be useful to include these additional node and edge features.
3. Since it is not a guarantee that every player I pulled data about for the pre Beyond Light analysis would have played the game since Beyond Light or would have played the game enough for me to pull a meaningful amount of data from them, I restarted the snowball sampling from patient 0 (myself). However, this time I cast a wider but more shallow net. I pulled the 50 most recent games from each player I encountered (rather than 250 as before), but only accepted games that were played after Nov. 10th. Therefore to get the same amount of data I needed more players. Thankfully, Destiny’s player population is high enough for me to do this and I pulled another ~23k unique players. However, the shallower net means that I lave less repeated data from each person which makes determining player-centric information less certain. Essentially, fewer samples per person means higher potential variance in my assertions.
4. The primary ethical concern of this work is that yes, the data is open to the public, but I am pulling people’s data who might not want their data being used by me. There really is no easy fix for this, but I have omitted identifying information as much as I could.

Code (linked again): https://github.com/aadharna/SocMed/blob/a3/Destiny