Overthinking Twilight Imperium, 4th Edition

Twilight Imperium is a space opera strategy board game by Fantasy Flight Games. The modern board game enthusiasts at Board Game Geek rank it in their top ten, but it is also a very complicated game: there are dozens of factions, an expansive technology tree, and almost 50 pages of rules in the living rules reference.

I found a data set from thousands of games played online asynchronously and will use this as a starting point to answer my personal questions about faction and hero strength.

Tip

Twilight Imperium is a complex strategy game that is, at its heart, about diplomacy and playing the table — that is, it’s a social game (though having the right plastic on the table helps too). Winning the game isn’t as simple as just picking the right faction or technology tree.

I do not think data analysis will tell you how to win the game at your table, but I think it is fun to do these kinds of analysis and think the results are an interesting statement on the current “meta” in this version of the game.

Faction Strength

Twilight Imperium has two dozen different factions, each with their own abilities and flavor of play. I tend to actually really enjoy playing as factions many consider weak, including the Arborec and Mentak Coalition.

Model Math

For each event E, we have P players (6 in this case) who are playing one of 1-P factions. Each game has one winner drawn from the categorical distribution based on the factions’ abilities.

Here is the code in Stan:

data {
  int<lower=1> E;                      // number of events
  int<lower=1> P;                      // total number of players
  int<lower=1, upper=P> players[E, 6]; // player IDs per event
  int<lower=1, upper=6> winner[E];     // winner index (1-6)
}
parameters {
  vector[P] ability;                   // faction strength
}
model {
  ability ~ normal(0, 1);             // priors

  for (e in 1:E) {
    vector[6] logit_p;
    for (k in 1:6) {
      logit_p[k] = ability[players[e, k]];
    }
    winner[e] ~ categorical_logit(logit_p);
  }
}

Potential ways to improve this analysis:

• Account for speaker position and slice strength.

Faction Combos

The presence of another faction in the game can have a large effect on a faction’s strength. For instance, the Yssaril benefit from other factions like the Naalu that have powerful agents they can copy.

Table 1

Select Target Faction: Arborec Argent Flight Barony of Letnev Clan of Saar Embers of Muaat Emirates of Hacan Empyrean Federation of Sol Ghosts of Creuss Keleres ~ Argent Keleres ~ Mentak Keleres ~ Xxcha L1Z1X Mindnet Mahact Gene-Sorcerers Mentak Coalition Naalu Collective Naaz-Rokha Alliance Nekro Virus Nomad Sardakk N'orr Titans of Ul Universities of Jol-Nar Vuil'raith Cabal Winnu Xxcha Kingdom Yin Brotherhood Yssaril Tribes

Heroes

Most Played Heroes

One of my pet theories is that good heroes are ones that you can play consistently.

Table 2

Faction	Hero Purged %
Titans of Ul	94.06%
Empyrean	91.33%
Naalu Collective	88.52%
Naaz-Rokha Alliance	87.41%
Keleres ~ Mentak	86.39%
Yssaril Tribes	86.20%
Emirates of Hacan	79.22%
Universities of Jol-Nar	76.13%
Vuil'raith Cabal	73.81%
Nekro Virus	72.70%
Yin Brotherhood	72.67%
Winnu	67.30%
Keleres ~ Xxcha	61.54%
Arborec	60.57%

Faction	Hero Purged %
Federation of Sol	58.81%
Mahact Gene-Sorcerers	58.06%
L1Z1X Mindnet	58.06%
Ghosts of Creuss	56.64%
Clan of Saar	45.24%
Embers of Muaat	41.42%
Argent Flight	38.55%
Mentak Coalition	35.18%
Keleres ~ Argent	31.96%
Sardakk N'orr	29.88%
Nomad	17.59%
Barony of Letnev	15.40%
Xxcha Kingdom	0.00%

Here we can see which factions have the most usable heroes ¹. The Titans hero gives a nice planet upgrade in the home system and gets used in almost every single game. On the other hand, the Barony hero is much more situational.

¹ Note that as of Codex III, the Xxcha hero is the only one that cannot be purged.

Hero Importance

To determine hero strength, we might ask: for each faction, to what extent does playing the hero help them win?

Figure 1: Estimated effect of purging each faction’s hero on win probability in Twilight Imperium. Points show posterior means; error bars show 95% credible intervals. Values above zero indicate factions that tend to perform better when their hero is purged.

Unsurprisingly, the Winnu game seems most dependent on their ability to use their hero, which can let them play the primary ability imperial strategy card at any point.

Mecatol Rex

Is it worth it to take Mecatol Rex?

Table 3

Scored Mecatol?	Games	Win Rate
Yes	6040	25.08%
No	12044	12.45%

Figure 2: Histogram of simulated changes in win probability from scoring at least one point from Mecatol Rex. The minimum result from the simulation is an increase of 12.1 pp.