Separate player rating systems for attackers and defenders

Question

Imagine a kind of tower defence game where each player specialises either in defence or attack (a player is either one or the other in all games). In each game the attacker and the defender get separate scores. I want a leaderboard for the best defenders and a separate leaderboard for the best attackers. What are appropriate player rating systems in such a scenario? The ideal system is also efficient in that it produces robust rankings even if only a fraction of all possible attacker/defender combinations are actually played.

All the scoring systems I am aware of (e.g. Elo ratings or Microsoft TrueSkill) assume that both players are treated on an equal footing. I'd be extremely grateful for any pointers to relevant scoring systems.

Answer 1

You can still use ELO rating in this situation.

ELO would not work properly if players sometimes play with advantage and sometimes with disadvantage. But that's not the situation you are in. When players always play the same role, they always have the same disadvantage. ELO makes no difference between a systematic disadvantage due to the game always being stacked against specific players or a disadvantage because some players simply have less talent.

You also don't need to have players play directly against each other in order for their ratings to be comparable. The whole point of ELO ratings is to be able to infer the relative strength of two players based on their performance against other opponents. It is even possible to compare the ELO ratings of chess players who weren't even active players at the same time. The ELO scores of two players who never met will be predictive as long as the graph of all games played has at least some remote connections between them.

ELO tells you the expected likeliness of a player beating another player. When there is a really successful defender who wins almost all games, then that defender will have a high ELO rating. When only a very few attackers are able to beat that defender from time to time, they must be exceptionally good attackers, so they also deserve a higher ELO rating than those who always lose against that defender.

When your game is asymmetrical with one role having a systematic advantage, then the ELO ratings of attackers and defenders won't be comparable. The disadvantaged players will have a lower average ELO. That means if players would be able to play both roles, you would need to track the defense-ELO rating and attack-ELO rating separately for each player. But you said you are already going to do this by having separate leaderboards for attack and defense and having each player create two separate user accounts if they want to play both.

Regarding Microsoft TrueSkill: I don't know enough about that system to tell if these points also apply to it or not.

Answer 2

This is possible with existing scoring systems. You need to treat attacking players separately from defending players, even if they are the same player.

Suppose you have three players (1, 2, 3), who have played a bunch of games against each other, both as attackers and as defenders. Instead of scoring them as if there were three players, split that into six: (A1, A2, A3, D1, D2, D3). That is, pretend that there are three players attacking exclusively, three players defending exclusively. No "A" player plays against another "A" player, same for the "D" players.

This is fine because the scoring systems should be able to rank players that don't play each other. The scores for attackers and defense would probably be different, say if the game was unbalanced between attack and defense, or if some players play attack more than defense and so on. You will need to scale each set of scores differently, in order to grade them.

Answer 3

Since the common part of a tower defense game is the tower, the scoring system could be based around the percentage of the tower remains at the end of the game.

An attacking player who does a lot of damage should receive a higher score than one who only does a little bit of damage.

Likewise, a defending player should score highly if a lot of their tower remains compared to one who's tower consistently gets destroyed.

This is assuming the play is one on one. If it's multiplayer, then the attacking player score calculation remains the same (based on individual damage caused with a small bonus for total damage) but the score for defenders should be put to lean more towards the number of individual attackers they kill with a small bonus for total remaining tower.