TrueSkill
Each player carries a skill estimate and an uncertainty; the shown rating is the conservative bottom of that range. Every match updates both, for duels, teams and free-for-all alike.
Bayesian: skill = μ - 3σ, updated per match
Best at
Global game leaderboards with many players in groups that never meet — it was built for exactly that, and it is the only advanced rating that handles all three match shapes.
Where it misleads
The uncertainty maths is invisible to players, the numbers are less graspable than an Elo rating, and large free-for-all fields are expensive to compute.
How it works
TrueSkill, developed by Microsoft Research for Xbox Live, is a Bayesian skill rating system that natively supports teams and free-for-all games with placements -- something Elo and Glicko cannot do.
How it works: Each player has a skill estimate (mu) and uncertainty (sigma). The conservative rating is mu - 3×sigma. After each match, a Bayesian update refines both values based on the outcome and the relative skills of all participants. It handles partial orderings, teams, and multi-player free-for-all matches.
When to use it: The most versatile advanced rating system. If your group plays FFA board games, team games, AND 1v1 games, TrueSkill is the only advanced rating that handles all three.
Watch out for: Computationally expensive, especially with large FFA fields. The mathematics are complex (factor graphs). Rating numbers aren't as intuitive as Elo (a "skill" of 25.0 ± 8.3 isn't as graspable as "1800 Elo").