Plackett–Luce (Ranking MLE)
Read the shape of this family
Family illustration · not a computed standing
Maximum-likelihood models — the most rigorous skill estimates. The formula and explanation below describe Plackett–Luce (Ranking MLE).
How it works About 1 min read
Plackett-Luce extends Bradley-Terry to handle full rankings in multi-player matches. It models the probability of any particular ordering of players, making it the gold standard for FFA statistical ranking.
How it works: The model treats a full placement as a sequence of "choices": 1st place is the most likely to win from all players, then 2nd from the remaining players, and so on. MLE finds the skill values that maximize the probability of the observed orderings.
When to use it: When you record full placements in FFA board games and want the most statistically rigorous skill estimates. It's essentially what TrueSkill approximates, but solved exactly.
Watch out for: Computationally expensive, especially with large fields or many matches. Requires iterative optimization. Only works with FFA placement data. Best for analytically-minded groups who appreciate statistical rigor.
Will it fit your results?
Also in Statistical Models
Maximum-likelihood models — the most rigorous skill estimates.