We present the KPMA Global Rating Model (KGRM), a probabilistic rating system for four-player Riichi Mahjong. Classical Elo models pairwise win/loss outcomes and does not natively handle ordered multi-agent results. KGRM addresses this via three integrated components: (i) a Plackett–Luce (PL) likelihood for full four-player rankings, (ii) Gaussian latent skill with uncertainty-adaptive updates in the Bayesian tradition of Glicko and TrueSkill, and (iii) a zero-sum, experience-weighted score-differential correction with provable boundedness. We derive the exact PL gradient, present a production-ready update rule, and prove key stability properties including bounded score injection and monotone uncertainty contraction. Synthetic simulations with N=2,000 players over 200,000 matches confirm that KGRM converges to a rating spread matching the true skill distribution (Std(µˆ) → Std(µ∗)), while achieving rank-order accuracy comparable to pairwise Elo (Pearson r = 0.978 vs. 0.979 at 60,000 matches) with the additional benefit of uncertainty-aware updates. Real-data validation on KPMA league results is planned as match records accumulate.
Seongho Jeong (Thu,) studied this question.