๐ค AI Summary
็ ็ฉถๆๅปบไบไธไธชๅบไบ้ป่พๅๅฝ็่ตๅ่็้ขๆตๆจกๅ๏ผ็จไบ้ขๆตใ่ฑ้่็ใ่ไธๆฏ่ต็ปๆ๏ผ้่ฟ็ปๅๅจๆๅ้ๆๅข้ๅฎๅ็ญๅ ็ด ๏ผๆ้ซไบ้ขๆตๅ็กฎๆงใ
๐ Abstract
We build and evaluate a pre-game win-probability forecaster for individual maps (``games'') in professional \emph{League of Legends} (LoL). The proposed model is a one-stage logistic regression fit end-to-end on the win/loss log-loss: each team's exponentially-weighted moving average of past same-side results, a ridge-shrunk stable strength that is the maximum-a-posteriori estimate of a logistic mixed model, and a first-pick draft covariate, natively calibrated out of sample (walk-forward slope $0.995$). It augments a purely dynamic Bradley--Terry specification with stable team strengths. A second, independently built two-stage composite mixed model under restricted maximum likelihood (REML) and best linear unbiased prediction (BLUP) shrinkage, with Platt calibration, serves as the strongest rival the authors could build. On $5{,}135$ games across six regional leagues and three international events (2024--2026), under paired per-game Diebold--Mariano inference, the two architectures are statistically indistinguishable on every protocol and window (global holdout $0.2230$ vs.\ $0.2257$; walk-forward $0.2207$ vs.\ $0.2215$), so the simpler model is preferred on parsimony, not accuracy; both improve on the classical dynamic benchmark ($0.2351$) by a clear margin and on the static fits ($0.2301$/$0.2268$) more modestly. Against Polymarket on $928$ matched maps, the forecasts are statistically indistinguishable from the market on its own per-game contracts, with a modest market edge concentrated on cross-region Worlds and series-decider maps.