The pool (Master+ mode). 31,000 players: 80 HC (High Challenger, 2500+ LP), 220 LC (Low Challenger, 2000–2500), 700 GM (Grandmaster, 1500–2000), 1,500 HM (High Master, 1000–1500), 5,000 MM (Mid Master, 500–1000), 23,500 LM (Low Master, 0–500).
MMR per tier (centred on LM = 0): HC +1275, LC +1000, GM +750, HM +500, MM +250, LM 0. Tier midpoints derived from LP cutoffs.
Diamond+ mode. Adds a 7th tier: DM (Diamond) at MMR −150 (working estimate; will be refined empirically as data accumulates).
Emerald+ mode. Adds an 8th tier: EM (Emerald) at MMR −350. Calibrated from the observation that a lone LM player on an otherwise-Emerald team beats a 5-Emerald team roughly 64% of the time: RT1 − RT2 ≈ 100 ⇒ EM ≈ −354 (rounded to −350).
No occurrence rates in Diamond+/Emerald+ modes. Match-occurrence requires a defined "pool" with population counts. The Master+ pool (31k players) is well-defined at hard-reset; the Diamond and Emerald populations are larger and far less constrained by ladder anchoring, and matchmaking targets balance rather than uniform random sampling, so static "1 in X" probabilities stop reflecting reality.
Team rating = soft-max with T = 400. Rteam = T · log(Σ exp(Ri / T)). T = 400 means the strongest player only starts to dominate when they're a full tier or more above their teammates. Aggregator direction (lean toward MAX over AVG) is supported by Dehpanah et al. (2021).
Win probability uses standard Elo with S = 400. P = 1 / (1 + 10^((Ropp − Rteam)/S)). A 400-point MMR gap makes the higher team 10× more likely to win.
Match-occurrence probability (Master+ mode only). Assumes uniform random sampling of 10 distinct players from the 31,000-player pool. Real Riot matchmaking targets balance, so genuinely lopsided matchups are even rarer in practice. Meaningful only right after a hard reset; once MMR data accumulates, occurrence numbers stop reflecting reality.
Row counts. Master+: C(10,5) = 252 distinct compositions across 6 tiers, 252² = 63,504 ordered matchups. Diamond+: C(11,5) = 462 across 7 tiers, 462² = 213,444. Emerald+: C(12,5) = 792 across 8 tiers, 792² = 627,264.
Data is computed in your browser on demand. No precomputed tables are shipped; switching modes triggers a quick recomputation (typically under a second on desktop). All math runs locally; nothing leaves your machine.