The pool. 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. These are tier midpoints derived from the LP cutoffs — HC's midpoint is mass-weighted up to ~2800 LP because the tier extends to 3290. The MMR values are roughly half the LP differences because LP gains in Apex are inflated relative to underlying skill movement: Riot's baseline ±30 LP per win for a fairly-matched game implies ~10–15 MMR per win once you account for the LP/MMR reconciliation Riot applies at the top of the ladder (see Riot /dev: MMR-to-Rank Distribution on the +10/−30 phenomenon and WhatIsMyMMR on the rough 2:1 LP:MMR compression). Only differences between tiers matter for the math, not the absolute zero.
Team rating = soft-max with T = 400. Each team's rating is a soft-max (log-sum-exp) of its five players' MMRs: R_team = T · log(Σ exp(R_i / T)). T controls how much the strongest player dominates: at low T the team rating ≈ MAX, at high T it ≈ AVG. T = 400 was chosen so that 5 GMs are roughly 60% favourites against 1 HC + 4 LMs (at T = 300 the same matchup gives 5 GMs ~43%, at T = 500 ~66%) — coordinated GMs beating one carry surrounded by passengers, which matches high-elo intuition. T = 400 is also of the same order as the 500-MMR gap between adjacent tiers, meaning the strongest player only starts to dominate when they're a full tier or more above their teammates. Lower T (e.g. 200) would make a single Challenger essentially unbeatable; higher T (e.g. 800) would make them barely matter. The aggregator direction (lean toward MAX, not pure AVG) is supported by Dehpanah et al. (2021), who found MAX-style aggregation predicts MOBA outcomes better than SUM/AVG. The exact value T = 400 is calibration to feel, not measurement — no published value exists.
Win probability uses standard Elo with S = 400. Once both teams have a rating, win probability is the standard Elo logistic: P = 1 / (1 + 10^((R_opp − R_team)/S)). S = 400 is the chess default — it means a 400-point MMR gap makes the higher team 10× more likely to win. The full Master+ MMR range here (~1275 between HC midpoint and LM) is roughly comparable to the active range in chess, so the chess scale transfers directly. With S = 400, an HC vs LM 1v1 is 99.9% — appropriately one-sided without being absurd.
Match-occurrence probability. Assumes uniform random sampling of 10 distinct players from the 31,000-player pool, then split into two teams of 5. The "1 in X games" column is the reciprocal of this probability. This is most accurate in the first few games after the Apex hard reset, when everybody starts at Master 0 LP and Riot's matchmaker has no rank/MMR history to work from — so genuinely random pool draws are the realistic expectation. As players accumulate games, Riot's matchmaker progressively tightens around team-MMR balance and pulls every player's expected win rate toward 50%, which means the lopsided matchups in the bottom of the table become even rarer in practice.
Why 63,504 rows? There are C(10,5) = 252 distinct 5-player team compositions across 6 tiers, and 252² = 63,504 ordered matchups (Team 1, Team 2). Each non-mirror matchup appears twice — once from each side's perspective — so it's easy to look up "what's my win chance if I'm on this side."
0 in the Team 1 GM, HM, MM, and LM boxes shows only matchups with HC and LC players on Team 1.