MMR Rating

Ranked competitions keep a persistent rating per player: the MMR. This page describes exactly how it moves.

The guiding principle: a match transfers MMR from one side to the other, it never creates any. The computation happens in two strictly separate steps — first how expected the result was (Elo on the team averages, producing a single team delta), then who takes which share of it (the discipline’s team interaction mode, producing normalised shares).

Scope

MMR only exists in ranked mode. A classic tournament — championship or bracket — never writes MMR, whatever its disciplines and outcome types are.

Season settings

Each ranked season carries its own tuning, set when the season is created and applied to every match played in it.

Competition ruleset

The scoring rules a match is valued with come from its discipline, but they are frozen onto the competition when it opens. Both the calculation and the display read that snapshot, never the live discipline.

While a competition is still a draft the snapshot follows the discipline — no match can exist yet. After that, only an explicit propagation moves it, and that propagation triggers the recalculation in the same pass, so a competition is never half under the old rules. Editing a discipline therefore has no effect on a running or finished competition: its numbers stay the ones it was played with.

An archived outcome type disappears from match entry but stays resolvable for matches already recorded with it.

The calculation

1. Short-circuit   counts-for-MMR off → every delta is 0
2. Averages        avgA, avgB = arithmetic mean of each side's MMR
3. Expected score  E_A = 1 / (1 + 10^((avgB − avgA) / 400))
4. Effective K     kEff = K × scoreMult × mmrMultiplier
                   scoreMult = 1 + |scoreA − scoreB| / (scoreA + scoreB)   ∈ [1, 2]
5. Team delta      teamDeltaA = round(kEff × (W_A − E_A))
                   teamDeltaB = −teamDeltaA        ← set, not recomputed
6. Shares          share_i per side, Σ share = 1
7. Allocation      integers by largest remainder, exact sum
8. Placement       delta_i ×2 for a player still in placement
9. Floor           newMmr = max(1, mmr + delta)

W is 1 for a win, 0 for a loss, 0.5 for a draw. Score amplification runs from ×1 (equal score, 0-0, or no score at all) to ×2 (a shutout) and depends on the gap, not on the winner — both sides take it identically.

teamDeltaB is set to −teamDeltaA rather than recomputed from E_B: that is what makes the two sides cancel exactly, since rounding is not symmetric on halves (round(2.5) = 3 but round(−2.5) = −2).

Sharing between teammates

The team interaction mode is the only calculation lever carried by the discipline. It applies at step 6 only: it never changes the strength of the result, only its distribution.

r_i     = clamp(oppAvgMmr / max(1, mmr_i), 0.75, 1.25)
sign    = teamDelta >= 0 ? +1 : −1
exp     = mode is Individual ? α × sign : α
w_i     = r_i ^ exp
share_i = w_i / Σ w

One formula, three values of α:

Collaborative with α = 0 gives a weight of 1 for everyone, so share = 1/n: the equal split is not a special case, it is the degenerate case of the general formula.

In 1v1 the mode has no effect. One player per side means a share of 1, so the player delta is the team delta, whatever the mode. The invariance is structural, not a special case in the engine.

Worked example: 2v2, {900, 1400} against {1150, 1150}. Both averages are 1150, so E = 0.5 and kEff = 32, giving a team delta of ±16 split between the two players.

The last row is what separates Individual from Shared Resource: same team, same match, responsibilities inverted.

Scale consequence. In 2v2 each player takes half the team delta, so MMR moves twice as slowly per match as in 1v1. That is the price of conservation, and the season K-factor is the lever to compensate for it.

One engine, three paths

Three situations compute MMR, and all three call the same engine with the same ruleset. They differ only in the MMR snapshot they are given:

Team averages, MMR multiplier, team interaction mode, the doubled placement delta and the counts-for-MMR short-circuit behave identically on all three. In other words: the delta shown before validation is, by construction, the one applied at finalisation.

Rounding is deterministic — allocation by largest remainder, equal remainders broken by ascending player id. Player iteration order therefore influences no result, which is a necessary condition for deterministic season replay.

Season start: carry-over and soft reset

Carry-over fills a set of seeds, never the live ladder: a seeded player who never plays appears neither in the standings nor in the percentiles.

eligible = players of the source season with matchesPlayed ≥ max(1, source placementMatches)
anchor   = median of the eligible players' current MMR
seed     = max(1, round(baseMmr + (mmr − anchor) × softResetFactor))

With carry-over off there are no seeds and everyone starts at base MMR. A soft reset factor of 0 is a hard reset; 1 keeps the full distance to the median, recentred on the new base. Median rather than mean, because a handful of runaway players must not drag the whole ladder’s reset point.

The entry MMR is resolved the same way everywhere:

match history  →  current MMR  →  carry-over seed  →  base MMR

Recalculation

The cascade exists because a backdated match rewrites the history of players who were not in it: it recomputes, in successive waves, everyone who crossed a player whose MMR moved, until it stabilises.

The deterministic replay processes each match exactly once in order (by date, then id), keeping per-player state in memory and making a single engine call per match, so every participant is valued on the same pre-match snapshot.

Worked examples

Baseline: K-factor 32, two players at 1000, MMR multiplier 1, placement over.

A draw is a real Elo result: the underdog gains MMR, the favourite loses some.

The invariant

Σ delta(side A) + Σ delta(side B) = 0

Exact, with two deliberate exceptions:

1. Placement. A player in placement has their delta doubled after the split, so a rookie converges twice as fast without their opponents risking double. The injection is bounded by placementMatches × K per player and disappears once placement is over.
2. The MMR floor of 1. A guard rail, unreachable in practice with a K-factor of 128 or below.

Things to know

1. Asymmetric matches carry no compensation. In 1v2 the lone player takes 100% of their side’s delta, against 50% each on the other side: their MMR moves twice as fast per match. It is coherent — they did all the work — but it is a choice, not a mechanical consequence.
2. Outcome type points play no role in MMR. They only feed championship points, so changing them has no effect on a ranked ladder.
3. An MMR multiplier of 0 and counts-for-MMR off both produce a zero delta, but only the second short-circuits the whole calculation.
4. The default mode is silent. A discipline created without a team interaction mode runs as Collaborative. The snapshot freezes it as such, so the default that was applied stays in force even if the discipline is corrected later.
5. Editing a discipline no longer affects any open competition. Each competition carries its own ruleset snapshot. Propagating a change is an explicit action that recalculates the competitions you pick, and finished competitions are never offered.
6. The stored effective K is the match K, doubled for a player in placement — not a display value recomputed separately.
7. A formula change re-runs unfinished seasons automatically. Each season records the engine version it was computed with. On startup, every unfinished ranked season left on an older version is queued for a deterministic replay, so an upgrade ships its own data migration. Finished seasons stay frozen — their carry-over seeds are already derived — and keep the stamp of the version that computed them. A recalculation can also be forced from the competition’s admin actions.