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 three strictly separate steps — first how expected the result was (Elo on the team averages, producing a single player delta), then how much is at stake (that delta scaled by the size of the sides), 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. Player delta    playerDeltaA = round(kEff × (W_A − E_A))
6. Stake           teamDeltaA = playerDeltaA × |A|   when |A| = |B|
                              = playerDeltaA         when the sides are uneven
                   teamDeltaB = −teamDeltaA        ← set, not recomputed
7. Shares          share_i per side, Σ share = 1
8. Allocation      integers by largest remainder, exact sum
9. Placement       delta_i ×2 for a player still in placement
10. Floor          newMmr = max(1, mmr + delta)
11. Settlement     the losing side is priced first; whatever the floor kept a
                   player from paying is withheld from the winners' pot

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).

The stake, and why it scales with the format

Step 5 answers a 1v1 question: how much would one player move on this result. Step 6 turns it into what the side plays for. On even sides the stake is that delta times the number of players, so each side splits a pot of the same size and every player moves by exactly what they would have moved in a 1v1 — a win in 3v3 at K-factor 32 is worth what a win in 1v1 at K-factor 32 is worth. Rounding happens before the scaling, not after, so the pot is a multiple of the side size and an equal split lands on the 1v1 figure rather than a point off it.

Uneven sides get no scaling at all: the stake stays one player delta, split within each side. Scaling on the larger side would make the shorter one swing by the size ratio times kEff — in a 1v11 that is eleven times a normal loss, enough to wipe a player out in a single match. One delta per side keeps every line-up inside the risk a 1v1 already carries: the lone player takes the whole stake, their opponents share it.

The stake is also settled, not just allocated. The losing side is priced first, and a player stopped by the floor at 1 pays what they have rather than what they owe; the difference is withheld from the winners’ pot instead of appearing from nowhere. In practice it only ever comes up at the very bottom of a ladder — a player below the match’s effective K — but it is what makes the invariant exact rather than nearly exact.

Sharing between teammates

The team interaction mode is the only calculation lever carried by the discipline. It applies at step 7 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 takes the whole stake, 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, kEff = 32 and the player delta is ±16 — the sides are even, so each plays for a stake of ±32 split between its two players.

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

Scale consequence. None on even sides: the Collaborative rows are exactly the ±16 a 1v1 at K-factor 32 pays, so the K-factor means the same thing in every format and needs no compensation. The mode only redistributes around that figure.

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 one deliberate exception:

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.

The MMR floor of 1 is not an exception. A player cannot pay more than they own, and what they cannot pay is withheld from the winners rather than created — see the settlement step above. It only comes into play when a player’s MMR is below what the match asks of them, which needs a low base MMR and a high K-factor at once.

How much a single match can ask of one player: on even sides it is exactly the 1v1 delta in Collaborative, and more than that in the weighted modes, where the level weighting hands one player a larger share of the stake. The ±25% clamp bounds how far — the ratio to the 1v1 delta tops out at (1.25 / 0.75)^α, so 1.29× in Shared Resource and 1.67× in Individual, and those limits are only approached on large teams: Individual gives 1.25× in a 2v2 and 1.43× in a 4v4 (the 2v2 table above shows 19 against a player delta of 16). On uneven sides nobody exceeds the 1v1 delta. Placement doubles whatever that figure comes to.

Things to know

1. Asymmetric matches carry no compensation. The stake is scaled by the side size only when both sides field the same number of players. In 1v2 it stays one player delta: the lone player takes 100% of it, against 50% each on the other side, so their MMR moves twice as fast per match — five times as fast in a 1v5. It is coherent — they did all the work — but it is a choice, not a mechanical consequence. Scaling there instead would let the shorter side swing past what its players own, and the floor would turn the shortfall into created MMR.
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.