Methodology

Arena has no official ladder, so this one is computed. Every constant the rating engine runs on is published below, live from the engine itself.

The model

Arena reports a placement, 1st through 6th, for a team of three, not a win or a loss. That rules out Elo, which needs a two-sided result. We use OpenSkill ThurstoneMostellerFull (MIT licensed), a Bayesian model in the same family as TrueSkill, which updates from a full ordering of 6 teams at once and tracks how confident it is in each estimate.

Every player carries two numbers: $μ$ (mu), the current best guess at their skill, and $σ$ (sigma), how unsure the system is about that guess. The rating shown on the site is the conservative estimate.

R = round ((μ - 3 σ) \times 75)

$R$: the rating shown on the site, next to your name
$μ$: mu — the current best guess at your skill
$σ$: sigma — how unsure the system still is about that guess. It starts high and falls as you play.
$3$: how many sigmas of caution to subtract. Three is the convention for “almost certainly at least this good”.
$75$: a fixed multiplier that puts the result on a four-figure scale players recognise
$round$: rounded to a whole number, because a rating is displayed without decimals

The consequence worth knowing: a new player's number climbs as the system grows certain of them, even if their results stay flat — the guess is not improving, the doubt subtracted from it is shrinking.

Constant	Value	Source	Why
Starting mu	25	Default	Scale convention. The absolute number is arbitrary because tiers are percentile-based.
Starting sigma	25/6 = 4.167	Default	A new player opens at 938, mid-ladder rather than at zero, so provisional reads as unrated rather than bad.
Beta (skill-to-outcome noise)	16.667	Default	Set wide. Placement in a six-team lobby is noisy: augment rolls and matchup order move results independently of skill, so one game is weak evidence.
Tau (dynamics)	0.0833	Default	Additive uncertainty per game, so a settled rating can still drift when a player genuinely changes.
Sigma floor	2.31	Derived	Average sigma at career game 150 on our own ladder, where the decay curve bends: the marginal drop is 5.6% per 25 games at game 100 and under 3% by 150.

Derived means the value came out of our own match archive and the derivation is published. Default means it is a reasoned starting value that has not been fitted yet. We label the difference rather than implying every number is measured.

The four stages

A match runs through four stages in order. The second is the OpenSkill model above, unmodified. The other three are ours, and they exist because a 3v3 placement ladder can be gamed in ways a plain rating system does not see. Each is listed with the constants that control it.

Unbalanced-lobby grace

A team of top players that matchmaking could not find opponents for has almost nothing to gain and a great deal to lose. Before rating, such a team's effective mu is shaved so the update is scored against a fairer expectation. The deltas are then applied to their true pre-match values, so grace only ever changes the size of an update, never a stored rating.

e = \frac{M_{team} - median (M)}{median (M)}

$e$: the excess — how far this team sits above the middle team in its own lobby, as a fraction of that middle. 0.2 means twenty percent stronger.
$M_{team}$: this team's strength: its three players' mus added together
$median (M)$: the middle value of M across the 6 teams in the lobby — the strength of a typical team in that game

$M$ 6 teams in the lobby, so "too strong for the lobby" is measured against the lobby actually present rather than the ladder at large. The excess is uncapped: capping it made queueing with a weak account the better play.

μ_{eff} = μ (1 - 0.5 e)

$μ_{eff}$: effective mu — the value this player is rated as if they had, for this one match. Their stored mu is untouched.
$μ$: their real mu going into the match
$0.5$: the share of the excess given back — the "Share of the excess neutralised" row below
$e$: the excess from the line above

Each player on that team is rated as if they were 50% of the way back down to the lobby's middle. Deltas land on the true $μ$ , not on this one.

Constant	Value	Source	Why
Master+ players required	2	Default	Grace only applies to teams stacked at the top, because the matchmaking ceiling it compensates for only exists there.
Share of the excess neutralised	50%	Default	Uncapped. Capping it made deliberately queuing with a weak account the better play.
Lopsidedness that voids grace	30%	Default	A team this uneven that also carries a recent teammate gets no grace: that shape is a duo running a weak account, not a stack matchmaking failed to place.

Rating

Standard OpenSkill over the 6 teams, ranked by placement. Nothing of ours runs here.

Team-gap damping

A strong player whose team includes someone far weaker learns less from the result, so their rating change is scaled down. The gap is measured against the weakest teammate, not the average of the two: in a 2v2 those are the same number, but in 3v3 an average lets one solid teammate hide one fresh account, which is exactly the boosting route.

Damping is relieved when the weak teammate is a stranger, because a teammate you did not choose is matchmaking's doing rather than a boost. That check is per teammate, so a repeat with one of your two teammates does not cancel the relief owed for the other.

g = 1 - \frac{μ_{weakest}}{μ_{you}}

$g$: the gap — how far behind you your weakest teammate is, as a fraction of your own mu. 0.4 means they are forty percent below you.
$μ_{weakest}$: the lower of your two teammates' mus
$μ_{you}$: your own mu

The gap is your mu against your weakest teammate's, so it is zero whenever nobody on your team is behind you.

s = \begin{matrix} 1 & if g \leq 0.15 \\ 1 - t (1 - 0.1) & if g > 0.15 \end{matrix}

$s$: the scale your rating change is multiplied by. 1 means the result counts in full; 0.1 means a tenth of it does.
$g$: the gap from the line above
$t$: how far into the damping range the gap has travelled: 0 where damping starts, 1 once it is fully applied. Defined on the next line.
$0.15$: the gap at which damping begins — the "Damping starts" row below
$0.1$: the smallest share of an update that ever survives — the "Smallest surviving share of the update" row below

So the result counts in full below the trigger, then slides down as the gap widens — and stops sliding at 10%, because a game you played is never erased entirely.

t = \min (1, (g - 0.15) / (0.5 - 0.15))

$t$: the position of the gap within the damping range, as a fraction of it
$g$: the gap
$0.15$: where damping starts — the "Damping starts" row below
$0.5$: where damping is fully applied — the "Damping fully applied" row below
$\min$: take whichever is smaller, which is what caps t at 1: past saturation the damping stops deepening

s \leftarrow s + (1 - s) 0.5

$\leftarrow$: “becomes” — this replaces the scale worked out above, it is not a second multiplication
$s$: the scale from the lines above
$0.5$: the share of the damping forgiven when you did not queue with that teammate — the "Damping forgiven for a stranger" row below

And when that weakest teammate is a stranger, the damping is partly given back — a teammate you did not choose is matchmaking's doing, not a boost.

Constant	Value	Source	Why
Damping starts	15%	Default	Below this the teammate is not meaningfully weaker.
Damping fully applied	50%	Default	Provisional.
Smallest surviving share of the update	10%	Default	A result is never erased entirely.
Damping forgiven for a stranger	50%	Default	A teammate you did not choose is matchmaking's doing, not a boost.
Games that make a teammate a repeat	5	Default	Checked per teammate, so a repeat with one of your two teammates no longer cancels the relief owed for the other.

AFK protection

If a teammate went AFK, this stage is a floor, not a cap. A game that would have cost you rating costs you nothing instead; a game you played well enough to gain still pays in full, so being down a player never limits what you can earn. The AFK player is excluded — they get no floor and take the full loss. A player counts as AFK when they finished last, took no kill, had at most a couple of assists, and cleared neither the damage nor the healing floor for their lobby.

Both floors are relative to the other seventeen players in that same match, not absolute. Absolute damage measures the game as much as the player: a zero-damage AFK in a long match banks more gold than an active player in a short one. Healing counts as contribution because a damage-only rule systematically false-flags enchanters, and the test is on healing rather than on champion because a champion allowlist would need upkeep every patch.

c_{\min} = 0.05 \times median (c)

$c$: a contribution channel — either damage dealt to champions, or healing done
$c_{\min}$: the floor for that channel: clear it and you counted as playing
$median (c)$: the middle value of that channel across all 18 players in the match
$0.05$: the share of that median the floor sits at — the "Contribution floor, as a share of the lobby median" row below

One floor per channel, each a share of that channel's median over all 18 players in the match. Clearing either counts as contributing. A lobby that healed nothing gives the healing channel no scale to measure against, so it drops out rather than excusing everyone.

Constant	Value	Source	Why
Contribution floor, as a share of the lobby median	5%	Derived	From the valley in the lobby-share distribution: last-place counts bottom out at 1% and climb from 5%. Measured against the lobby rather than an absolute number because absolute damage measures the game as much as the player.
Assists still consistent with being AFK	2	Derived	Augments hand assists to players who are not participating: 21 of the 658 players who dealt literally zero damage still had one. Kills stay pinned at zero because augments do not grant those.

Tiers

Tiers are assigned by position on the ladder, not by fixed rating thresholds, so they mean the same thing as the board grows. Challenger and Grandmaster are fixed slots — Challenger is literally the top 200 players, Grandmaster the next 400 — because a slot is scarce in a way a threshold is not: to take one, somebody has to lose it. Everything below is a percentile band, so those tiers describe where you stand in the population rather than which number you cleared. You need 5 rated games on Arena to be placed at all.

Tier	Starts at	Players
Challenger	3,076	200
Grandmaster	2,790	400
Master	2,397	2,598
Diamond	1,943	12,986
Emerald	1,550	38,957
Platinum	1,278	58,436
Gold	1,019	77,914
Silver	759	71,421
Bronze	364	51,943
Iron	-812	9,785

These are the live cutoffs, recomputed on a schedule, not a snapshot pasted into this page. Arena and Bravery are rated as separate ladders, because the two queues are different games.

Seasonal resets

The ladder runs in seasons, and a season here begins where the game's own season does — pinned to the first match played on its opening patch, so the boundary sits at the moment the game actually changed rather than at a calendar date we picked. A boundary players already feel beats an administrative one they do not.

Seasons here begin where the game's own seasons do — each boundary is pinned to the first match played on its opening patch, then applied by the replay. When Riot announces the next season it appears on this calendar automatically. Next boundary: applied on the patch that opens Riot's next season. The dashed region marks Season 1 2027 — an expectation, not a schedule; the boundary pins itself from the match stream when that patch goes live.

At each boundary the board closes: the standings are certified into a permanent archive, and every rating is transformed once by the rule below before the new season's first match is rated. The reset is a rule inside the replay rather than an edit we make, so rebuilding the whole archive from scratch reproduces every boundary exactly — and the receipt on your match history shows the very numbers it produced for you.

Why a season needs a ceiling

A rating has no natural top: play well long enough and it just keeps climbing. Without a limit, a new season would open with last season's best already so far ahead that nobody could realistically catch them. So the reset squeezes the very top of the ladder harder than everywhere else: the higher you finished, the smaller each extra point is worth on opening day, and no opening rating can pass a hard ceiling. For everyone below the bend the rule is much simpler — your rating moves part of the way back toward the starting value, and that is all.

Find where you finished along the bottom; the gold curve is where you open. For most of the ladder it is a straight line, and only the very top bends — that bend is what keeps every opening rating under the 2,349 ceiling. The faint diagonal is what no reset at all would look like. (Both axes are board ratings, drawn for a settled player whose uncertainty sits at the reset floor.)

Two consequences worth stating plainly. Below-average players regress upward toward the opening value, because compressing toward the middle lifts as well as lowers — a reset is a fresh start, not a punishment. And the climb re-opens for everyone: the distance a brand-new account has to cover to reach the top of the board is a fraction of what it would be without a boundary.

What the reset actually did

Not a promise — the record. This is the certified Season 2 2026 board next to the opening ratings the reset produced from it, from the #1 player down to the bottom of the ranked ladder.

Real certified numbers from the Season 2 2026 archive, not an illustration. The p-rows are percentiles of the ranked board: p99 is the rating 99% of ranked players finished at or below (only the top 1% finished above it), p50 is the exact middle of the ladder — the median player — and p1 is the very bottom. The middle barely moves; the change concentrates at the top, which is where it was aimed.

μ′ = \begin{matrix} 25 + 0.7 (μ - 25) & if μ \leq P \\ 25 + 0.7 (P - 25) + 0.7 C (μ - P) / (C + μ - P) & if μ > P \end{matrix}

$μ′$: the skill estimate entering the new season
$μ$: the skill estimate at the season's final match
$25$: the opening value everyone starts from — the "Starting mu" row above
$0.7$: how much of the distance from the opening value survives — the "Compression below the pivot" row below
$P$: where the curve begins to bend, 33 μ — the "Where the curve begins to bend (mu)" row below
$C$: how gradually the top flattens, 14.75 — the "How gradually the top flattens" row below

The two pieces meet without a kink: the curve leaves the pivot at exactly the same slope it arrives with. Written as a fraction rather than with a library function on purpose — every rating here is re-derived by replay on whatever machine runs it, and the results have to agree to the last bit.

σ′ = \max (σ, 3.2)

$σ′$: the uncertainty entering the new season
$σ$: the uncertainty at the season's final match
$3.2$: the re-inflation floor — the "Uncertainty re-inflation floor" row below

A reset adds uncertainty and never removes it, and the floor never exceeds a brand-new player's — so a veteran is never made less known than someone who has never played. It restores roughly double the per-game movement for a settled player; most of the board already sits above this floor and is left alone.

Because the curve has a limit and uncertainty is never below its floor, there is a rating no player can open a season above — however high they finished. That bound is published as a constant of its own below, computed from the four values rather than written down, so it cannot drift from the rule that enforces it.

Constant	Value	Source	Why
Compression below the pivot	70%	Default	At each season boundary mu compresses toward the starting value, so the spread narrows and the climb re-opens; below-average players regress UP toward the opening rating — a fresh start, not a punishment. Provisional.
Where the curve begins to bend (mu)	33 mu	Default	Below this the compression is a straight line; above it the curve flattens. It is set on mu rather than on tier because a tier-keyed rule could reorder players: tiers rank by displayed rating, and a very settled Master can hold a lower mu than a Diamond above him. Provisional.
How gradually the top flattens	14.75	Default	Above the pivot each further point of skill returns less than the last, so the curve approaches a ceiling instead of running away. Solved from the ceiling below rather than chosen by eye. Provisional.
Uncertainty re-inflation floor	3.2	Default	Uncertainty is restored at the boundary, which roughly doubles how far a settled veteran moves per game. It only ever raises uncertainty, and never past a brand-new player's. Provisional.
Highest rating a season can open at	2,349	Default	The strict consequence of the four values above: however high you finish, this is a bound your opening rating cannot reach. Published from the engine rather than written down, so the promise and the rule that enforces it cannot drift apart. Provisional, and it moves if any constant above moves.

One honest limit on the wording. The rule is strictly order-preserving in skill — no player's estimate passes another's — but not in the displayed rating, and the difference is real. The displayed number subtracts uncertainty, and a reset returns uncertainty only to those the system had grown most certain about, so a heavily-played veteran gives back more of it than a lightly-played one and the two can cross. That is the design working rather than failing: a season re-opens the question of who is best.

Every constant here is a provisional design default until the boundary simulation fits it against our own archive — the same standard every other constant on this page is held to. Closed seasons keep the boards they were certified with, whatever the constants do later.

What this does not model

Stating the limits is part of publishing the method.

Partial AFK. Someone who disconnects halfway is only caught if their whole-game contribution lands under the floor. Round-level data would fix this and the Riot API does not expose it.
Shielding and crowd control are real contribution channels we do not measure yet.
Champion strength. A rating measures the player, and picking a strong champion is part of playing well.
Regional differences. Every derived constant here was measured on NA data and will be re-derived per region before the ladder goes global.

Credits

The rating engine is our own work. It builds on openskill.py, used under the MIT licence, for the underlying OpenSkill ThurstoneMostellerFull model; the four adjustment stages, the AFK detection and the tier system are ours. Champion, item and augment text comes from Riot's own game data and the League of Legends Wiki (CC BY-SA 3.0), reproduced rather than paraphrased so it stays accurate across patches.

ArenaGOATs isn't endorsed by Riot Games and doesn't reflect the views or opinions of Riot Games or anyone officially involved in producing or managing Riot Games properties. Riot Games, and all associated properties are trademarks or registered trademarks of Riot Games, Inc.

Full licensing and attribution detail: Legal & attribution.

Every rating change on a player's match history shows which of these stages touched it and by how much.