COMPLETE RATING SPECIFICATION

HOW RATINGS WORK

A transparent explanation of the five Glicko-2 ladders, participation rules, forfeits, calibration and the exact mathematics behind every update.

Glicko-25 separate laddersParticipation-aware

1500 / 350 / .06New-player rating, RD and volatility starting state.

Not zero-sumGlicko-2 estimates skill instead of transferring a fixed pool of points.

Participation-awarePartial appearances contribute controlled evidence.

COMPLETE RATING SPECIFICATION

How the rating system works

This is the full specification for Zipnar's five competitive Quake Live ladders: what gets rated, how results are translated into Glicko-2 evidence, the exact Glicko-2 mathematics, how partial participation is handled, how quits and forfeits are treated, and why a visible rating is not automatically an official numbered rank.

Rating engineGlicko-2 + Zipnar V4 policyFive independent mode ladders

THE MODEL IN ONE PARAGRAPH

A rating is an estimate, not a score counter

Each player has a separate Glicko-2 state in FFA, Clan Arena, Freeze Tag, Duel and Team Deathmatch. A result does not simply add a fixed number of points for winning or subtract a fixed number for losing. The update depends on the player's current rating, the opponent or opposing team's rating, both sides' uncertainty, the outcome, and—in Zipnar's participation-aware layer—how much competitive evidence the appearance should contribute. New or uncertain ratings can move rapidly; established ratings usually move less. The five ladders never feed into one another.

FFACAFTDUELTDM

01Initial state

1500 rating, 350 RD and 0.06 volatility.

02Results are contextual

Beating stronger competition is more informative than beating weaker competition.

03Uncertainty is explicit

RD controls how confident the system is in the rating estimate.

04Participation is evidence

Partial team appearances carry less evidence; anti-dodge rules stop quitting from becoming advantageous.

RATING STATE

The three numbers Glicko-2 tracks

Rating r

The familiar skill estimate shown on the site. Everyone begins at 1500. A difference in rating changes the expected result, but rating by itself does not say how certain that estimate is.

Rating deviation RD

Uncertainty around the rating. Everyone begins at 350, which is intentionally broad. Lower RD means the system has stronger evidence about current skill. A useful interpretation of the standard Glicko scale is approximately r ± 2×RD as a 95% uncertainty interval.

Volatility σ

A model of how much the player's underlying strength appears capable of changing. Everyone begins at 0.06. Volatility is updated iteratively and affects how RD evolves.

Why a 1900 can still be “Calibrating.”

A high rating with a very large RD means “the current best estimate is high, but the system is not yet very sure.” Zipnar deliberately displays that estimate while withholding an official numbered rank until enough evidence exists.

THE MATHEMATICS

Full Glicko-2 update

The formulas below are the standard Glicko-2 procedure from Professor Mark Glickman's published specification. Zipnar's custom policy determines which competitive results and evidence weights are fed into this update; it does not replace the underlying Glicko-2 model.

Start with r, RD and σ

For a new player, Zipnar uses r = 1500, RD = 350, and σ = 0.06. Existing players carry their latest values forward.

Convert to the internal Glicko-2 scale

μ = (r − 1500) / 173.7178

φ = RD / 173.7178

The displayed rating scale is convenient for people. Glicko-2 performs the update on the normalized μ and φ scale.

Compute opponent impact and expected score

g(φ_j) = 1 / √(1 + 3φ_j²/π²)

E(μ, μ_j, φ_j) = 1 / [1 + exp(−g(φ_j)(μ − μ_j))]

g(φ_j) discounts information from an uncertain opponent. E is the expected score against that opponent: near 1 means heavily favored, near 0 means a major underdog, and 0.5 means roughly even.

Estimate outcome variance v

v = [ Σ_j w_j g(φ_j)² E_j(1 − E_j) ]⁻¹

In ordinary Glicko-2 every result has weight 1. Zipnar's participation-aware implementation can assign an evidence weight w_j between 0 and 1 for partial appearances. A smaller weight means “learn less from this evidence,” not “pretend the result was different.”

Compute performance improvement Δ

Δ = v Σ_j w_j g(φ_j)(s_j − E_j)

Here s_j is 1 for a win, 0.5 for a draw and 0 for a loss. The term s − E is the surprise: an expected win contributes little surprise; an upset contributes much more.

Solve for the new volatility σ′

Glicko-2 does not update volatility with a single closed-form line. It solves for the root of a function. Let:

a = ln(σ²)

f(x) = [e^x(Δ² − φ² − v − e^x)] / [2(φ² + v + e^x)²] − (x − a)/τ²

The algorithm brackets the root and iteratively narrows it using the stable procedure in Glickman's current specification until the interval is smaller than a tiny tolerance ε. Then:

σ′ = e^A/2

τ is the system volatility constraint. It controls how freely volatility itself can move. This is an administrator/model parameter, not a player score.

Inflate uncertainty with the new volatility

φ* = √(φ² + σ′²)

This is the pre-update uncertainty after allowing for the possibility that true skill changed.

Update RD and rating

φ′ = 1 / √(1/φ*² + 1/v)

μ′ = μ + φ′² Σ_j w_j g(φ_j)(s_j − E_j)

The first line combines previous uncertainty with the amount of information in the new results. The second line moves the rating in proportion to the result surprise and the player's remaining uncertainty.

Convert back to the displayed scale

r′ = 173.7178 μ′ + 1500

RD′ = 173.7178 φ′

The website and in-game commands show r′ and RD′ on the familiar scale.

Primary mathematical reference: Mark E. Glickman, Example of the Glicko-2 system, revised March 22, 2022. Zipnar-specific participation and outcome construction is documented below.

FROM QUAKE TO GLICKO

How a match becomes mathematical results

Glicko-2 is fundamentally a head-to-head comparison model. Quake Live includes Duel, team games and free-for-all, so Zipnar first translates each completed match into one or more win/draw/loss comparisons. That translation is the most important custom layer.

Duel

One opponent, one result. Winner receives s = 1; loser receives s = 0. A clean tie would be s = 0.5. A completed one-player forfeit is normalized as a real win/loss rather than allowing Quake's sentinel rank to masquerade as a favorable finish.

FFA

FFA is converted into pairwise placement comparisons inside one Glicko update. If Alice finishes ahead of Bob, Alice gets a win against Bob and Bob gets a loss against Alice. A tied placement/score becomes a draw. This means every rated player's result is measured against the actual field rather than pretending only first place matters.

CA / FT / TDM

Each team is summarized as a virtual opponent. The opposing team's rating is a participation-weighted mean of its players' ratings; its RD is a participation-weighted RMS of their RDs. Every member is then evaluated against the opposing virtual team with the final team result.

Why it is not zero-sum

Glicko-2 updates individual estimates and uncertainties. Rating points gained across a match do not have to equal rating points lost. That is normal: the system is estimating skill, not transferring chips from one account to another.

EVIDENCE WEIGHT

Participation, late joins and effective matches

Zipnar tracks the fraction of a completed match that each player actually played. Participation is approximately play time ÷ game length, capped at 1.0; anything at or above 98% is treated as a full 1.0 appearance. This avoids tiny timing discrepancies turning an essentially complete match into a partial one.

Participationp = min(1, play_time / game_length)

Full appearance normalizationif p ≥ 0.98 → p = 1.0

Effective match countadds the evidence increment, not necessarily 1.0

The separate effective rated matches counter is why a player can have more raw rated appearances than effective matches. A half-match can contribute roughly half of a full-match equivalent. Once the count exceeds the 10-match establishment requirement it continues to accumulate internally; progress displays simply cap the requirement at 10/10.

MODE-BY-MODE POLICY

Exactly what happens in the special cases

DUEL

Full match or forfeit

A normal completed Duel is one ordinary head-to-head Glicko-2 result.
A single unambiguous quitter is treated as the loser and the remaining player as the winner.
A Duel quitter cannot erase the loss by leaving before the end screen.
If the roster or forfeit state is ambiguous, the system refuses to invent a competitive result.

FFA

Pairwise field comparisons

A normal finisher needs at least 90% participation to enter the rated field.
A short, materially late appearance can remain in match history while being NR for rating.
Finishers are compared pairwise by rank, falling back to score when necessary.
Against a quitter, a finisher who surpasses the quitter's abandoned score receives a win; otherwise the comparison is a draw rather than awarding the quitter a locked-in win.
A rated quitter receives an explicit field-forfeit loss against the average strength of the remaining rated field.
The quitter's computed rating mean is never allowed to finish above the pre-match rating. Leaving cannot manufacture a rating gain.
Two-player declared forfeits are canonical win/loss results.

CA / FT / TDM

Team outcome + partial evidence

The opposing team is represented by a participation-weighted virtual opponent.
A normal partial finisher must have at least 15% participation to receive a rating update.
For a partial winning appearance, the win evidence is reduced by participation. A player cannot collect a full win from a small slice of the match.
For a player who leaves a losing team, the rating mean receives the full losing result so quitting cannot reduce the downside.
However, the uncertainty/effective-match side still learns only from the fraction actually played, so the system does not pretend the player observed a full match.
Ambiguous team identity or contradictory team results are not guessed.

The anti-dodge principle

Every special rule is built around the same constraint: joining late should not be excessively punitive, but leaving early must never be a profitable way to avoid a bad result. Winning players who leave early receive only the evidence they actually earned; losing players cannot shrink the loss by disconnecting.

RANK CREDIBILITY

Rating estimate vs official numbered rank

The Glicko-2 estimate updates as soon as a qualifying result is rated. Zipnar then applies a separate presentation/credibility policy before attaching a numbered leaderboard rank. This policy does not alter the rating value.

Calibrating

Visible estimate, no # rank

Any of the establishment gates is still incomplete: fewer than 10 effective rated-match equivalents, RD above 100, or fewer than 5 distinct rated opponents. Calibrating players remain visible so their progress is transparent.

Official ranked

Eligible for #1, #2, #3…

Requires effective matches ≥ 10, RD ≤ 100, distinct rated opponents ≥ 5, and a rated result in the last 30 days. Official eligible players are ordered by their actual Glicko-2 rating.

Inactive

Established history, no current rank

An established player whose latest rated result is older than 30 days keeps the rating and history but leaves the active numbered ladder. Playing another qualifying rated match can restore active eligibility.

For CA, Freeze Tag and TDM, the five-opponent gate counts rated opponents on the other team, not teammates. If historical team identity is ambiguous, that opponent is not counted toward the gate.

WORKED INTUITION

Why different matches move ratings differently

Upset win

A 1500 player beats an established 1800 player. Expected score E was low, so s − E is strongly positive. The winner usually gains much more than they would for beating a 1200 player.

Expected win

An established 1800 player beats a 1200 player. E was already close to 1, so the result contains little new information. The winner's rating should move only modestly.

New player

Two players have the same 1700 rating, but one has RD 250 and the other RD 70. The high-RD player's estimate can move dramatically because the system is still learning; the low-RD player's estimate is much more anchored.

Late team join

A player joins a CA win halfway through. Their outcome is still a win, but the evidence weight and effective-match increment are reduced. They do not receive the same confidence gain as someone who played the whole match.

Leaving while losing

A player disconnects from the losing team after 40% of the match. The mean rating is calculated with the full loss to remove the incentive to dodge; uncertainty/effective-match accumulation still reflects only the 40% actually observed.

FFA second place

Second place can gain rating. In an eight-player FFA, second place beat six players and lost to one. The update depends on who those players were and how surprising those pairwise results were—not simply on whether the player finished first.

IMPLEMENTATION BOUNDARIES

What is deliberately kept separate

No competitive Overall rating: FFA, CA, FT, Duel and TDM are independent. Historical Overall data is archived, not updated as a live competitive ladder.
Warmup does not create rating evidence: warmup-only player stats are excluded from rating input.
Aborted or non-competitive outcomes are not forced into the ladder: when the competitive result cannot be established safely, the system skips rather than guesses.
Raw match history and rating history are distinct: a player can appear in match history without that appearance moving rating.
Official rank is a UI/credibility layer: it does not secretly modify the underlying Glicko-2 estimate.
Glicko-2 is not zero-sum: there is no requirement that rating gains equal rating losses within a match.

GLOSSARY

Terms used on the site

Rating (r): The current skill estimate on the familiar 1500-centered scale.
RD: Rating deviation: uncertainty around the estimate. Lower is more certain.
Volatility (σ): The Glicko-2 parameter describing how much underlying strength appears capable of changing.
μ, φ: The normalized Glicko-2 versions of rating and RD used internally by the formulas.
E: Expected score against a particular opponent.
v: Estimated rating variance from the new results.
Δ: Estimated performance improvement based on observed results versus expectation.
Participation: The fraction of the completed match actually played, normalized to 1.0 at 98% or more.
Effective match: A full-match-equivalent unit of competitive evidence. Partial appearances can add fractions.
NR: Not Rated for that appearance. The match can still exist in history/statistics.
Calibrating: Rating visible, but at least one establishment gate is still incomplete; no numbered rank.
Official: Established, active, evidence-qualified rating eligible for a numbered ladder rank.
Inactive: Established rating retained after the 30-day activity window, but without a current numbered rank.
Virtual team opponent: The participation-weighted opposing-team rating/RD summary used to turn a team result into a Glicko-2 comparison.

FOR THE TECHNICALLY CURIOUS

What is standard and what is Zipnar-specific?

Layer	Responsibility
Standard Glicko-2	Rating, RD, volatility, expected score, variance, volatility iteration, and final mathematical update.
Zipnar outcome construction	FFA pairwise comparisons; team virtual opponents; Duel/forfeit normalization.
Zipnar participation policy	Evidence weights, effective-match increments, 90% FFA finisher threshold, 15% team minimum, anti-dodge behavior.
Zipnar rank policy	10 effective matches, RD ≤100, 5 distinct opponents, 30-day activity gate, and Calibrating/Official/Inactive presentation.

The rating engine is versioned independently from the website so explanatory/UI changes do not silently alter competitive history.