Queue Fairness Simulation Results

Methodology

Glossary

What the numbers on this page actually measure.

Game-count spread

How many total games each player played by the end of the session — spread is the (most games played by any one player) minus (fewest games played by any one player). A spread of ~5 means the busiest player averaged 9 games and the quietest 4, out of ~6.4 each over 4 hours. This is about total playtime fairness, not queue delay.

Mate repeat %

Of the 3 people a player shares a court with in a game, the share who were also their groupmates in their immediately-previous game. Lower means more rotation — players face new partners and opponents instead of the same foursome every round. Fixed groups (duos/trios pinned by the manager) are intentionally exempt.

Wait time (mean / median / max)

Minutes a player actually sat in the queue before being assigned to their next game — a queue-delay metric, separate from game-count spread. A player can have an average game count but still occasionally endure one long wait, or vice versa.

stdev(games/player)

Standard deviation of games played across all 48 players — a single number summarizing how evenly playtime was distributed. Lower means more even; 0 would mean every player got the exact same number of games.

Stranded players

Players who finished the 4-hour session having played 0 games — the most severe fairness failure we tested for.

Gender gap %

Percentage difference between the average number of games played by male players vs. female players.

Court utilization

Percentage of total available court-time actually spent playing, versus sitting empty waiting for enough players to form a group.

Anti-starvation rescue / rescue threshold

Once a candidate group’s longest-waiting member has waited past this threshold, that group is exempted from the skill-gap check and guaranteed to be chosen — so no one can be skipped forever just because their skill level is rare. Tied to the session’s “Timer Warning” setting (default 15 min).

Pairing weight

How much group selection favors wait-time fairness versus skill-matching. 0.65 (the shipped default) means 65% wait-time fairness, 35% skill fit.

Mixed vs. Skill-matched mode

Mixed allows a wider skill-rating gap within a group (default ±1.5); Skill-matched enforces a tighter gap (±0.5) but falls back to an unlimited gap if no group can be formed at all. Both modes now share the same anti-starvation rescue.

The fairness fixes

The simulation surfaced two real problems. First, starvation: because groups are built from a rating-sorted sliding window, a rare skill tier (or an unlucky gender split) could only ever be grouped with its immediate rating-neighbors — in the worst case, a player could go the entire session without playing. The fix: once a candidate group’s longest-waiting member has waited past the rescue threshold, that group is exempted from the skill-gap check and given a large score bonus, guaranteeing it wins — regardless of queueing mode.

Second, repetition: a foursome that just finished re-enters the queue together with identical wait clocks and coherent ratings, so it kept out-scoring mixed alternatives and re-formed game after game — in our measurements, ~60% of a player’s groupmates were the same people as their previous game. The fix: a novelty penalty scores candidate groups down for every pair that shared a court within a recent rotation window, rotating partners and opponents naturally (fixed groups pinned by a manager are exempt by design).

A later refinement (v1.7.0): the rescue originally treated every qualifying window as equally desirable, so the first rescued group won regardless of how wide its internal skill spread was — producing rare but extreme mismatches. Rescued candidates are now scored by the same spread-penalty formula as normal candidates, so among all groups eligible for rescue the tightest skill match wins. The zero-starvation guarantee is unchanged (the rescue bonus still dominates), and every number on this page is re-run against the refined algorithm.

Both changes shipped with before-and-after numbers from this same simulation setup — see the changelog for the measured impact of each.

Fixed groups & fair expectations

“Expected games” is the per-player fairness yardstick — it answers “how many games should this player get, given when they checked in?” Fixed groups move their own expectation by design, and the simulation’s expectation model accounts for that:

• A full-court fixed four carries a blended, honest target. Because it can only field when all four members are simultaneously present, resting and no-shows cost it court time it can never reclaim — unless the manager breaks the group. So its expectation is a probability-weighted blend of the held case (discounted to what it can physically achieve) and the broken case (members queue as free agents, full pace). In the sim it runs ~5.5–6 games — elevated by the ~1-in-4 seeds where the manager frees it — while the blended expectation sits between the held and broken outcomes.
• Duos and trios keep the standard pace. They share courts with fillers, so a single member’s rest doesn’t idle a court and they’re not deficit-prone. A pinned pair inclines slightly the other way — it slots into partial courts easily and runs a mild, bounded surplus (up to ~1.3 games) over its per-check-in expectation. That’s a small structural edge of playing as a pair, reported transparently rather than hidden.
• Fairness is measured against what’s achievable. In the shipped Mixed mode, ~75% of players land within half a game of their (fixed-group-aware) expectation, and every non-pinned player lands within one game — the only players beyond that are pinned pairs carrying the mild pair surplus above. The manager-break wrinkle is a deliberate honesty cost: it makes an incomplete four’s outcome bimodal (pinned at its discounted count, or higher the ~1-in-4 time it’s freed), so a single target straddles both — even as freeing those members measurably tightens the actual spread and cuts repetition.

One example session (seed 42)

A single concrete run, with the shipped default settings and anti-starvation rescue enabled, for both modes side by side. All other tables on this page average across 5 seeds for statistical robustness — this one is a single illustrative run.

Full parameter sweep

Every mode/gap variant tested against every anti-starvation threshold (including “OFF”, the pre-fix behavior), averaged across 5 seeds each, at the same 48-player / 4-court / 4-hour session as the sims above — with the same real-world wrinkles (fixed groups, resting, no-shows, manager overrides, late check-ins) applied to every variant, so each configuration still isolates the rescue threshold’s effect from the config being varied. Lower stdev and spread are fairer; lower stranded is better.

Winner: Mixed, gap 1.5 (current default) · rescue 20 min (avg stdev 1.111, avg stranded 0.00) — but the gap between mode variants is small once any rescue threshold is enabled, and no configuration stranded anyone at this session size. The rescue itself is what drives fairness, not the specific gap or mode chosen.

Pairing weight & catch-up games

With mode and rescue threshold held at the Phase 1 winner (Mixed, gap 1.5, rescue 20 min), we swept pairing weight (wait-time fairness vs. skill fit) and the catch-up-games toggle.

The app’s shipped default — weight 0.65 · catch-up OFF — posted the tightest stdev (1.111); weight 0.5 · catch-up ON was a close second (1.128). Differences within Phase 2 are small relative to the rescue effect, so no change is recommended.