Fair court time: the maths behind the waiting

Fair court time starts with an uncomfortable fact: on a busy night, most of the waiting is not an organisational failure. It is arithmetic. Four players fit on a doubles court. Once more than four players per court attend, somebody has to be sitting out.

That distinction matters because clubs often try to solve a capacity problem with increasingly elaborate rotation rules. If every court is continuously occupied and the average player is still waiting too long, the queue is not broken. The session is full.

Start with the physical capacity

For doubles, the theoretical average share of time on court is:

4 × courts ÷ players present

Cap the result at 100%. It assumes every court is occupied continuously and ignores changeovers, so reality will normally be a little worse.

This is the number organisers should know before promising "plenty of games". Eight players per court means that, even under perfect utilisation, the average person is waiting as much as playing.

That may be acceptable. Many clubs deliberately trade some waiting for a lower fee and a larger social group. The important thing is to recognise the trade rather than blame the person running the board.

Why games played is only a proxy

Most clubs count games because it is easy. Four games each sounds fair.

But one game might take nine minutes and another twenty-four. A player who wins three quick games 21-8 can record more "games" while using less court time than someone who has two long deuce games.

So there are at least three things a club could mean by equal court time:

• equal starts: similar number of games;
• equal minutes: similar actual time on court;
• equal opportunity: similar share of the available session while each person was present and willing to play.

For most social clubs, equal opportunity is the best practical target. Exact minutes would require timing every game and can over-correct normal variation. But when the differences become large, pretending all games are equivalent stops feeling fair.

Fairness needs a denominator

Two players with four games each are not necessarily equally treated.

If Priya was available for the full two-hour session and Dan arrived for the final hour, equal game counts would mean Dan received twice the game rate.

That is why the denominator should be time available, not attendance on the sign-in sheet.

Availability matters too. If somebody chooses to sit out for twenty minutes, that period should not build a claim on the next three courts. Likewise a player who leaves, changes clothes and spends fifteen minutes talking before checking out should not be accumulating "wait".

A useful fairness record therefore needs states:

playing → waiting → voluntarily resting → waiting again → gone.

A pegboard can represent some of that. An organiser can remember some. A digital system can timestamp all of it. The principle is the same whichever tool you use.

Long games create hidden inequality

Imagine Court 1 finishes three games while Court 2 is still grinding through a 29-27 marathon.

The four on Court 2 have not been treated badly - they have been playing the whole time. But when they finally come off, a simple "put them at the back" rule can produce odd totals because the rest of the room has cycled through more starts.

This is where clubs need to decide what they value.

If you optimise games played, you may try to get the long-game players back on quickly so their count catches up. That actually gives them even more court time.

If you optimise court-time share, they have already received plenty of the scarce resource and can wait normally.

The second interpretation is usually more coherent. It also explains why counting wait duration is more useful than simply comparing game totals.

The one kind of waiting you can eliminate

Some waiting is mathematically unavoidable. Idle court time while willing players are waiting is not.

A three-minute gap between games on four courts, repeated six times during a night, loses 72 court-minutes:

3 minutes × 4 courts × 6 changeovers = 72 court-minutes

In doubles terms that is 288 player-minutes of capacity - nearly five hours of individual playing opportunity collectively lost to changeovers.

You will never get transitions to zero. Players need to leave, scores need recording and the next four need to reach the court. But the next game should be decided before the previous one ends whenever possible.

This is often the highest-return operational improvement on a crowded night: not a more sophisticated fairness formula, just fewer empty courts.

Late arrivals and voluntary sit-outs

Latecomers expose whether a club is tracking fairness or merely preserving a line.

When somebody arrives, they have accumulated zero previous waiting. Put them into the live queue without pretending they were available earlier.

From that moment onwards, however, their waiting is real. Once people who were ahead have played and returned, the newcomer should be able to move ahead of them naturally. "You arrived last, so you stay behind everybody all night" is no more defensible than putting them straight on court.

Voluntary rests are similar. Pause the fairness clock while somebody sits out by choice; restart it when they become available again. Otherwise the system rewards somebody for taking a break with immediate priority over people who remained ready to play.

When the night is simply too busy

Suppose your rotation is transparent, every court is constantly occupied, late arrivals are handled properly and the average player still spends an hour of a two-hour night off court.

You have exhausted the scheduling fixes.

The remaining levers are physical or commercial:

• add a court;
• extend the session;
• cap attendance or use booking;
• split the session into two groups or standards;
• add a second club night;
• or accept the wait and price/describe the session accordingly.

Software cannot create court capacity. Any product that implies otherwise is solving the wrong equation.

A manual fairness method that works

If you run a physical board, keep the rule set small:

1. Players become eligible when they come off court or explicitly rejoin after a rest.
2. Record the order in which they became eligible.
3. Normally include whoever has waited longest in the next game.
4. If you skip somebody to avoid a terrible match, keep them at the front for the next suitable game.
5. Do not "catch up" players purely because their game count is low if their previous games were unusually long.
6. Prepare the next four before a court becomes free.

This will not equalise every minute. It will produce a system members can understand and audit, which is often more important than theoretical optimisation.

What software can and cannot solve

ePegboard can timestamp the states a board only implies: who is playing, waiting or sitting out, how long they have waited, and what has happened earlier in the session. Its picker can use that alongside player level and pairing history when selecting the next four.

The advantage is consistency rather than magic. The quiet player does not need to remind the organiser they have been waiting; the late arrival does not receive fictional credit for the first hour; a deliberate skip can remain visible.

But the capacity equation still wins. If thirty-two players are sharing four doubles courts, only sixteen can play at once. The best software can distribute the other sixteen people's waiting well and keep changeovers short. It cannot make Court 5 appear.

Frequently asked questions

How much court time can each player get?

For doubles, four places are available on each court. If N players share C continuously occupied courts, the theoretical average playing share is 4C divided by N, capped at 100%. With 24 players and 3 courts, for example, only 12 can play at once, so the group average cannot exceed 50% of the session.

Is the same number of games always fair?

No. Games have different lengths and players are present for different amounts of time. Equal game counts can hide substantial differences in actual minutes played, while a late arrival should not be given a whole evening's game count in the remaining hour.

Should a player who had a very long game wait longer afterwards?

There is no universal rule, but if your fairness objective is actual court time rather than number of starts, game duration matters. A player who has just had a 28-minute game has received more of the scarce court resource than someone whose previous game lasted 11 minutes. Clubs can choose whether to compensate for that.

How should late arrivals be treated?

Give them no credit for time before they arrived, then count their waiting normally from arrival. They should not jump people who were already waiting, but nor should they remain permanently behind players who have since returned to court.

Can software create more court time?

No. It can reduce avoidable idle time and distribute the available capacity more consistently, but it cannot beat the physical limit set by courts, players and session length. If waits remain unacceptable with every court occupied, the solution is more capacity, fewer attendees or a longer session.

For the broader policy behind who plays next, see badminton club-night rotation. If your next question is whether to restrict attendance or add courts, the same capacity arithmetic should drive the decision.