Round robin

Counting the matches

Each entrant plays every other entrant once. The count is the group size, times one less than the group size, divided by two.

That growth is the practical limit. Adding two teams to a group of eight adds 17 matches. It is why big fields are split into several small groups, and why fencing caps its pools at seven fencers.

The rounds column has a quirk. With an even number, everyone plays in every round, so the group needs one round fewer than it has entrants. With an odd number, somebody has to sit out each round, so five entrants take as many rounds as six.

Who plays whom, and when

The schedule is not improvised. Chess uses fixed tables, the Berger tables, in the handbook of the International Chess Federation (FIDE). For six players the first round is 1 against 6, 2 against 5 and 3 against 4, and it takes five rounds for everyone to meet.

With an odd number of players, the same table is used and the highest number counts as a bye. Here a bye means a round off, not a free win. Five players still need five rounds, with one player resting in each.

Fencing prints its own order. A pool of seven fences 21 bouts starting with 1 against 4, 2 against 5 and 3 against 6. A pool of six fences 15, starting with 1 against 2. A fencer is allowed three minutes' rest between two consecutive bouts.

The order is not only about rest. Two rules show organisers thinking about the last matches of a group, when some entrants already know where they stand.

• In table tennis, if one player is to qualify from a group, the final match is between the players numbered 1 and 2. If two are to qualify, it is between those numbered 2 and 3. The match that settles qualification is kept for the end.
• In fencing, when a pool contains fencers from the same country and they are not the majority, they must fence each other before meeting anyone else.

Neither rule book states its reason. The effect of the fencing rule is that team-mates meet before either of them knows what result would suit the other.

How a table is scored

Tables look alike and count different things.

Three designs sit behind that list.

Where a match cannot be drawn, the simplest table counts wins. Table tennis and basketball add a twist: a point for losing. It is there to separate a side that played and lost from one that did not turn up, which gets nothing.

Where a match can be drawn, the draw needs a value. Three for a win and one for a draw makes two draws worth less than one win and one defeat.

Ice hockey has it both ways. Every game ends with a winner, but a win inside the regular 60 minutes earns three points and a win after it earns two, with one for the side that lost late.

A worked table

Basketball's rules print an example that shows a table being read. Four teams play each other once.

A and B are level on five points. A beat B, so A is first. C and D are level on four, and C beat D, so C is third.

Look at B. It finishes second with a points difference of minus 35, above two teams on minus 5. In basketball the game between the tied teams is asked first, and the margin over the whole group only later. A sport that asked for the margin first would order this table differently.

Ties are normal, and every sport breaks them differently

A table is ranked first by results. After that the rule books part ways.

Two things stand out. The result between the tied teams comes first in curling, softball and basketball but third in judo. And curling turns to a skill measured before each game, where softball's list ends with a coin.

So the same final-day table can send different teams through, depending on the sport. The page on tie-breaks goes through the kinds of measure and why three tied teams are harder to separate than two.

Once, twice or more

A single round robin has each pair meet once. A double round robin has them meet twice, and curling's rules provide for one. Basketball's rules give an example of groups of four "playing home and away", six games each. Sailing's match racing rules go further and allow for a multiple round robin, in which competitors sail against each other one or more times.

Playing twice does two things. It doubles the matches, and in team sports with home grounds it lets each side host once.

Results can also travel. In basketball's example of a tournament in phases, the top three teams from two groups go into a new group "carrying forward their results and classification points", and then play only the teams they have not met. Sailing's team racing rules take the opposite default: results from an earlier round-robin stage are carried forward only if the event's notice of race or sailing instructions say so.

Building the groups

When a field is split into several groups, the split is designed so that no group is stronger than the others.

Fencing lays the ranked fencers out in a snake. With three pools, the fencer ranked 1 goes to pool A, 2 to pool B and 3 to pool C. Then the direction reverses: 4 goes to C, 5 to B and 6 to A and so on down the list. Fencers from the same country are then moved into different pools as far as possible.

Breaking's manual shows the same idea with 16 competitors in groups of four: the first group gets those seeded 1, 8, 9 and 16, the second gets 2, 7, 10 and 15.

Group size has rules too. Fencing pools are of seven if the entry divides by seven, otherwise of seven and six, and never fewer than six. At a World Cup or Grand Prix the host country may add fencers of its own to bring every pool up to seven.

Where it is used

As the whole event. World Curling's rules allow events with no play-off, where the table after the round robin is the final ranking.

As a first stage. The softball six-team format plays one single round robin and sends the top four to the play-offs. At the Paris 2024 Olympic badminton competition every player or pair played the others in their group, and a ranking order was produced for each group. The 3x3 basketball World Cup puts 20 teams into four pools of five before its single-elimination rounds. In breaking, the two top-ranked athletes of each group of four advance to the Top 8.

To seed a bracket without eliminating many. Pickleball's rule book names two formats in which a round robin is played first purely "to seed the players or teams" for a play-off. Fencing's pools do both jobs: they eliminate a share of the field and they rank everyone who is left.

For small fields. Combat sports fall back on it when a knockout bracket would be nearly empty. In wrestling, a weight category with fewer than six wrestlers becomes one group where everyone meets everyone. In judo's system for three athletes, a round robin ranks them and the best two then meet in a final. Wheelchair tennis sets a threshold: with five players or fewer in a singles main draw at its international and development grades, the tournament must play a round robin with no separate final. Para badminton plays a single group when there are too few entries for groups and a knock-out draw.

As a consolation event. In wheelchair tennis the draw for players already beaten may be run as a round robin.

When a team leaves

A round robin depends on everyone finishing their schedule, so the rules say what happens when someone does not. There are two choices, keep what was played or erase it, and the rule books split.

Erasing a team's results is the cleaner sum, but it takes a win away from everyone who beat it. Keeping them is kinder to those teams and harder on whoever was still due to play.

Sailing also covers a round robin that cannot be finished at all. If a single round robin is stopped early, each competitor's score becomes the average points per match sailed. If any competitor has completed less than one third of the scheduled matches, the whole round robin is disregarded.

What it is good at, and what it costs

This section is reasoning from the structure, not something a rule book states.

A round robin is the fairest format on its own terms. Nobody's result depends on the draw, because everybody meets everybody. One bad day does not end a tournament. And it ranks the whole field, not just the winner.

The price is matches, and something less obvious: matches that do not matter. Late in a group, some entrants are already through or already out, and some know exactly what result they need. The rules above about the last match, about team-mates fencing first and about pools being "fenced up to the last bout" are aimed at that.

It can also fail to produce a clear answer. A knockout always ends with one unbeaten entrant. A round robin can end with three teams who each beat one of the others, which is why its tie-break list matters as much as its results.

It changes from event to event

The one thing to remember: in a round robin the table decides, and the table is only as clear as its tie-break order. That order is in the competition's own regulations, under a heading such as standings, ranking procedure or tie breaking, and it is worth reading before the last round.