Group tournament ranking system

In a group tournament, unlike a knockout tournament, there is no decisive final match. Instead, all the competitors are ranked by examining the results of all the matches played in the tournament. Points are awarded for each match, with competitors ranked based either on total number of points or average points per match. Usually (though not always, e.g. the 1895 County Championship in English cricket) each competitor plays an equal number of matches, in which case rankings by total points and by average points are equivalent.

In several leagues and competitions, like the National Hockey League, league tables during the regular season are also determined by points. Since this calculation is not based solely on wins and losses, like winning percentage or games behind, the statistic is also known as points percentage.

Points calculation

In two-competitor games where ties are rare or impossible, competitors are typically ranked by number of wins, with ties counting half; each competitor's listings are usually ordered Wins-Losses(-Ties). (In such games a games behind figure is sometimes included in listings for a tournament still in progress, to allow comparison of competitors who have not completed the same proportion of their allotted matches.) Giving a half-point for a draw in chess was introduced in 1868 by the British Chess Association; previously, drawn games in chess tournaments were replayed. Where draws are more common, the award may be 2 points for a win and 1 for a draw, which is mathematically equivalent but avoids having too many half-points in the listings. These are usually ordered Wins-Draws-Losses. If there are more than 2 competitors per match, points may be ordinal—for example, 3 for first, 2 for second, 1 for third. An extreme example of this is Formula One, where the top ten racers in each Grand Prix are given 25, 18, 15, 12, 10, 8, 6, 4, 2 and 1 respectively.

Some games may have more complex ranking criteria. For example, in rugby union, bonus points may be awarded for scoring a certain number of tries in a match, usually four, or for losing by a relatively small margin, usually 7 (the value of a converted try) or less.

Additionally in many leagues, the governing body is able to penalize a competitor who has broken the league's rules (for instance by allowing an ineligible player to play) by deducting points from that competitor's total. Sometimes this deduction may be carried over to a following season, particularly if the infraction occurs during the off-season, meaning that the competitor will start the following season with a negative points total rather than zero.

In association football, where draws are relatively common, many leagues give 3 points for a win and 1 for a draw in an attempt to encourage attacking play. Besides the traditional 2-1-0 points and newer 3-1-0 points systems for win-draw-loss, various other systems have been used to try to encourage attractive play. Some examples:

• 3-2-1 as in the Greek League 1959-73; or 4-2-1. Giving 1 point extra in each case for losing may be simply cosmetic, but does allow for awarding 0 points for forfeiting a match. (The FIFA standard is to count a forfeit as a 3-0 defeat.)
• The W-League in 2002 gave 4-1-0 with a bonus point for scoring three goals.
• The League of Ireland in 1981-82 had 4-3-2-1-0 points for away win — home win — away draw — home draw — loss
• In China in the 1970s and 80s, bonus points were for scoring headed goals, and for teams whose players were selected for the national squad.
• Bulgaria for three seasons 1984-7 gave no points for scoreless draws.
• France gave a bonus point for scoring 3 goals in 1973-6, but stopped after rumours this encouraged match fixing. However, Michel Hidalgo has reported to the French Football Federation similar proposals to encourage attacking play.

Some leagues have used penalty shootouts after drawn games, in which case points will vary for regulation win — penalties win — penalties loss — regulation loss:

• In the playoffs of the French women's league, 4-2-1-0.
• Yugoslav League had 2-1-0-0 from 1989-92
• Major League Soccer had 3-1-0-0 from 1996-9.
• The original Japan Football League had 3-3-1-0 in 1996
• In the North American Soccer League in 1975-84, 6-1-0-0, with a bonus point each for up to 3 goals scored
• In the Western Soccer League in 1989, 6-4-2-0, with a bonus point each for up to 3 goals scored

In FIBA (basketball)-sanctioned tournaments, where ties are impossible (a game goes into as many extra periods — or overtimes — as necessary to determine a winner), the following method is used:

• Win (including by forfeit) = 2 points
• Loss = 1 point
• Loss by default (all players were ejected/disqualified/injured) = 1 point
• Loss by forfeit (fails to show up for a scheduled game or withdraws from the court before the end of the game) = 0 points

For an example, see 2006 FIBA World Championship.

In the National Hockey League (and various other minor hockey leagues), where regular season games tied after three periods go into a five-minute sudden-death overtime period and then a shootout if needed, the following method is used:

• Win: 2 points
• Loss in regulation time: 0 points
• Loss in overtime or shootout: 1 point

Most European ice hockey leagues including KHL use an improvement to the NHL method that does not encourage regulation draws by awarding more combined points than regulation decisions. This system was also used at the 2010 Winter Olympics in the preliminary round-robin games:

• Win in regulation time: 3 points
• Win in overtime or shootout: 2 points
• Loss in regulation time: 0 points
• Loss in overtime or shootout: 1 point

Summary

League/organizer	Full-time win	Overtime win	Draw	Overtime loss	Full-time loss	Forfeit loss
Association football	3	—	1	—	0	—
Australian Football League	4	—	2	—	0	—
Chess	2	—	1	—	0	0
Cricket (Limited Overs)	2	—	1 (NR)	—	0	—
FIBA basketball	2	2	—	1	1	0
Field hockey	3	—	1	—	0	—
Go (game)	2	—	1	—	0	0
Handball	2	—	1	—	0	—
IIHF ice hockey	3	2	—	1	0	—
National Hockey League	2	2	—	1	0	—
Rugby league	2	—	1	—	0	—
Rugby union	4	—	2	—	0	—
Volleyball	3 (3 or 4 sets)	2 (5 sets)	—	1 (5 sets)	0 (3 or 4 sets)	—

Tiebreaker criteria

When competitors are level on points, there is usually some tiebreaker criterion.

Sometimes, however, ranking ties may stand: prior to 1994, the Five Nations Championship in rugby union could result in joint champions; likewise for the British Home Championship in association football until 1978. In college football in the United States, many conferences permit joint champions. However, if ranking within the conference determines eligibility for a postseason bowl game, tiebreak criteria will be required to separate the joint champions. Similarly, U.S. college conferences in other sports, notably basketball, use tiebreak criteria as needed to determine seeding in postseason conference tournaments.

A tiebreaker may be a play-off, with extra matches between the tied competitors. This may be a full match or a reduced format such as a penalty shootout or speed chess. If there are more than two tied competitors in a 2-competitor game, the play-off may be a round-robin or knockout tournament.

Instead of a playoff, the original matches may provide the tie-breaker criteria:

head-to-head

considering only results of matches between the deadlocked competitors. If more than a single match is involved, a subtable may be used recursively for the ranking. For example, in the Super League Greece 2006-07, part of the final table was:

Pos	Team	P	W	D	L	Pts
11	Xanthi	30	8	12	10	36
12	Iraklis	30	10	5	15	35
	Apollon Kalamarias	30	9	8	13	35
	Kerkira	30	8	11	11	35
15	Egaleo	30	7	7	16	28

The three teams tied on 35 points were separated by considering only matches between any two of them....:

Pos	Team	P	W	D	L	Pts
12	Apollon Kalamarias	4	3	0	1	9
13	Iraklis	4	1	1	2	4
	Kerkira	4	1	1	2	4

...and then again for the two teams still tied:

Pos	Team	P	W	D	L	Pts
13	Iraklis	2	1	1	0	4
14	Kerkira	2	0	1	1	1

scoring average

the ratio of points (goals, etc.) scored to those conceded.

scoring differential

the difference between points (goals, etc.) scored and those conceded.

points scored

irrespective of points conceded.

points scored away

valuing scores "on the road" above scores on one's home ground.

number of wins

in games where draws are possible

disciplinary record

fouls conceded, players sent off, etc.

seeding or pre-tournament ranking

This may be defined to favour the higher- or lower-ranked competitor.

Neustadtl score, now commonly known as Sonneborn-Berger score, and which reduces to SODOS if ties cannot occur

the sum of defeated opponents' scores plus half the sum of drawn opponents' scores; this method is especially common in round-robin chess tournaments; in chess or Go Swiss system tournaments (which use Swiss pairing) it is used as a secondary tie-break criterion. Ties remaining on one of these criteria may be resolved by resorting in turn to others of them. Where a group is the qualifying phase of a larger tournament, such that ties are not admissible, it may be necessary as a last resort to use drawing of lots as a tiebreaker (as was used in Group F of the 1990 FIFA World Cup to separate second and third place). Sum Of Defeated Opponents' Scores (SODOS) suffices if draws cannot occur, such as in Go when komi is set to 6.5 or another half-point value.

SOS

the sum of opponents' scores (SOS). While SODOS works well, SOS fails as tie-breaker in tournaments with Swiss system pairing or that have all players play all others. But SOS makes more sense than SODOS does as tie-breaker in tournaments with McMahon pairing.

Swiss system tournaments use Swiss pairing and for tie-breaking use a variety of criteria not found in other types of tournament which exploit features specific to the Swiss system: see tie-breaking in Swiss system tournaments. Chess and some Go (game) tournaments use Swiss pairing.

McMahon pairing is designed to improve upon Swiss pairing, and is now used for most amateur Go tournaments at least in the U.S. and Europe.

External links

• Scoring Systems, USA leagues lists many other systems used in soccer leagues in the USA