Group tournament ranking system

In a group tournament, unlike a knockout tournament, there is no scheduled decisive final match. Instead, all the competitors are ranked by examining the results of all the matches played in the tournament. Typically, points are awarded for each match,^{[n 1]} with competitors ranked based either on total number of points or average points per match. Usually each competitor finishes with an equal number of matches, in which case rankings by total points and by average points are equivalent at the end of the tournament, though not necessarily while it is in progress. Examples with unequal numbers of matches include the 1895 County Championship in English cricket, and the U.S. National Football League prior to 1972, when tie games were excluded from the winning percentage used for regular-season standings.

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). 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.^[1] 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 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.

Official listings while a tournament is in progress may need to take account of competitors having played differing fractions of their schedules. Some use average points (such as the "points percentage" of the National Hockey League^[2]) and others total points (such as the English Premier League, although comparisons between teams typically mention where one has "games in hand" on the other). The games behind figure in Major League Baseball gives the same rank order as average points.

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:^[18]

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. In 2018 FIFA World Cup Group H, Japan eliminated Senegal by after recevining fewer yellow cards.

seeding or pre-tournament ranking

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

Neustadtl score or Sonneborn–Berger score^[19]

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.

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.^[20][21]

Swiss system tournaments and variants thereof use a variety of tie-breaking 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 tournaments use Swiss pairing.^[22]

Footnotes

References

External links

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