Goal differential

Goal difference, or goal differential or points difference is a form of tiebreaker used to rank sport teams which finish on equal points in a league competition. Either "goal difference" or "points difference" is used, depending on whether matches are scored by goals (as in ice hockey and association football) or by points (as in rugby union and basketball).

Goal difference is calculated as the number of goals scored in all league matches minus the number of goals conceded, and is sometimes known simply as plus–minus. Goal difference was first introduced as a tiebreaker in association football, at the 1970 FIFA World Cup, and was adopted by the Football League in England five years later. It has since spread to many other competitions, where it is typically used as either the first or, after tying teams' head-to-head records, second tiebreaker. Goal difference is zero sum, in that a gain for one team (+1) is exactly balanced by the loss for their opponent (–1). Therefore, the sum of the goal differences in a league table is always zero (provided the teams have only played each other).

Goal difference has often replaced the older goal average, or goal ratio. Goal average is the number of goals scored divided by the number of goals conceded, and is therefore a dimensionless quantity. It was replaced by goal difference, which was thought to encourage more attacking play, encouraging teams to score more goals (or points) as opposed to defending against conceding. However goal average is still used as a tiebreaker in Australia, where it is referred to as "percentage". This is calculated as points scored divided by points conceded, and then multiplied by 100.

If two or more teams' total points scored and goal differences are both equal, then often goals scored is used as a further tiebreaker, with the team scoring the most goals winning. After this a variety of other tiebreakers may be used.

Goal difference v. goal average

Team A

3–0

Team B

Game reference

---

Team B

6–0

Team C

Game reference

---

Team A

0–1

Team C

Game reference

Under goal average, Team A would win:

Pos	Team	Pld	W	D	L	GF	GA	GR	Pts
1	Team A	2	1	0	1	3	1	3.000	3
2	Team B	2	1	0	1	6	3	2.000	3
3	Team C	2	1	0	1	1	6	0.167	3

Under goal difference, Team B would win:

Pos	Team	Pld	W	D	L	GF	GA	GD	Pts
1	Team B	2	1	0	1	6	3	+3	3
2	Team A	2	1	0	1	3	1	+2	3
3	Team C	2	1	0	1	1	6	−5	3

Goal average was replaced by goal difference due to the former's encouragement of lower-scoring games. For example, a team that scores 70 while conceding 40 would have a lesser goal average (1.750) than another team that scores 69 while conceding 39 (1.769). Or, for the team that has scored 70 while conceding 40, conceding another would reduce the goal average by 0.043 (to 1.707), whereas scoring another would increase it by only 0.025 (to 1.775), making not conceding much more important than scoring again.

The opposite effect occurs when the number of goals scored is less than the number of goals conceded, with goal difference encouraging more defensive play for teams in relegation battles. Consider a team that scores 10 while conceding 20. Under goal difference, an extra goal scored cancels out an extra goal conceded. However, under goal average, an extra goal would increase the goal average by 0.05, while conceding would reduce it by only 0.024.

Another issue with goal average is that, if a team has conceded no goals (e.g. England in the 1966 FIFA World Cup Group 1), the value cannot be calculated, as division by zero is undefined.