In sports such as ice hockey and football (soccer), goal difference (that is, goals scored minus goals conceded) is often the first tiebreaker used to rank teams which finish a league competition with an equal number of points.

If a team's points and goal difference are equal, then often goals scored is used as a second tiebreaker, with the team scoring the most goals winning. Alternative tiebreakers that may be used include looking at the head-to-head results between sides, playing a playoff, or the drawing of lots.

Goal average is a different scheme that predated goal difference. Using the goal average scheme the number of goals scored is divided by the number of goals conceded. Goal difference replaced goal average in the 1970 World Cup finals and from 1976-1977 season in the English Football League. Goal average is also used as the tiebreaker in Australian rules football where it is referred to as "percentage". It is calculated as points scored for divided by points scored against multiplied by 100.

Goal difference v. goal average

The different schemes can lead to strikingly different results. Consider the result of the following matches:

Under goal average, Team A would triumph:

However, under goal difference, Team B would triumph:

Goal average was replaced by goal difference due to the former's encouragement of lower-scoring games. A team that scores 70 while allowing 40 would have a lesser goal average (1.750) versus another team that scores 69 while allowing 39 (1.769).

It's notable, though that teams who've scored fewer than they've conceded can improve their goal average with a score draw. For example, a team with 15 for and 30 against has a goal average of 0.5, but a 2-2 draw would increase their goal average to 0.53.

A more extreme case:

Under goal average, Team A would triumph. 1 divided by 0 is a meaningless expression that, in the context of goal average, was taken to mean "infinite".

Team	Pts	Pld	W	D	L	F	A	GA
Team C	5	3	1	2	0	2	0	${\displaystyle \textstyle {\frac {2}{0))}$	Team A	5	3	1	2	0	1	0	${\displaystyle \textstyle {\frac {1}{0))}$	Team D	3	3	0	3	0	0	0	${\displaystyle \textstyle {\frac {0}{0))}$	Team B	1	3	0	1	2	0	3	0

However, under goal difference, Team B would triumph:

And even stranger:

Again, division by zero is meaningless. There is no mathematical reason why 2/0 should exceed 1/0; nor can any well-defined valuee xist for 0/0.

Team	Pts	Pld	W	D	L	F	A	GA
Team C	5	3	1	2	0	2	0	${\displaystyle \textstyle {\frac {2}{0))}$	Team A	5	3	1	2	0	1	0	${\displaystyle \textstyle {\frac {1}{0))}$	Team D	3	3	0	3	0	0	0	${\displaystyle \textstyle {\frac {0}{0))}$	Team B	1	3	0	1	2	0	3	0

However, under goal difference, Team B would triumph:

Real Examples

England, 1989

Arsenal famously won the championship on goals scored in 1989, thanks to a 2-0 victory over Liverpool on the last day of the season at Anfield. The second and decisive goal in the match was scored by Michael Thomas in injury time at the end of the match. Arsenal and Liverpool finished equal on points and goal difference, but Arsenal were ahead by 73 to 65 on goals scored. Had the league still been decided on goal average, Liverpool would have won by 2.321 to 2.028.

Scotland, 1965 & 1986

In Scottish football, Hearts have more reason than most to curse these rules. In 1965, Hearts lost 2-0 at home on the final day of the season to Kilmarnock, which meant that Kilmarnock won the championship on goal average, 1.88 to 1.84. Had the first tie-breaker been goal difference, Hearts would have won the championship (41 to 29).

In 1986, Hearts lost 2-0 at Dundee on the final day of the season, which allowed Celtic to win the championship on goal difference. Had the first tie-breaker been goal average, Hearts would have won the championship. Due to these two near misses and the rule change, Hearts have not been Scottish league champions since 1960.