For instance, in volleyball they use set quotient or points quotient as tie-breakers. They are simply the result of sets/points won divided by sets/points lost. But what if sets/points lost is
0? What is the conventional value that is used?
In volleyball at least, this is shown as "Max" and means the team wins the tie-breaker over any other tied teams. For example, see Pool D of the FIVB Women's World Championship 2018: Serbia won 15 sets and lost none, giving them a sets ratio of "Max".
Aside: in the very common case of a full round-robin, any team with a set ratio of "Max" is always going to have more wins than any other team; the team with a set ratio of "Max" must have won all its matches, so every other team must have lost a match - therefore the tie-breaker won't be used anyway. In some odd cases where you don't play a full round-robin, the tie-breaker might be relevant.
In the unlikely event two or more teams actually conceded no points there is no mathematical solution. The quotient will not be calculated, simply because it's not possible. The team(s) involved will just be ranked highest of the tied teams.
Quotients involving dividing by zero:
- One team = this team will be ranked higher than the other tied teams; it "wins" the tie breaker
- Two or more = The number of scored points will be used as a tie breaker between those teams
- If there's still a tie it will depend on the league how to break it (often only the matches between the teams involved will be taken into account to create a new mini table)