How can I properly rank a win / loss ratio while taking into account the number of matches that take place?

Question

I'd like to find a way to properly rank items that have competed against each other. Sorting by percentage alone is not an option as lots of items will have only been in one match.

Well the problem is that the difference between the number of matches could be very pronounced. In my case there could be items with 100 matches and items with just 1, and a whole mess in between.

What i'd like is for some way to know whether a 4 out of 6 team is better then a 20 out of 30 team.

Answer 1

You could do what baseball does in "games ahead or behind".

Team A's record is 7 wins, 4 losses. Team B's record is 6 wins, 5 losses. Team B is one game behind Team A; that is, if they played each other once, Team B could tie Team A by winning.

If Team A's record is 7 wins, 4 losses and Team B's record is 6 wins, 4 losses, then Team B is 1/2 game behind Team A; that is, if they played each other once, Team B could pass Team A by winning.

Thinking of this another way is to think of how far ahead or behind .500 (in baseball) or 50% a team is. A team with a 7-4 record is 1.5 games above a .500 team, regardless of how many games that team has played. I believe that would be the most useful solution for you.

Team A 50 wins, 25 losses = .667, 12.5 games over .500
Team C 18 wins, 2 losses = .900, 8 games over .500
Team B 7 wins, 0 losses = 1.000, 3.5 games over .500

In baseball, the teams are shown in games behind the leading team, thus:
Team A 0 games behind (1st place)
Team C 4.5
Team B 9.0

The implicit assumption is that the team with fewer games played will win half and lose half of those games.

Answer 2

If you are concerned about ranking against each other with only one match I dont see the problem. There should be one winner and one loser from each game- the winners will always be ranked higher than the losers by percentage. The problem comes in when you have a high percentage winner with only a few games that gets ranked ahead of a team with a slightly lower winning percentage but many more matches completed. In this case, the usually approach is to rank by teams with the most matches and then by the winning percentage.

This brings the dilemma of a really high winning percentage getting ranked at the bottom of the list becaue only a few matches have been played. This can be rectified by assuming they lose the difference in number of matches. For example, some clubs have played 8 games and other have only played 5. If the team with only 5 games were to lose the next three (8-5), their winning percentage could still be higher than other clubs. In this case, they move up the ranking list to the appropriate position.

Of course these are my ideas and there are many other possibilities.