This score is converted to matchpoints (MP) by comparison with other contestants who
played the same board. The lowest score gets 0 MP, the next higher
2 MP, et cetera. When there are two or more equal scores the available MP
are equally distributed. For example for a bottom shared by 3 pairs
each pair gets
(0 + 2 + 4)/3 =2 MP. The bridge laws describe this process as follows (Law 78A):
In matchpoint scoring each contestant is awarded, for scores made by
different contestants who have played the same board and whose scores are
compared with his,
- two scoring units (matchpoints or half matchpoints) for
each score inferior to his,
- one scoring unit for each score equal to his,
- and zero scoring units for each score superior to his.
We will assume throughout that the scoring units are equal to matchpoints.
In some jurisdictions, notably the USA, one uses half matchpoints.
Notice that in the "scores made by
different contestants who have played the same board"
the contestant under consideration is not counted.
If on a board a certain score occurs m times, and there are k lower scores,
then the number of matchpoints for this score is