# Matchpoint scoring

In a duplicate bridge contest with matchpoint scoring, 3 steps are involved in obtaining the score.
1. First the trick score is determined, based on the contract, the number of tricks made, and the vulnerability. For instance, 4 hearts bid and made vulnerable, has a trick score of 620 points.
2. 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

 S = 2k + m - 1
(1)
3. The third step is the conversion from MP to a percentage. The simplest way to do this by taking 100 × (MP obtained) / (maximum possible MP), or:
 P = 100 · S 2n − 2
(2)
where P is the percentage, S the score in matchpoints and n the total number of scores available.

We will call the scoring method described above the classical method. This is not the only possibility. There are methods that lead to a different percentage, such as the Neuberg formula and the Ascherman method.

All alternatives that we will consider may be described by the formula:

 P' = (P − 50) ·A + 50
(3)
where P is the percentage from the classical method, see equation (2), P' the alternative percentage, and A is a factor that depends on the method used.