Matchpoint Bridge scoring is relatively simple, having been developed from handwritten processes. Many people
know it well enough to understand how an ordinary club event is scored, but, there seems to be some confusion as to
how the results for multiple clubs are merged. This document endeavours to clear up that confusion.

For any given movement, once results are in, we must sort the scores within each board. Once this is done we can
allocate matchpoints for each board.

This is done by first calculating the top allocation for the board. The top allocation is equal to twice the
number of times the board was played minus two. Note that not all boards are guaranteed to have the same top, more to
come on that later. Points are allocated to each pair with the largest score getting the top allocation, the next the
previous allocation minus two. Where scores are identical, the allocation will be the sum of the allocations taken up
divided by the number of times the score occurs.

An example  A board where we have 11 scores. The top score is therefore 20. After sorting we have them layed
out as follows 

Score  Number of times score occurred  Matchpoints


+1430  1  20
 +690  1  18
 +680  3  14
 +660  2  9
 +650  1  6
 100  2  3
 200  1  0


Note the matchpoints allocated for the +680 score. It is ( 16 + 14 + 12 ) / 3, which equals 14.

This process must be followed for each board.

We then turn our attention to any boards that have been played less than the maximum number of times any board
was played. The matchpoints for these boards must be factored up to match the maximum amount. As matchpoints have been
allocated in whole numbers up to this point we now see decimals coming in.

An example  Most boards were played 28 times, some were played 24 times. The scores for the boards that were
played 24 times must be multiplied by ( 28 / 24 ) to make all boards have equal weight.

We can then add up the scores for each pair.

Some pairs may have played less boards than the maximum number played by any pair. These pairs must have their
score factored up to again give their score equal weight to the other pairs.

An example  Most pairs have played 30 boards, some played 33 boards. The scores for the former must be multiplied
by ( 33 / 30 ) to make all scores have equal weight.

We then add up the final scores for each pair and calculate its percentage relative to the maximum possible score.
This is all that is needed to determine the result within the club. This percentage will be what the players see diplayed
at their club. The confusion comes when one club's results are merged with another.

The percentage score attained at the club is not retained  the event is completely rescored.

This means that each board has a new top and new maximum times played, the event has a new maximum number of
boards played and a new maximum score.

It is probable that a pair's percentage will be different. It is not uncommon for the order of pairs to change,
particularly when their scores at the club are close.

An example  Using the previous example of a board where we have 11 scores, and thus a top of 20. We now have
101 scores, and thus a top score of 200. After sorting we have them layed out as follows 

Score  Number of times score occurred  Matchpoints


+1430  1  200
 +690  21  178
 +680  23  134
 +660  22  89
 +650  21  46
 100  12  13
 200  1  0


Note the score for +690, it was 18 out of 20 in the first example and is now 178 out of 200. Equally, the +660
score was 9 out of 20 and is now 89 out of 200. This is proportionately about the same, but, note that the new scores
were distributed evenly about these two scores  what happens if they are not?

Score  Number of times score occurred  Matchpoints


+1430  1  200
 +690  1  198
 +680  93  104
 +660  2  9
 +650  1  6
 100  2  3
 200  1  0


Note the score for +690, it was 18 out of 20 and is now 198 out of 200. The +660 score was 9 out of 20 and is
now 9 out of 200. What has happened is that all of the new scores have gone in between the +690 and the +660 scores. This
is an extreme example, but, it can happen. What it is important to realise is that when new results come in, all bets
are off and the event is completely rescored.
