# The Bussemaker model, use of the program

For a discussion of the model and some examples click here.
In the following its implementation and use is described.

The calculation is started by a call:

score2 -b [-s <number of samples>] <movement-file>

The program first shows the results for an assignment as given in the movement-file with the strength coupled to pair number as described. Then the scores are shown for 10 arbitrary assignments of pair numbers. For instance, the renumbering "4 2 3 1" means the original pair 1 now gets pair number 4, etcetera However, for the score calculation the original pair numbers are used, so pair 1 remains the strongest pair even though it plays with a different pair number.

Subsequently the average deviation (standard deviation) of the ideal value is determined by taking a large number of random assignments of pair numbers. This average deviation should be taken with a grain of salt as the distribution is by no means a normal distribution. Deviations of more than 3 times the average deviation are not uncommon.

To make the results look a little less extreme, Bussemaker gave an extra constant number of MP's to every pair before calculating the total score in percent. This has not been done here, but a similar effect is obtained by simply dividing the difference from 50% by 3. These reduced values are shown in a separate column.

Finally a probability table is output. This is a N x N - matrix showing the percentage probability that pair i ends up at place j in the final ranking. (N is here the number of pairs, i and j are numbers from 1 to N). In the ideal case this is a diagonal matrix with all diagonal elements equal to 100.

## Weighted Bussemaker.

A variation on the Bussemaker model is the following. We assign a strength to every pair. Not all pairs have to be of different strength. The score is now determined by the difference in strength, instead of the difference in pair numbers. Strength 1 is very strong, 2 somewhat less, etcetera
The strengths are to be given on the command line:
score2 -bw <movement-file> <strength1> <strength2> <strength3> ...
Note that
score2 -bw <movement-file> 1 2 3 ...
is equivalent to the original Bussemaker model, while
score2 -bw <movement-file> 1 1 2 2 2 2 ...
is the case of the "2 strong pairs" model that was the purpose of 'score2' in the first place.

## Division into separate groups

Some movements allow the calculation of separate scores for subgroups of the total field. This is true for instance for Mitchell movements where separate NS and EW scores are possible, and for movements designed for "scoring across the field".
The command line
score2 -b -D<n> <movement-file>
assures that the subgroups are kept separate when assigning the random pair numbers. If, e.g., the number of pairs in the movement is 14 then option "-D2" results in keeping pair 1 ..7 apart from pair 7 ..14. Notice that the score is always calculated across the whole field, only the participants of the each group are kept separate. This option may be combined with Weighted Bussemaker. Example:
score2 -bw -D2 24p6r.txt 1 2 2 2 2 2 2 2 2 2 2 2 3 4 4 4 4 4 4 4 4 4 4 4
BEWARE! The program assumes that the pairs in each subgroup have consecutive numbers.

## Controlling the amount of output.

By option
-v n
you can specify for how many cases (normally 10) detailed output is wanted. E.g. with "-v 1" you only get the output for the initial assignment 1 2 3 4 ..., with "-v0" no details at all.

The detailed output normally consists of the result (Pair, strength, MP, percent). With the option

-S
you get, in addtion, the scores per board.

## Survey of options, program score2 -b

 -s samples (default 40000) -w -D n_divisions -S -v n_cases