The formula for scoring fouled and adjusted boards is the one used by the World Bridge Federation and adopted by the ACBL.
For the mathematically minded, the fouled board formula is:
N x S N - n
M = ----------------- + -----------------
n 2n
where
M = final matchpoints on the board
N = number of scores on the board
S = matchpoint score within own group
n = number of scores within own group
Note this formula is used only when there are four or more scores within the same comparison group. The formula is also used on groups of three scores when it is the larger group (e.g., a board is played five times, three times fouled and twice unfouled). Otherwise the scores in a group of three are awarded matchpoint scores of 70%, 60% and 50% of top. In groups of two, the better score receives 65% of the matchpoints and the worse receives 55% of the matchpoints. A single score is awarded 60% of top for each direction. Scores are rounded to the nearest hundredth, .005 is rounded up.
These arbitrary awards are assigned since small groups are not large enough to warrant matchpoint assignments.