I am trying to calculate a season score for each sailboat for a series of races. Basically, each boat receives a high point score based on their position and the number of competitors in their class. If there are 10 boats, the first place boat receives 10 points, second 9, and so on.
The calculation of season score is the sum of points scored in each race divided by the sum of possible points had the boat won each race. Summing the numerators and denominators separately weighs races with more competitors more heavily). The challenge is that each boat's season score is calculated from the 7 races that produce the maximum result. It is choosing those races that has proved challenging. (Note that each boat sails a different number of races of their choice).
In the following example, the season consisted of 14 races. Sea Fiddler Sailed in 10 of those races. The straight forward solution (select the 7 highest individual race % scores) would select races 1, 2, 4, 5, 7, 11 and 14. This produces a score of .5333. In fact, races 1, 2, 3, 5, 7, 11 and 14 produce a better score (.5385) because the reduced number of competitors in race 3 more than offsets the better performance in race 4.
Season Scoring Example.jpg
Race 1 2 3 4 5 6 7 8 9 10 11 12 13 14
Finish 2 3 3 5 4 DNC 2 DNC DNC 6 2 4 DNC 3
Points 2 1 1 3 4 1 1 2 1 3
Competitors 3 3 3 7 7 3 2 2 5 6 3 4 2 5
* DNC = Did Not Compete and is not scored.
I would greatly appreciate any insight from those with more experience than me.
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