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I might be creating a bike event with a number of different events. The competitors can choose which if the many events they want to do. There may be the chance for individual competitors to challenge others to impromptu events too.
I am trying to think of a slightly more scientific way of creating a scoring system which is fairly easy to administer and flexible enough to cope with an unknown number of events each of which has an unknown number of competitors. Both unknowns have an upper limit of the total number of competitors and a minimum of two. I also want to reward people who take part in lots of events.
Current thinking is shown in the spreadsheet below but if it doesn't format properly, here is a summary:
1) For each event we record the number of competitors and the positions they finished in.
2) We give then a score based on 100 divided by the number of the competitors divided by their position
3) At the end of the event we add up all their scores to get the total for each person
4) We divide that score by the number of events they took part in
5) We then add twice the number of events they entered, to encourage lots of participation
Point 2 causes me most concern. Anyone who knows maths or stats - please advise what effect point 2 will have for events with lots of people or events with 2 people. I don't want either case to over weight the final score. Any better equations welcome.
Person Position
Event # Competitors John Paul George Ringo
Duel Track 4 1 2 3 4
Race 2 0 1 0 2
Race 3 1 0 2 3
XC 4 4 3 2 1
Race 2 0 1 2 0
Race 2 0 1 2 0
Race 2 0 2 1 0
Person Score
John Paul George Ringo
25 13 8 6
0 50 0 25
33 0 17 11
6 8 13 25
0 50 25 0
0 50 25 0
0 25 50 0
Total 65 196 138 67
# Events 3 6 6 4
Avg 22 33 23 17
Final Score 28 45 35 25
Forgot to add, probably a max of 30 competitors and average of 20 on most events, just a few duels