Competition scoring/ranking algorithm

Question

The gist

I'm implementing a website that hosts fitness competitions, and I need a good way to generate a "score" or "rank".

How the competitions work

Competitions consist of a team of one or more athletes/contestants from a given gym challenging the same number of contestants from one or more other gyms. There isn't any limit to the number of gyms that can enter the competition - there could potentially be over one hundred gyms that enter the competition. Points are assigned to each team based on various factors: time, reps, heaviest lift, etc.

Attributing a score to each team within a single competition is the easy part; things get a little more interesting when we try to generate a ranking for each gym based on their history of competitions. Intuitively, a team that places 1st amongst 10 other gyms in a competition should rank higher than a team that places 1st among 5 other gyms from a different competition.

I'm having trouble coming up with an intuitive, fair ranking mechanism. Any concrete ideas or suggestions on perhaps a family of ranking algorithms would be appreciated.

Answer 1

How about treating each team as 'beating' all the teams it placed above in a particular competition, and 'losing' to all teams it placed below? You could then compute an ELO for each team over time.

Answer 2

To rank with competitions of varying size, couldn't you simply award last place +1 and first place +n (where n is the number of contestants) which rewards all gyms for competing, and rewards a first place win in a larger competition a great score than a smaller.

Answer 3

If you see the competition as gym. Maybe the fair rank depends on their muscle which surely relies on how many exercise they have done and how regular it is. Of course some variable from 'before' and 'after' exercising must be taken. In a brief, calculate the effectiveness of the exercise they do.

For example:

Normally, when exercise x is done 40 times, one can increase his muscle 5 points

Mr. A does exercise x 30 times and got 4 muscle. Hence Score for Mr. A = (4 / 30 ) / (5 / 40)

The total score is the sum of another exercise done by Mr. A. Total = Score(x) + Score(y) + Score(z)

This is fair enough since the actual result is compared directly to expected result. This can also prevents a stronger person taking an easy exercise. Since, you know, Arnold Schwarzenegger can't increase his muscle using 1 kg dumbell.

Of course the unit (muscle) may vary depends on the exercise.