Statistical Rankings/Points with Tied Scores

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comprankings

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I administer a statistical ranking system that coverts scores at athletic competitions to rankings (1st, 2nd, 3rd, etc.) then assigns series points to the rankings so a champion can be crowned at the end of each season.


Comp Score = rank = series points
Highest Score = rank 1 = 30 points
2nd Highest Score = rank 2 = 26 points
3rd Highest Score = rank 3 = 22 points
4th Highest Score = rank 4 = 18 points
5th Highest Score = rank 5 = 14 points
6th Highest Score = rank 6 = 10 points
7th Highest Score = rank 7 = 6 points
8th Highest Score = rank 8 = 2 points
--------------------------------------------------
Total points awarded: 128


The problem is how to allocate rank and points in the case of tied scores? The committe that organizes the sporting events uses one method, I recommend they use another. The two methods produce different results at the end of the season, meaning they are not equal. My question is which option should be used, and why?


Option A


Comp Score = rank = series points
Highest Score = rank 1 = 30 points
2nd Highest Score = rank 2 = 26 points
2nd Highest Score = rank 2 = 26 points
2nd Highest Score = rank 2 = 26 points
3rd Highest Score = rank 5 = 14 points
4th Highest Score = rank 6 = 10 points
5th Highest Score = rank 7 = 6 points
6th Highest Score = rank 8 = 2 points
--------------------------------------------------
Total points awarded: 140


Option B


Comp Score = rank = series points
Highest Score = rank 1 = 30 points
2nd Highest Score = rank 2 = 22 points
2nd Highest Score = rank 2 = 22 points
2nd Highest Score = rank 2 = 22 points
3rd Highest Score = rank 5 = 14 points
4th Highest Score = rank 6 = 10 points
5th Highest Score = rank 7 = 6 points
6th Highest Score = rank 8 = 2 points
--------------------------------------------------
Total points awarded: 128
 
comprankings said:
I administer a statistical ranking system that coverts scores at athletic competitions to rankings (1st, 2nd, 3rd, etc.) then assigns series points to the rankings so a champion can be crowned at the end of each season.


Comp Score = rank = series points
Highest Score = rank 1 = 30 points
2nd Highest Score = rank 2 = 26 points
3rd Highest Score = rank 3 = 22 points
4th Highest Score = rank 4 = 18 points
5th Highest Score = rank 5 = 14 points
6th Highest Score = rank 6 = 10 points
7th Highest Score = rank 7 = 6 points
8th Highest Score = rank 8 = 2 points
--------------------------------------------------
Total points awarded: 128


The problem is how to allocate rank and points in the case of tied scores? The committe that organizes the sporting events uses one method, I recommend they use another. The two methods produce different results at the end of the season, meaning they are not equal. My question is which option should be used, and why?


Option A


Comp Score = rank = series points
Highest Score = rank 1 = 30 points
2nd Highest Score = rank 2 = 26 points
2nd Highest Score = rank 2 = 26 points
2nd Highest Score = rank 2 = 26 points
3rd Highest Score = rank 5 = 14 points
4th Highest Score = rank 6 = 10 points
5th Highest Score = rank 7 = 6 points
6th Highest Score = rank 8 = 2 points
--------------------------------------------------
Total points awarded: 140


Option B


Comp Score = rank = series points
Highest Score = rank 1 = 30 points
2nd Highest Score = rank 2 = 22 points
2nd Highest Score = rank 2 = 22 points
2nd Highest Score = rank 2 = 22 points
3rd Highest Score = rank 5 = 14 points
4th Highest Score = rank 6 = 10 points
5th Highest Score = rank 7 = 6 points
6th Highest Score = rank 8 = 2 points
--------------------------------------------------
Total points awarded: 128
Click to expand...


Normally the three tied scores are averaged [(26+22+18)/3] and each gets the average score (22)
 
I agree with Subhotosh Khan. If a different total of points are awarded at different events, the winners (and other places) points are deleted. For example, suppose we have two (of the best) contestants with the same record except for 6 events. In three of those events one contestant placed 1st, 2nd, and 3rd (no ties) and the second contestant place 5th in all three. In the other three events contestant two place 2nd (no tie), 2nd (3 way tie, so also 4th) and 2nd (3 way tie so also 4th) and the first contestant placed 5th in all of those three.

I think we would all agree that contestant number one with a 1st, 2nd, and 3rd (no ties) deserved the championship even though under option A they both have the same number of points.
 
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