Hi!
PS. I have put the problem in a google sheets document in a more readable format, that you can freely edit, and play with. https://docs.google.com/spreadsheets/d/1NGxP1hHFcYXPh8Sy2w_52FSFAURIDRo83utXp97uHp0/edit?usp=sharing
This is the problem I am stuck with:
Runner : Speed cumulative frequency best ---> worst
Percentile (top x percentile)
1 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 99
runner
A 0.00 0.00 0.38 0.50 0.50 0.50 0.63 0.63 0.63 0.63 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.88 0.88 0.88
B 0.00 0.00 0.25 0.25 0.42 0.50 0.75 0.92 0.92 0.92 0.92 0.92 0.92 0.92 0.92 0.92 0.92 0.92 0.92 0.92 1.00
C 0.00 0.00 0.00 0.00 0.23 0.31 0.46 0.46 0.46 0.46 0.54 0.62 0.62 0.69 0.69 0.77 0.85 0.92 0.92 1.00 1.00
D 0.00 0.00 0.13 0.13 0.13 0.25 0.38 0.63 0.63 0.88 0.88 0.88 0.88 0.88 1.00 1.00 1.00 1.00 1.00 1.00 1.00
E 0.00 0.00 0.00 0.00 0.00 0.14 0.14 0.29 0.43 0.43 0.43 0.43 0.43 0.57 0.71 0.71 0.86 0.86 1.00 1.00 1.00
F 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.07 0.14 0.14 0.14 0.21 0.21 0.36 0.43 0.43 0.43 0.64 0.79 0.86 0.93
G 0.00 0.00 0.00 0.00 0.25 0.25 0.25 0.25 0.25 0.38 0.63 0.63 0.63 0.88 0.88 0.88 0.88 0.88 0.88 0.88 0.88
H 0.00 0.00 0.00 0.00 0.00 0.20 0.60 0.60 0.60 0.80 0.80 0.80 0.80 0.80 1.00 1.00 1.00 1.00 1.00 1.00 1.00
(numbers show frequency of runs within that percentile, eg 0.38 means 38% of the runs that runner made were within that percentile)
From here, how does one calculate most accurately, what the probability each runner has of coming first, second, third, fourth, fifth, sixth, seventh, eighth?
Thanks everyone, have been stuck with this problem for ages now, I will not describe what calculations I have tried so far because it may not be the best way at all.
Best Regards,
Joe
PS. I have put the problem in a google sheets document in a more readable format, that you can freely edit, and play with. https://docs.google.com/spreadsheets/d/1NGxP1hHFcYXPh8Sy2w_52FSFAURIDRo83utXp97uHp0/edit?usp=sharing
This is the problem I am stuck with:
Runner : Speed cumulative frequency best ---> worst
Percentile (top x percentile)
1 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 99
runner
A 0.00 0.00 0.38 0.50 0.50 0.50 0.63 0.63 0.63 0.63 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.88 0.88 0.88
B 0.00 0.00 0.25 0.25 0.42 0.50 0.75 0.92 0.92 0.92 0.92 0.92 0.92 0.92 0.92 0.92 0.92 0.92 0.92 0.92 1.00
C 0.00 0.00 0.00 0.00 0.23 0.31 0.46 0.46 0.46 0.46 0.54 0.62 0.62 0.69 0.69 0.77 0.85 0.92 0.92 1.00 1.00
D 0.00 0.00 0.13 0.13 0.13 0.25 0.38 0.63 0.63 0.88 0.88 0.88 0.88 0.88 1.00 1.00 1.00 1.00 1.00 1.00 1.00
E 0.00 0.00 0.00 0.00 0.00 0.14 0.14 0.29 0.43 0.43 0.43 0.43 0.43 0.57 0.71 0.71 0.86 0.86 1.00 1.00 1.00
F 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.07 0.14 0.14 0.14 0.21 0.21 0.36 0.43 0.43 0.43 0.64 0.79 0.86 0.93
G 0.00 0.00 0.00 0.00 0.25 0.25 0.25 0.25 0.25 0.38 0.63 0.63 0.63 0.88 0.88 0.88 0.88 0.88 0.88 0.88 0.88
H 0.00 0.00 0.00 0.00 0.00 0.20 0.60 0.60 0.60 0.80 0.80 0.80 0.80 0.80 1.00 1.00 1.00 1.00 1.00 1.00 1.00
(numbers show frequency of runs within that percentile, eg 0.38 means 38% of the runs that runner made were within that percentile)
From here, how does one calculate most accurately, what the probability each runner has of coming first, second, third, fourth, fifth, sixth, seventh, eighth?
1st | 2nd | 3rd | 4th | 5th | 6th | 7th | 8th | |
A | ||||||||
B | ||||||||
C | ||||||||
D | ||||||||
E | ||||||||
F | ||||||||
G | ||||||||
H |
Thanks everyone, have been stuck with this problem for ages now, I will not describe what calculations I have tried so far because it may not be the best way at all.
Best Regards,
Joe
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