First I decided to total up the contestants' scores from the speed climbing and bouldering as they had already happened and could no longer be changed:
Lopez - 7
Ondra - 24
Coleman - 6
Narasaki - 6
Schubert - 35
M. Mawem - 6
Duffy - 20
B. Mawem - 64
As Bassa Mawem was ingered and unable to compete, he must come last in all of the climbs, including in the lead climbing, giving him a score of 8×8×8=512.
Next I created a table showing the scores of the contestants depending on where Schubert came
1st. 2nd. 3rd. 4th. 5th. 6th. 7th.
Lopez. 28. 28. 28. 21. 21. 21. 21.
Ondra. 48. 24. 24. 24. 24. 24. 24.
Coleman. 30. 30. 30. 30. 24. 24. 24.
Nurasaki. 36. 36. 36. 36. 36. 30. 30.
Schubert. 35. 70. 105. 140. 175. 210. 245.
M.Mawem. 42. 42. 42. 42. 42. 42. 36.
Duffy. 60. 60. 40. 40. 40. 40. 40.
B.Mawem. 512. 512. 512. 512. 512. 512. 512
Things I noticed:
Lopez is garenteed a medal, and will get gold unless Schubert comes 2nd or third.
Ondra gets a medal unless Schubert comes first, and gets gold if Schubert comes 2nd or third, and gets silver if Schubert comes worse than third.
Coleman is garenteed a medal, but get gold.
Narasaki gets a bronze medal if Schubert gets 5th or worse.
Schubert can only get a medal if he comes first: even at this point he only gets bronze.
M.Mawem, Duffy and B.Mawem can all never get medals.
Only Lopez or Ondra can come first.
My scoring methord(s)
1. Add all numbers together and then times by the smallest. The winner is the one with the smallest overall score.
1st. 2nd. 3rd. 4th. 5th. 6th. 7th.
Lopez. 12. 12. 12. 11. 11. 11. 11.
Ondra. 24. 11. 11. 11. 11. 11. 11.
Coleman. 12. 12. 12. 12. 11. 11. 11.
Nurasaki. 22. 22. 22. 22. 22. 20. 20.
Schubert. 13. 28. 45. 64. 85. 90. 95.
M.Mawem. 24. 24. 24. 24. 24. 24. 22.
Duffy. 36. 36. 22. 22. 22. 22. 22.
B.Mawem. 192. 192. 192. 192. 192. 192. 192
Evaluation: the results are similar to the multiplication method, but now Duffy and M.Mawem also have chances to get a medal, and Coleman also could get gold.
A disadvantage of this method is that there seem to be a lot of similar scores, which would result in either silver and/or bronze medals not being awarded or using qualifying rounds to determine the winner. Additionally, for better or for worse, in this method getting first is extremely good for keeping the score low, as in this case the score is just the sum of the numbers.
A benefit of this method is that if someone was worse at one of these events but really good at the others they would still have a chance at a medal (eg. They got 7, 2, 1 and their score would be 10.)
2. Sum of the squares of their scores
1st. 2nd. 3rd. 4th. 5th. 6th. 7th.
Lopez. 66. 66. 66. 59. 59. 59. 59.
Ondra. 56. 53. 53. 53. 53. 53. 53.
Coleman. 62. 62. 62. 62. 53. 53. 53.
Nurasaki. 49. 49. 49. 49. 49. 38. 38.
Schubert. 75. 78. 83. 90. 99. 110. 123.
M.Mawem. 62. 62. 62. 62. 62. 62. 49.
Duffy. 50. 50. 45. 45. 45. 45. 45.
B.Mawem. 192. 192. 192. 192. 192. 192. 192.
I wanted to see how this would change if I added the climber's highest score:
1st. 2nd. 3rd. 4th. 5th. 6th. 7th.
Lopez. 73. 73. 73. 66. 66. 66. 66.
Ondra. 62. 59. 59. 59. 59. 59. 59.
Coleman. 68. 68. 68. 68. 59. 59. 59.
Nurasaki. 55. 55. 55. 55. 55. 43. 43.
Schubert. 82. 85. 90. 97. 106. 117. 130.
M.Mawem. 69. 69. 69. 69. 69. 69. 55.
Duffy. 55. 55. 50. 50. 50. 50. 50.
B.Mawem. 200. 200. 200. 200. 200. 200. 200.
EVALUATION:
Adding the highest score did not make much difference, there only significant things I noticed are that Ondra can now get silver and that Duffy will be awarded gold if Schubert gets first or second. All the changes only happen if Schubert gets first or second.
This scoring system heavily weighs worse scores. A two and a three is about equivalent to an one and a four. A one and a seven is about equivalent to a four and a six or exactly equal to two fives.
Evaluation of the actual method used at the 2020 Olympics:
Benefits:
Do not have to be good at everything; a 1 in any of the climbs means the overall score is the product of the other two.
Works well with the fact none of the climbers are really really good at all three, and that they focus on different climbing skills. -> also helpful for the speed climbers.
Disadvantages:
It is nearly impossible to get gold without getting first in at least one climb (at least shown with by scores from 2020).
2 and 3 is valued the same as 1 and 6
To account for the speed climbers, the judges would have wanted to have a scoring system where getting one 'bad' score would not limit a climber from getting a medal, as long as they did well in the other two. For example not weighting the lower scores so much that it would be impossible to get a medal if a climber got 7 or 8 in one of the climbs.