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Questions about Calculating Resistance

Feb 2nd, 2019
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  1. Source: https://assets.pokemon.com//assets/cms2/pdf/play-pokemon/rules/play-pokemon-tournament-operation-procedures-en.pdf
  2.  
  3. First of all, is this explanation accurate:
  4.  
  5. Once a tournament has completed, opponent's win percentage is calculated by doing the following:
  6.  
  7. -If any opponent had a bye, subtract 1 from the total number of rounds for that player for each bye that opponent had. For example, if an opponent went 4-3 in a 7 round tournament with 1 bye, they instead are counted as going 3-3 in a 6-round tournament.
  8. -If any opponent dropped, their total number of rounds is equal to the actual number of rounds that opponent played prior to dropping. For example, if an opponent went 1-3 drop in a 6 round tournament, they instead are counted as going 1-3 in a 4 round tournament.
  9.  
  10. Next, for each opponent, calculate their win percentage by dividing the number of won rounds by the total number of rounds. For example, if in an 8 round tournament some players go 8-0, 6-2, and 3-5, then their win percentages are 100% (8/8), 75% (6/8) and 37.5% (3/8).
  11.  
  12. -If an opponent has a win percentage of less than 25%, make it 25%.
  13. -If an opponent dropped AND their win percentage is greater than 75%, make it 75%.
  14.  
  15. Next, average the win percentage of all opponents; this is the final opponents' win percentage.
  16.  
  17. Questions:
  18. 1. Do players that are DQed count as dropped players for the purposes of resistance? That is, suppose I am 5-1 playing another 5-1 and they are DQed (now I am 6-1). Is their contribution going to be as a 5-1 (83.33%, rounded down to 75%), a 5-2 (71.42%), or something else?
  19. 2. Is the rounding to two decimal places purely for display purposes, or are values really rounded in the end (e.g. is 66.504 the same as 66.503 and would result in opponent's opponent's being applied to break the tie at 66.50)?
  20.  
  21. 3. Are the percentages the result of rounding or flooring? I know the final standings are rounded to two decimal places. Is this actual rounding, or is it a sort of floor function (e.g. 66.503 = 66.506 because the program only considers the 66.50 part).
  22. 4. Is this rounding to two decimal places done throughout the calculations, or does it try to maintain full precision until the very end (e.g. is a 5/2 opponent in a 7-round event counted as 5/7, as 71.43%, or something else).
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  24. From my personal testing for 3 and 4, it appears the answer to 3) is rounding, because in the below example, 63.8 repeating = 63.89. It appears the answer to 4) is that this rounding waits until the end, because 2/3 is not treated as 0.66 or 0.67.
  25.  
  26. Example:
  27. https://twitter.com/OweVGC/status/1091657230464831490
  28. The 2nd Place player had a 3-0, 2-1, and 0-3 in his resistance. The 0-3 is treated as a player with 25% resistance. If you rounded early, you'd have (1 + 0.67 + 0.25) / 3 = 0.64, which is contradictory to the actual opponents' win percentage, 63.89%. This would most plausibly be explained if the calculation was actually (3 + 2 + (3*0.25)) / 3^2, which is 5.75/9 = 63.89%.
  29.  
  30. 5. Is the averaging with respect to byes and drops done in the same way? For example, suppose a player had these opponents in a 6-round tournament:
  31.  
  32. 6-0
  33. 4-2
  34. 4-2
  35. 3-3
  36. 1-5
  37. 2-3 drop.
  38.  
  39. Is this 2-3 player considered to have 40% resistance with respect to the 6-round tournament, or only with respect to the 5 rounds? By that, I mean which of these is correct for calculating the resistance of this player:
  40.  
  41. 6+4+4+3+1+[6*(2/5)] / 6^2 = 20.4/36 = 56.67%
  42. OR
  43. 6+4+4+3+1+[2] / 6^2 - 1 = 20/35 = 57.14%
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