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math bork 2nd try

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Date Editor Before After
2/29/2016 7:44:10 PMPLrankAdminSprung before revert after revert
Before After
1 [quote]I wondered if teamstrengths are still proportional to win probabilities that were calculated by inserting this new team elo in the FFA solution. This would show that "playerstrength" is really fundamental. Unfortunately it didn't hold true 1 [quote]I wondered if teamstrengths are still proportional to win probabilities that were calculated by inserting this new team elo in the FFA solution. This would show that "playerstrength" is really fundamental. Unfortunately it didn't hold true
2 (...) 2 (...)
3 FFA solution with team elo from teamstrength: 1: 31.9%, 2: 22.6%, 3: 45.5% 3 FFA solution with team elo from teamstrength: 1: 31.9%, 2: 22.6%, 3: 45.5%
4 proportional to teamstrength: 1: 29.0%, 2: 19.5%, 3: 51.5%[/quote] 4 proportional to teamstrength: 1: 29.0%, 2: 19.5%, 3: 51.5%[/quote]
5 Here's a reasoning which is contradictory to the above but I'm not sure where the error is: 5 Here's a reasoning which is contradictory to the above but I'm not sure where the error is:
6 1) player strength can be summed linearly. 6 1) player strength can be summed linearly.
7 2) if two teams cooperate perfectly, they might as well be treated as one team with summed strength (this is how individual players are summed in a team). 7 2) if two teams cooperate perfectly, they might as well be treated as one team with summed strength (this is how individual players are summed in a team).
8 3) under the two-team system, team 3 defeats a combined 1+2 team with 51. 5% chance, since the win chance is proportional to strength. 8 3) under the two-team system, team 3 defeats a combined 1+2 team with 51. 5% chance, since with two teams the win chance is proportional to strength.
9 4) if teams 1 and 2 don't cooperate perfectly, team 3's win chance gets higher, ergo the 51.5% is a minimum (with perfect cooperation between 1 and 2) 9 4) if teams 1 and 2 don't cooperate perfectly, team 3's win chance gets higher, ergo the 51.5% is a minimum (with perfect cooperation between 1 and 2)
10 5) the Elo solution gives less than 51.5%, so Elo is wrong. 10 5) the Elo solution gives less than 51.5%, so Elo is wrong.
11 \n 11 \n
12 \n 12 \n