I have an idea for computing the tier list using a complex analysis of matchups in a given metagame and I'm curious if people would be interested in this. What I'd like to do with this is take an initially perfectly diverse metagame (equal number of players playing each character), and then evaluate the respective power levels of every character using the following formula:
P = S(M * N)/T
P: Power
S: Sum of all characters
M: Matchup vs. a given character (Taken from Phanna chart)
N: Number of players playing a given character
T: Total number of Players
Then I plan to have some form of formula to determine how players will change their character decisions based on the relative powers of each character. I was thinking of something simple, along the lines of:
Version 1.0
N = T * (P / S)
N: Number of players playing the character
T: Total number of players
P: Relative power of the character
S: Sum of all character's powers
Version 1.1
N = T * (wP / wS)
N: Number of players playing the character
T: Total number of players
wP: Weighted power of the character (wP = e ^ P)
wS: Sum of the weighted powers of all chatacter's (sigma(wP))
Repeating this calculation for a large number of iterations should result in giving a fairly accurate assesment of the optimal power level and ranking of each character. What I'd like to know is how high the interest level for this sort of thing is and if anyone would like to see something done differently.
My main motivation in this sort of endevor would be to provide the comunity with some sort of concrete tier list and ranking of characters based on a purely mathematical approach so that when arguments arise, there is some reference. Of course it wouldn't be perfect, as it would be assuming correctness of the Phanna chart, as well as ignoring the fact that not all players select their character based on tournament viability, but I think it might go a long way to settling tier list disputes.
Stable Tiers Version 1.1
Falco Players: 17.96% Power Level: 5.80
Sheik Players: 15.68% Power Level: 5.66
Marth Players: 12.63% Power Level: 5.44
Fox Players: 12.16% Power Level: 5.41
Peach Players: 8.87% Power Level: 5.09
Ice Climbers Players: 5.98% Power Level: 4.70
Samus Players: 5.88% Power Level: 4.68
Jigglypuff Players: 4.49% Power Level: 4.41
Ganon Players: 2.97% Power Level: 4.00
C. Falcon Players: 2.60% Power Level: 3.86
Doc Players: 2.25% Power Level: 3.72
Luigi Players: 1.57% Power Level: 3.36
Mario Players: 1.20% Power Level: 3.09
Y. Link Players: 0.95% Power Level: 2.86
Link Players: 0.76% Power Level: 2.64
DK Players: 0.61% Power Level: 2.41
Roy Players: 0.50% Power Level: 2.22
Ness Players: 0.49% Power Level: 2.20
Zelda Players: 0.48% Power Level: 2.17
Pikachu Players: 0.45% Power Level: 2.11
Kirby Players: 0.38% Power Level: 1.93
Yoshi Players: 0.37% Power Level: 1.90
Mr.G&W Players: 0.28% Power Level: 1.62
Pichu Players: 0.20% Power Level: 1.29
Mewtwo Players: 0.18% Power Level: 1.20
Bowser Players: 0.11% Power Level: 0.70
Also, for reference here is the All-Characters Matchup chart, created by Phanna (Thanks a bunch to Phanna for permission to use)
I think some slight changes may need to be made, but I'm going to go ahead and use the un-altered chart for the first run through the program. If something upsets you on this chart and you want it changed permanantly, here's the link to Phanna's Thread: http://smashboards.com/showthread.php?t=92025
P = S(M * N)/T
P: Power
S: Sum of all characters
M: Matchup vs. a given character (Taken from Phanna chart)
N: Number of players playing a given character
T: Total number of Players
Then I plan to have some form of formula to determine how players will change their character decisions based on the relative powers of each character. I was thinking of something simple, along the lines of:
Version 1.0
N = T * (P / S)
N: Number of players playing the character
T: Total number of players
P: Relative power of the character
S: Sum of all character's powers
Version 1.1
N = T * (wP / wS)
N: Number of players playing the character
T: Total number of players
wP: Weighted power of the character (wP = e ^ P)
wS: Sum of the weighted powers of all chatacter's (sigma(wP))
Repeating this calculation for a large number of iterations should result in giving a fairly accurate assesment of the optimal power level and ranking of each character. What I'd like to know is how high the interest level for this sort of thing is and if anyone would like to see something done differently.
My main motivation in this sort of endevor would be to provide the comunity with some sort of concrete tier list and ranking of characters based on a purely mathematical approach so that when arguments arise, there is some reference. Of course it wouldn't be perfect, as it would be assuming correctness of the Phanna chart, as well as ignoring the fact that not all players select their character based on tournament viability, but I think it might go a long way to settling tier list disputes.
Stable Tiers Version 1.1
Falco Players: 17.96% Power Level: 5.80
Sheik Players: 15.68% Power Level: 5.66
Marth Players: 12.63% Power Level: 5.44
Fox Players: 12.16% Power Level: 5.41
Peach Players: 8.87% Power Level: 5.09
Ice Climbers Players: 5.98% Power Level: 4.70
Samus Players: 5.88% Power Level: 4.68
Jigglypuff Players: 4.49% Power Level: 4.41
Ganon Players: 2.97% Power Level: 4.00
C. Falcon Players: 2.60% Power Level: 3.86
Doc Players: 2.25% Power Level: 3.72
Luigi Players: 1.57% Power Level: 3.36
Mario Players: 1.20% Power Level: 3.09
Y. Link Players: 0.95% Power Level: 2.86
Link Players: 0.76% Power Level: 2.64
DK Players: 0.61% Power Level: 2.41
Roy Players: 0.50% Power Level: 2.22
Ness Players: 0.49% Power Level: 2.20
Zelda Players: 0.48% Power Level: 2.17
Pikachu Players: 0.45% Power Level: 2.11
Kirby Players: 0.38% Power Level: 1.93
Yoshi Players: 0.37% Power Level: 1.90
Mr.G&W Players: 0.28% Power Level: 1.62
Pichu Players: 0.20% Power Level: 1.29
Mewtwo Players: 0.18% Power Level: 1.20
Bowser Players: 0.11% Power Level: 0.70
Also, for reference here is the All-Characters Matchup chart, created by Phanna (Thanks a bunch to Phanna for permission to use)
I think some slight changes may need to be made, but I'm going to go ahead and use the un-altered chart for the first run through the program. If something upsets you on this chart and you want it changed permanantly, here's the link to Phanna's Thread: http://smashboards.com/showthread.php?t=92025