Alright, I'm no math major but I do have some college-level mathematical background so maybe I can be of some use here.
I noticed that, a lot of times, some characters are Top Tier because they are just plain powerful. And then other characters are Top Tier or close to Top Tier NOT because they are particularly powerful, BUT because they counter the characters that ARE Top Tier.
To me, this brings to mind the Yomi Layer concept as defined by David Sirlin:
http://www.sirlin.net/articles/yomi-layer-3-knowing-the-mind-of-the-opponent.html
Let's look at MK and Snake. MK is good in a general sense no matter what your opponent picks. Since this choice doesn't require that you know what your opponent will pick, you could call this a Yomi Layer 0 pick.
So let's say your opponent has picked MK and you get to CP. Well, Snake is a good matchup against MK, so you decide to pick Snake. This is a Yomi Layer 1 pick.
As far as I know, there's no mindgames involved in picking characters. I'm not implying that there is. But mind-reading isn't the only facet of the Yomi Layer concept. Another facet of the Yomi Layer concept is the idea of moves and counter moves, and it's that facet that I am deciding to focus on.
However, because of the uniqueness of this situation, we only REALLY need to focus on two layers: Yomi Layer 0 and Yomi Layer 1. (After all, the MK player isn't going to be able to change his character after his opponent CPs Snake. There's no concept of Yomi Layer 2 here.)
Here's what I suggest: Make 2 different tier lists. One tier list will be based upon Yomi Layer 0. This will be the most basic form of the tier list assuming that players will just pick characters at random (that is, characters that they "like") with no regard to what their opponent is going to pick.
*Note: from this point on my values are totally made up*
(Yomi Layer 0 Tier List)
For each character:
-Determine the MU ratios for each MU relevant to this character. For example, if the current character is MK, and he has a 99:1 chance to win vs. Ganondorf, then we say MK has a 0.99 win ratio. However you do this is up to you. This process is very algorithmic and as a result, if you put garbage in you'll get garbage out. But assuming you have accurate values here, this process should hopefully work fine.
-Take the average of the MU win ratios for each MU relevant to that character. We'll call this number the character's Average Success Rate (ASR). So if MK, on average, wins about 99% of the time, then his ASR be 0.99. It's important that this number be between 0 and 1 (inclusive), because we're going to be using this as a weight later.
Once you've taken the averages of all the MUs, arrange them in order so that the characters with the highest averages are at the top and characters with lower averages are at the bottom.
That part was pretty obvious to some, maybe all of you. But the next part might not be so obvious.
The next step is to evaluate each character as a potential CP. This assumes that you already know what character your opponent is going to use and are freely able to pick a proper counter.
(Yomi Layer 1 Tier List)
For each character:
-Use the same MU ratios as before. Only this time, multiply that ratio by the opponent's ASR. So if MK vs. Ganondorf is still 99:1, but Ganondorf's ASR is .01, then MK gets .99 * .01 = .0099 for his Gandondorf MU. In short, pwning a weak character is useless.
-Sum up the weighted ratios and divide it by the total number of characters to get the Weighted ASR, or WASR.
Now hold the WASR in your hand and go "PEW PEW PEW"
One you have the calculated the WASRs for all characters, arrange them to make the YL1 Tier List.
This way the tier lists might be a bit more insightful, since the tier list somewhat changes based upon the given situation.
That might be too long and complicated, so here's an example of how this might work:
Consider a fighting game with only 4 characters: Mary, Larry, Zeno, and Rick. Mary, Larry, and Zeno are all intended to be "balanced" characters, but we all know already that they aren't. Rick is totally a joke character.
Assume that the following chart is the accurate measurement of their MU ratios.
\ M L Z R
M .5 .25 .75 1
L .75 .5 .60 1
Z .25 .40 .5 1
R 0 0 0 .5
That is to say, Mary has a 50% chance to beat Mary, a 25% chance to beat Larry, a 75% chance to beat Zeno and a 100% chance to beat Rick.
And so on.
So for the YL0 Tier List, Mary's ratio total would = .5 + .25 + .75 + 1 = 2.50.
Mary's ASR = 2.5 / 4 = 0.625.
Using this process for each character we get the following tier list:
Top Tier
Larry (0.7125)
Middle Tier
Mary (0.625)
Low Tier
Zeno (0.5375)
Joke tier
Rick (0.125)
Now to use this information to calculate the WASRs for each character.
For example:
Mary's WASR = (.5*.625 + .25*.7125 + .75*.5375 + 1*.125 ) / 4 = 1.01875
After calculating the WASRs for all characters we get the following tier list:
Top Tier
Larry (~0.318125)
Middle Tier
Mary (~0.254688)
Low Tier
Zeno (~0.20875)
Joke Tier
Rick (~0.015625)
Notice that, the way the system works, you don't get much for winning a lot against a weak character that no one will ever play. You could essentially remove Rick from this tier list and still have the same ranks.
I could go on but I think I'll stop here.
Edit: Actually, I did some more experiments with this and discovered something very interesting about this system. First off, I changed Rick from the Joke Character to the God Character, making him win against MOST characters 100% of the time. Then I added a new character named L.O.L. and had him do very poorly against almost everyone except for Rick, which he effectively counters. The end result is this:
Layer 1 Tier list:
God Tier
Rick (~0.73) (Because he pwns everyone except for L.O.L.)
L.O.L. (~0.61) (Even though he sucks vs. just about everyone, he counters God-Rick, so he's worth learning how to play as long as Rick isn't banned. If Rick were taken out of consideration, LOL would end up at the bottom tier with no real use.)
Top Tier
Larry (~0.47)
Middle Tier
Marry (~0.42)
Bottom Tier
Zeno (~0.38)
I'm willing to say that this is pretty much working as intended. Also, note that since I'm only using 5 characters, my graph is a bit more sparse than it would be for, say, Brawl. With Brawl's 35+ characters to consider, its tier list should look a lot better.
