The only possible ways tiers can work is if you go “Assuming this matchup is 6.5 : 3.5…” OR is if you just say “In what would be considered a 6.5:3.5 matchup” (without giving specific ones, but just using the 6.5 : 3.5 matchup itself as a example). If you assume that, then you can just do the math on probability of winning with given sets based off characters alone, disregarding player skill. In a 1 game set, obviously its 65% - 35% chance. There was a thread on this before, but in a 2/3 matchup, the math changes and it becomes something like
(6 ways the matchup can go)
-Winning 2 in a row - 1 way only
W (.65) * W (.65)
42.25%
Winning 2-1, 2 ways this can go
(winning one, losing one, then winning the last, or losing the first and then winning the next two)
W (.65) * L (.35) * W(.65)
x2
29.58%
Losing 2-1 2 ways this can go
(winning one, losing the next two, or losing one, winning one, losing the last)
L (.35) * W (.65) * L (.35)
x2
15.93%
And finally, losing 2 in a row
.35 * .35
L (.35) * L (.35)
12.25%
So if we add those up, 42.25 + 29.58 = 71.8% chance of winning vs the 28.2% chance of losing. So in a 6.5 : 3.5 matchup, the longer the set, the better chance you have of winning if you’re playing the higher tier character.
Joshthefunkdoc did this equation in a thread a while back, but I don’t feel like searching for it. This is about as far as tiers go mathwise tho. It’s just statistics. But as many people said, tiers are somewhat subjective so it’s hard to find a definite value because there’s just way too many variables to even count when it comes to matchups.
You could do a double-pass tierlist where on you first get the tiers based strictly on the sum of all their matchups, then the second time around you weight them according to who has the best matchups against the higher tiers established by doing that. I think you could pretty much do this infinitely to get more and more precise results…
Well, Joo used math for his combos. here is a zip file containing excel sheets with all his frame data. He used all of it for his DVD (Magnetro | Joo’s DVD)
Tho only some of it is in English, the main idea to get from it is that he would find all the possible data (start-up times, recovery etc) for all the moves in the game, stare at it and then come up with a combo based on the findings that he transcribed.
So I guess if you wanna talk about combos and math in fighting games, you can go for that approach. Essentially it’s combining the scientific method, transcribing everything and then “creativity”.
I don’t think you can disregard player skill given that those ratios on tiers tend to be based on the skill of players. At least, not if you want something accurate. Even if you were to disregard player skill as you are suggesting, then the ratio itself is just a made up number with no real merit whatsoever. If I say this matchup is 6.5 : 3.5, and I’m not basing it on the skill of players who played this matchup over a long series of games, then what am I basing it on? I could just as easily make up a ratio and have it be just as valid. Without any actual empiricism, the ratio is useless, at least, if you care about it actually being accurate. So if Sim vs Hawk in vanilla ST was 7:3 Sim (I don’t know the actual ratio but it is heavily in Sim’s favor) and a player’s skill isn’t relevant in determining the probability that Sim would win, would you bet $1000 on Sim winning if an awful Sim player who has no knowledge of the matchup was playing a pro Hawk player from Japan who knew the matchup well? Do you honestly think the Sim player would win 70% of the time?
I did the presentation today and I have a feeling I did pretty well. The teach was the only one to tell me that I had an interesting one and it was never done before in her classes.
Hence why you can’t count on player skill for examples. You have to assume both players are of equal skill and that difference in player skill isn’t a factor that comes up. What you’re doing is assuming that player skill is different, and not equal, hence why it doesn’t matter if it’s 7:3 if the player skill is that different. They have to be assumed to be equal in order for any sort of tiering to matter. You get what I’m saying when I mean “disregard player skill?” I guess I worded it poorly, and rather meant to say “Assume player skill is equal and at the level required for the matchup to be what it is” Obviously with 2 beginners or mid level players, it doesn’t matter much.
Shinjigohan - Yeah, that was his thread. I didn’t remember exactly but it had something to do with the longer the set, the more the difference in matchups begins to show.