The Absolute Fundamental Problem With Matchup Charts


#1

Matchup charts tell how in a set of ten rounds, what the average wins would be for each competitor. Ex) 7-3 means that competitor one would win 7 of those ten rounds while competitor two would win 3 of those rounds.

Here’s the problem. It’s very misleading. We have to go into some rather deep statistics to prove it though.

The problem is that real life tournament matches are a best 2 out of 3 rounds per match (you have to win 2 rounds for the match win to count as yours). At least in SF and most fighting games that’s how it works.

So what we should really be looking at is the odds of characters to win 2 out of 3 rounds!

This is how it works: We’ll take a 7-3 matchup and look at the true chances of player two winning the match. We have to look at all possible outcomes.

The first possible outcome is that player two wins both the first and second round. What are the odds of player two winning the first round? The answer is 30%. Okay, so what are the odds that he wins the first round and second round? The answer is 30% times 30% which is 9%.

But this is just one possible outcome. The next possible outcome is that player two loses the first round but wins the next two. What are the odds for this? The answer is he has a 70% chance of losing the first round times a 30% chance of winning the second round times a 30% chance of winning the third round: 70% times 30% time 30% = 6.3%. So he has a 6.3% chance of this outcome occuring.

The final possible outcome is that player two wins the first round, loses the second round, and then wins the third (final) round. The odds follow the same method as used before: 30% times 70% times 30% = 6.3%.

Now is the moment of truth. We find the true odds of player two winning his disadvantageous 7-3 matchup while taking into account that winning a match means winning a best 2 out of 3 rounds. All we have to do is add the seperate chances!

9% + 6.3% + 6.3% = 21.6%.

I hope this is somewhat of an eye opener for people.
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When you see 7-3 matchup, it does not mean player two has a 30% chance of winning the match. They really have a 21.6% chance.
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Please let me know if my math was wrong all you ppl with statistics knowledge!


#2

“Deep statistical knowledge” lol. Really all it comes down to is your definition of what a “win” is; a 7-3 could mean a 70% chance of winning a round, winning a game, or winning a bo3. And even then this is entirely down to gut feelings, so it’s kind of silly to put it to statistics.

Now, what would be interesting is creating a statistical tool set to turn matchup charts into tier lists, such that a good matchup against a high tier character would be worth more than one against a low tier character.


#3

Well in any case it does raise an important question. When we say 7-3 what exactly does it mean? Does it mean odds for winning a single round, or odds for winning a best 2 of 3 rounds in one game? It has to be one or the other.


#4

Some also claim that matchup charts should be changed according to each country, eg USA charts, Japan charts etc rather than accept a common version for all.
Especially for games like KOF where gameplay may vary globally from region to region and in every match you have 5 rounds with different characters.


#5

Honestly, I’ve stopped reading MU-charts as actual numbers, and started interpreting MU-charts as following:

5 - 5: Even matchup. Whoever plays best wins every time.
5.5 - 4.5 - Slight advantage to character A. Nothing that can’t be overcome if you know what you’re doing, however.
6 - 4: Advantage to character A. Noticable at any level of play, but can be overcome by understanding the matchup and playing the player correctly.
7 - 3: Large advantage for character A, with the risk-reward terribly skewed. Not completely unwinnable, but large risks have to be taken to overcome this.
8 - 2: Character A more or less invalidates character B. To win, character B needs to more or less prevent character A from playing. Good luck with that bro.
9 - 1: oh, fuck off


Street Fighter V Balance/Match Up Discussion - SHOW ME YOUR MATCH UPS
#6

I believe the ratios are win-loss out of ten matches and not rounds. What happens in round 1 can greatly affect what happens in round 2 and onward, especially in modern games with meter (as well as other variables such as health, positioning, etc.).

The other thing you’re forgetting is that match-up charts are calculated not just with any specific tournament setting in mind. Rather, it’s for that specific match up in general, regardless of where it’s played, as long as it’s at the highest level of play. Rating match ups out of 10 is just easier for people to understand, because you’re simply saying that a character has a X in 10 chance of winning against this other character in a single match. It’s a nice number that people can easily wrap their heads around considering that we all tend to count using a base 10 system.

Honestly, a better title for this thread would have been “How to Calculate Tournament Match Chances Based on Match Up Chart Values.”


#7

I would like a t-shirt with Anakaris’ portion of the matchup chart. =)


#8

Rather deep statistics? This is basic probability, if you have something to say you don’t need to exaggerate it as some brilliant or earth-shattering discovery. Besides which LoyalSol has already done this stuff years ago, it’s nothing new. The scores are just a gauge for what a MU feels like, little else. We could just as well use “small edge”, “advantage”, “large advantage”, “counterpick”, “hard counterpick”, “oh, fuck off” for all I care (5.5, 6, 6.5, 7, 8, 9+ respectively).


#9

It’s always meant matches, not rounds. I have no idea why you’d assume it means rounds.


#10

Personally, just because the format for matchup charts is based on matches, I never looked at it from a percentage standpoint because that makes no sense to me. Even if you were to look at it as a 7-3 matchup means you have a 70% chance to win, wouldn’t that only make sense for a 10 game set? Not even a first to 10, literally play 10 games and see what happens. Matchup charts also assume that both players are of the same skill level and both characters are being played at the highest possible level, two things that are virtually impossible in real life.

Matchup charts are not a statistic average of how likely you are to win, they are a comparison between relative character strengths and weaknesses. If anything, you shouldn’t see 7-3 as a “70% chance to win”, you should see it as slightly more than twice as likely to win as your opponent, and even that is kinda missing the point of matchup charts. Naeras basically has the right idea, it’s just a relative means to show at how much disadvantage a certain matchup is.