Winning a matchup 60-40, what does it even mean?

Alfred - March 27, 2018

"That's definitely a 60-40 matchup man, it's like impossible to do anything"

"Nah man, I swear it's no more than 55-45".

What does this mean? Do the players have a common understanding of the numbers meaning? Is there even a mathematical definition behind these matchup ratios? More importantly, is this definition reasonable and does it allow us to accurately compare opinions? Or should we maybe stop using these numerical ratios completely?


The percentage definition

Surprisingly some players are not even aware of the matchup ratio definition, but will still go into war to discuss their opinion on a specific ratio. More experienced players have probably come across some kind of definition similar to this:

"In a 60-40 matchup with two players of equal skill you would win 60 % of the time".

In generalized form this definition should solve the whole problem. We now have a common understanding of matchup ratios with a mathematical foundation and can use it to accurately predict and compare ratios, right? Or maybe not?


Problems with the percentage definition

1) People are not using it.

When you come to a conclusion that a matchup ratio is 55-45, how did you conclude that? Did you actually imagine two players of equal skill and accurately estimated one players win percentage down to the nearest 5 % as the number of games approach inifitely? 

Let's take a look at Dabuz's matchup chart for a second. Rosalina vs Jigglypuff is 55-45, indicating a 55 % chance of winning as Rosalina between two players of equal skill. Let's say a top player close to Dabuz level (say Nairo) picked up Jigglypuff and played her from release. If they were to play 100 games today, would Dabuz be predicted to lose 45 of them to the Jigglypuff?

I don't have the answer, but this is something I see pointed out regularly on matchup charts: if they were to correctly use the percentage definition, the ratios might be alot more liberal. More 90-10 matchups, more 70-30 matchups, less 55-45 matchups.

A more reasonable explanation is that people don't actually use the definition. They simple use 55-45 as a reference for what they perceive as the slightest form of advantage, and then add 5 % for every step of advantage they feel is distinguishable. And then again, we have the problem with no common foundation. How can we know that my perception of 55-45 is the same as yours?


2) It's too hard to accurately use the definition.

There are lots of research showing how human act irrational and have bad intuition when it comes to probability and utility theory (e.g. Allais paradox). Is it really reasonable to expect us to estimate the win percentage down to the nearest 5 percentage point?

3) What happens if the players are not of equal skill?

Anyone studying math related studies would notice that we need one more value for an exhaustive definition which enables us to compare any two players. We need one value to say the ratio of two players of equal skill, and then we need one value for telling how much this ratio would change with varying skill levels.

And what does equal skill mean? That the players perform the same result-wise? 

Let's go back to the Rosalina - Jigglypuff matchup. Obviously there are no Jigglypuff's with the same results as Dabuz, so what does he do? Should he imagine a hypothetical Jigglypuff which gets top 8 regularly at majors and then estimate how he would do against it? Or should he try to imagine a player with the same prerequisites and qualities as Dabuz, playing the game for the same amount of hours as himself but maining Jigglypuff from the start?


Putting a numerical figure on something that shouldn't have it

Matchup ratios are still useful, we just need to acknowledge the limitations. When Dabuz says Rosalina wins 60-40 against Luigi, but only 55-45 against Jigglypuff, we still get useful information. We know that he thinks Luigi is an easier matchup than Jigglypuff, we just don't know exactly by how much.

The point I'm getting to is that matchup ratios are by nature a vague and inaccurate concept. Numbers and units on the other hand, should have a very precise meaning in any context they are being used. Saying that a matchup is "60-40" or "+2" gives the impression of a stadardized, exhaustive and complete syntax where the meaning of ratios are set in stone. But they are not. My perception of 55-45 is probably different from yours.

My proposal is to stop using numbers for describing matchup ratios. Using labels like "slight advantage", "big advantage" etc. is, in my opinion, much better since it doesn't falsely put exact values on vague concepts. Everyone knows that what one player considers "slight advantage", might be a bit different from others. Matchup ratios are by nature ambiguous, and we shouldn't put exact values on them which might indicate otherwise.



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