# The Math of Fighting Games

#1

Hello all. I was deciding to write a paper and do a presentation on the math involved in fighting games. I was wondering if I could give some advice here on structure, games, and topics to discuss.
As of now, I believe I should be covering the following topics:
Frame Data
Damage Output
Damage Scaling
Tiers
Character Health
Combos

I would like to give you all my thanks in advance.

#2

At a glance, most of the math involved fighting games is just basic algebra with a bit of geometry, calculus, and discrete mathematics to handle stuff like collision, hitboxes, and trajectories. TBH, there is likely more math going on in the visual department of a game like SF4 than there is with the actual fighting game mechanics.
What level and type of course are you planning to give this presentation to?

#3

how about something on game theory?

#4

This is for a Survey of Mathematics class. She just told us to do a presentation on any subject related to math.

#5

What is mathematical about the tiers? I’d say thats one of the least mathematical things you could choose.

#6

Velocities and accelerations. For example, for every character’s jump, there will be an initial X and Y velocity and a Y acceleration (gravity) that will determine the arc.

#7

You know, the neverending discussion of weighting the matchups against the most and least played characters. There’s some statistics you can do and it and that alone could be worth the paper.

#8

Yeah but the numbers people come up with for matchup charts have no statistical base. It’s all estimates, partially based on non quantitative concepts like “options” and “adaptability.”

If there was something concrete or scientific about tiering, it wouldn’t be one of the most constantly argued topics in fighting games. You certainly don’t see people arguing that much about whether or not Honda does a lot of damage.

#9

I’m pretty interested in knowing how SF2 ST does the math for the damage output seeing how some moves end up doing more damage than normal >_>;

Using math in Tiers is…well I just think it’ll require a lot of probabilities and advanced algebra and such @_@

#10

You could write up a section on statistics, like tournament player’s stats. You could write a paragraph on tonamento.com.

#11

Pretty sure the moves are just given a damage range and the final damage is picked at random within that. Same goes for charge time, move leniency and stun value.

ST is hella random sometimes

#12

QFT. One could probably write a book about how the tiering arguments illustrate innumeracy.

#13

There is a right way and a wrong way to do this kind of topic. I don’t know what you plan on doing with the things that you have mentioned above, but as it stands right now, this is not sufficient. In fact, based off of what you have mentioned, it naturally begs the question: Where’s the math? You just list elements of fighting games. While the damage scaling probably uses a mathematical formula, so what? So does taxation. You would actually have to find the formula which would mean actually looking at the code since its not public knowledge.

I can see a couple of ways of applying mathematical analysis towards these things (eg using game theory, probability, and statistics), but I’m going to guess that you do not have the mathematical tools to do such an analysis. Besides, doing these kinds of analyses is well beyond the scope of a survey of mathematics class and the payoff of getting a decent grade on your paper would not be worth all the time and effort to actually undertake such an analysis. Therefore, since you are asking to bite off more than you could chew, you should pick another topic, that is, if you want a decent grade.

#14

you can look at some of the “all about” books.

I think the damage equation is here (pure guess though as I can’ translate the kanji) on page 184.

I know the life points is 200, and you need to acque more than 201 points of damage to KO the opponent.

and since the makers of SFEX were the same as the original SF2 design team the equation for the damage is probably very similar.

Bare in mind the original SFEX1 game had random damage like ST did, but it did away with the randomness in EX2 and onward. Hope that helps.

on page 185 there appears to be the variables for the equations
like what the damage is per damage settings in options.
defensive rating for characters
how much damage scaling takes place dependant on how much health is left on the opponents lifebar
what looks like the damage scaling per hit of a combo etc…

http://homepage3.nifty.com/gore/stex2p/damage.html
has the equation for EX2P which did away with the random number affecting the damage.

#15

That stuff is kind of in Japanese. Does anyone know how damage scaling works in SSF4 or are there any match videos that demonstrate the mathematical aspects of the game thoroughly?

I was planning on using a tier and a match video to show the likely hood that this character has to beat this character.

#16

why do dudes always wanna do a presentation on video games

#17

Tier lists alone would be useless because that probability would be contingent on the player using the character, which you’re going to have a hard time quantifying, let alone getting any sort of reliable data. Further, different players would have different probabilities of winning. Finally, you would also have to consider all 1225 possible matchups, along with how each individual top player would do against each other given that particular matchup. Your characterization of all this is overly simplistic and does not take these conditional probabilities in mind and is therefore an inaccurate one.

Because they are looking for an easy grade.

#18

Can’t speak for everyone. For me it’s because that’s my passion.

Well, I was going to ignore that piece of info. Well, I was lying. I wasn’t going to ignore it entirely, I was planning on using it without that fact, but I would mention it.

I don’t see why I would need all 1225 matchups? I’m only going to use one example for that department since I’m going to cover other subjects as well. From what I see around here and from what I’ve been hearing from other people is that other characters are above others in tiers because they have a greater math. Rose’s frame data on her normals are better than Viper’s. Such and such character has low health. Such and such character has good range and a high damage output. Things of that nature.

#19

Risk/Reward is the only math I ever needed.

#20

The fact that you don’t see why you would need all 1225 matchups is a major problem…

A “greater math?” What does that even mean? This honestly sounds like something that you haven’t put much thought into.