Metagame Balance For eSports & Fighting Games

all right come on then great okay thank you guys so much for coming my name is Alex Jaffe you can follow me on twitter at blankety I'm a data scientist a designer and a programmer at spry Fox and today I'm gonna be talking about meta game balance and it's gonna be it's gonna be sort of a deep dive into this one really really focused aspect of game balance it's kind of like the twenty finit 25-minute lightning talk for some 800 minute Ring cycle talk that I'll give in my bathtub or something and I'm really gonna be developing one big idea this whole time so sort of hold tight and listen up this work alright oh it goes that way okay so in the fall of 2012 I worked on this game PlayStation all-stars battle royale it's a four player icon brawler with all the Sony characters and it was my job to sort of take all the data that was coming in from players playing the game and help the designers balance it so figure out where the game could be more

interesting or deep or more fair or you know just kind of more fun for players look at what they're doing and by the way the game is actually really great and a pretty unique despite its passing resemblance the other four player icon brawler shrek super slam so um you know yes we wanted to understand a lot about the game but one of the things that we cared the most about was it doesn't work I have to point it probably okay I'm using my keyboard there we go what I think secured the most about was character balance so this is here I'm not talking about how the game feels to play how players play the game it's more just I have a character that I like I'm coming to this game and I want to be able to play this character and win right I want to be able to feel like this character is not over it's not underpowered or that some other character isn't overpowered it's a it's a really important concept it's almost like players need to be able to play the meta game in a way that feels good it's not the only thing that matters but I think anyone who's worked on eSports knows that this kind of concern is pretty paramount whether you're worrying about classes in tf2 or you know loadout

profiles and Cod or races and Starcraft or sort of team dynamics and League of Legends this is an issue that you have to wrestle with now for most of this talk I'll be talking about fighting games because they kind of actually have one of the simplest meta games out there but I just want you to think throughout this whole thing about how the stuff I'm going to talk about is still relevant to these other genres of games with some modifications so we care about character strength but how do we evaluate it and what are we even talking about when we say a character is overpowered this is kind of one of the central questions I'm wrestling with there are a lot of different ways we talk about character strength and I'll focus on two right now one is win rate that is how often does Kratos win against in an average game okay and you can if you have data from the game you can plot it you can look at it you can say okay these characters look a little overpowered these characters look a little underpowered or if you're feeling really masochistic you can listen to players and players will tell you something completely unlike anything you've actually seen the data and it's totally perplexing right this is a tier list from IGN from shortly after the game came out and you know it

says that these two characters Kratos and Ryden are just completely overpowered and dominating the game in contrast if we look at their win rates sort of doesn't look like it as much correlation there at all right one of them is sort of middle the others middle high so while we work on this game you know I think I was really confused by this discrepancy and it's really tempting to say well the players don't know what they're talking about or something right they're not great players or even if they are they only care about the guys with the big swords or something like that and yet you know we still do take their views into account even when we say something like that when we patch the game we tried to address wind rates as well as the characters that players perceived as unbalanced and so okay one of the things that I realized was happening here one of the properties that these characters that these characters had who players really thought were overpowered was play frequency was very very high this clicker okay that is crayons and writing we're by far the most played characters in the game so okay this maybe starts to point to what's going on right the

players are just facing these opponents over and over again it's like it's no wonder it's frustrating and we have to think about player experience that's what we're doing right we're trying to create a good player experience so this suggests a totally different way to think about game balance maybe we could just look at play frequency as our sort of canonical truth of what it means for a character or an asymmetric option in general to be unbalanced and maybe we just nerf the you know most plate options I mean there are several reasons why that's not a good idea but I still think there's some fundamental nugget of truth to why this is good first of all let's say we restrict to expert players so we just look at the play frequency for the best players in the game okay then okay this isn't just gonna be people like big swords these players are playing to win right they're picking their characters in a way that is going to let them get to the top of the rankings right so okay all of the characters who they're playing frequently are going to be winners so then the question is okay is that enough can we just look at play frequency and that's our that's our you know source of truth on on what is what is too much what needs to be addressed in the game

but there is another problem and there's the instability of play rates here's some data from the game shortly after our first patch so what these are are play rates for different characters on the second week after that patch and the fifth week after that patch okay and what you see is they are all over the place right if these players are playing to win right and these are indeed high skilled players why are they changing so much why is Kratos almost doubling in popularity over the course of a few weeks your first guess should be that okay the patch came out players have figured out something new about the game right so now they are they're realizing Kratos is more powerful they've gotten better technique and they are winning with him some more players play him but here are the wind rates in the same time period this graph is extremely okay so they're essentially not changing at all these characters are staying fixed in effectiveness and yet players are adopting them and leaving them behind for seemingly no good reason okay so if play rates are so unstable first of all why okay well I said players are playing to win but there are multiple

viable options right as we can see like there are actually a lot of good characters in this game at the at the top level it's relatively balanced and unfortunately players have free will and so we can't just you know know exactly what they're gonna do there are a lot of options we would love it if we could just predict a future like okay this game comes out it's been out for a couple days we sort of get all the data on the left side now we want to know where the game is heading like it's some character just going to completely dominate the meta game so it'd be great if we could predict the right side of this graph right know right away okay like kratos is just gonna start dominating we want to pass him or something or maybe even predict it solely from playtesting right got some data ourselves never release the game and put it out in a state where this doesn't happen but of course as I said the problem is players have freewill they have choice there are all these different states Drake might go to right he might you know play you're gonna decide to play him less they might decide to play him a ton it's pretty hard to just predict the future when you know we're dealing with human being so I have a more meager goal and that's to predict all the futures so that is

basically to know what if we could say just something about the range of possible values for how often Drake will be played kind of understand this whole span of possible possible meta games that we might up and end up in right and also know you know that within a few weeks say once players have learned that kratos is effective and they've adopted him that say all of the meta games that we might end up in involve credits being played way too much so much that's gonna frustrate players who have to play em frustrate players who face him and also frustrate spectators if we're dealing with these sports well this this would be great this would be a great future I'm sorry a great reality because we can actually you know balance our games before players have kind of unbalanced them for us and I this is actually what I'm proposing I call it meta game bounds it's a new way to think about asymmetric strengths you can sort of do this basically produce these bounds on the most that sort of the highest frequency you might expect to see a character be played in reasonable metagame full of expert players and the lowest frequency you

know won't be perfect but I think by the end you'll be convinced that you know there's actually a way to do this okay so I'm gonna talk about the meta game as I view it it's a very very kind of focused specific view of the meta game talk about how that helps us enable this construction these these meta game bounds and then finally how we can use those bounds to find imbalances in the game alright so after I finished working on playstation allstars III did I finished my PhD at the University of Washington with my dissertation was on game balancing and near the very very end of it I was looking at this matchup charts for Street Fighter 4 and it's something struck me about it so here's how these charts work you pick a character on the row like sea viper you pick a character column like uh who was that Akuma and and then the six there in the middle uh means there's a six in ten chance of that of a long beating Akuma in a fair match of high skill game okay another thing about these charts is they

are totally made-up but they're still pretty good so literally a bunch of people got in a room who you know pretty sieve themselves to be expert players and they decided what these numbers should be so you should think okay I shouldn't believe these at all but I argue they're still really useful first of all they're well-defined unlike cheerless str8 here these don't actually mean anything everybody has a different definition for what this means whereas a 60% win rate is very very well defined it's something we can we can discuss and we can figure out what the right number is we can even you know look at actual data and figure out some approximation of the truth here on top of that it's unaffected by play frequency so remember part of the problem we're trying to wrestle with is we can't just look at the current metagame because it's sort of it's all over the place it moves with time naturally a sort of converges into these different equilibrium and moves around and and what we need to know is the whole possible space of this so we need some source of data that is unaffected by this play frequency and indeed this is you know if a lot more players start playing see Viper that doesn't mean her win rate against Akuma is going to substantially change it might change a little because players will learn more about how to play her right but that

that change will be much slower developing new techniques for a game happens slowly compared to moves movements in the meta game which as I showed you happen very very quickly so even knowing the matchup chart right now is tremely useful so my goal sort of is to is to take these matchup charts these these sort of impenetrable walls of numbers and and to find their secrets like the protagonist in PI who has this 216 digit string of numbers who's trying to find the secrets of God through it it's kind of like that it's like are there some fundamental secrets of the game that we can find in these matchup charts right do they define like how the meta game might work in all possible universes and and I think they do some people who have tried to analyze them before I in fact everyone who makes these match up charts produces these averages these sorry these sums on the right side it's just the sum of all the numbers and so they say okay seth has the highest sum of numbers he's maybe the strongest character in the game nobody actually believes these because it's totally overly simplistic it says basically basically it's how often - Seth win against an average opponent but you never face an average opponent you

face other strong opponents who are themselves defined by their ability to face strong opponents it's the cyclical thing that's very very hard for a human to reason about but it is possible for a computer to reason about and that is where I'm going to do that we need to treat this matchup chart itself as kind of the source of information the source of definition for some game basically metagame the game not that meta game the game Erik Simmons benefit convene but but a different meta game the game literally the game that is playing the meta game of any sort of competitive game and what if we take it seriously as a game worthy of analysis in itself all right of its own and you know and actually you know analyze it well I call it the selection game just to be really clear it needs a name and it's super simple we're coming to play game of Street Fighter we sit down we're gonna pick characters to play we do it simultaneously and in secret then there's some chance that I win based on the character I chose and I'm not even going to play the game I'm just selecting my character just like you and then robots who play just like us will play for us and then you know if I play

Zangief or you play guile I win 60% of the time but it's just randomness so my goal now is just to pick the right characters will treat ties as 50% win chance for simplicity okay what kind of game is this well it's basically rock-paper-scissors which makes it sound super boring but there's still something interesting here it's a generalization of rock-paper-scissors write this like Princess Bride poisoning game we're like you know trying to figure I'm trying to think about what you're trying to think about I'm trying to think this Yomi game but the good news about these games is that they are well covered by game theory we know how to analyze them extremely well and the most important concept you need to know here is the notion of an optimal strategy which just means it's a way that I can play such that I win at least half of my games no matter what you do no matter what you know about my strategy I'm always going to guarantee that I win half the games ok the problem is that any fixed strategy can be exploited right if I just play rock and you know that then you will win every time because you'll win paper you'll play paper excuse me

but if I play randomly if there's some unpredictability then I can do better right so we have this notion of a mixed strategy which is a probability distribution over these pure strategies and so if I play 1/3 Rock 1/3 paper and 1/3 scissors then there's nothing you can do to exploit the knowledge of that strategy right even if you decide ok I'm just going to be you decide to play rock you win half the time if you win play paper you win half the time no matter what if you play some random ice dredger you still win at most half the time so uniformly win random it wins half the time and that's optimal since the game is symmetric I can't ever do better than guaranteeing winning half the time right ok so that's all the game theory I'm going to teach you it's like one slide or something I recommend Frank Lance's game 30 talk it's an hour and there's a lot more interesting stuff in it but this is all we need for now ok so now I can actually talk about how we construct these metagame bounds so you might see where I'm going we have a you know say a selection game like this this is some Starcraft 2 data from some tournaments a

few years ago and now we want to know what rate should I play each of these characters right how often should I play Terran to ensure that I don't get dominated by say my bad matchup against or - check late Protoss make sure I don't get amin aided by my bad matchup against Protoss that example anyway the way we solve this is with a linear program it's just like this it's really simple you just plug it into an LP solver let it run and voila you get your probabilities you don't actually need to know how that works but it is it is actually quite simple if you have the right libraries literally it's just a few lines of code and you know you can efficiently find the solution to these games these are some games can find the probability distribution that you must play to you know win this best you can so here let's say it's 36% area and 34% protists could these be like should we think of these are the expected frequencies that we would see Terran and Protoss and Zerg appearing in the wild since that's our goal well no because they're actually two problems with that the first is that I've been treating

this game of selecting say characters in a fighting game as this one time thing I sit down we play together every round I'm gonna pick a character independently from the last but that is not how communities work and specifically about how eSports work these games have huge execution barriers require a ton of skill and you know for a game like Street Fighter say you know a character may sorry a player may spend years training with one character they're not just gonna pick the character that's gonna you know do the best in this particular matchup they're gonna be kind of stuck on their character so it seems like these single round games these zero-sum games the selection games can't really say much about what a real community will look like right because it has to do with this very human properties kind of like spanning outside the magic circle of what people train over time but I have an argument that there actually is a much deeper connection between these two models than you might think so consider the following model for how a community forms okay imagine you have say a third reuse a third Zangief some if they're camis and some community of street fighter players and they're basically stuck on their characters

everybody plays their character almost all the time because it's so important to train with that one but then a new player comes along and he's gonna play for a while and pick the character it lets him totally dominate the current characters so he picks Fei Long right because Fei Long you know has an advantage against each of these and the new player comes along and she picks me long to write because Fei Long has this advantage it's great right you can basically exploit the weakness in the current community and this keeps happening for a while until finally there are a lot of fate logs and then someone has this amazing idea they realize like I'm gonna play Balrog because Balrog has an advantage against Fei Long and now I can get more wins right so imagine this is a process this is the process that describes how your community forms seems not so crazy far from reality but the amazing fact is that this process is identical to an algorithm called fictitious play and this algorithm is a way to compute the optimal strategy to a selection game which means that over time the percentage of players who we see sort of playing ryu in a community is going to converge to the percentage chance that

you should play were you in a single round of this game okay this is really important this means that we have this selection game right we have this you know this little game where we just you and I just play once but however it is that I should play that game is actually how we should see an entire community of players kind of like adopting characters over the course of years again I've oversimplified the model but I think it points to some fundamental truth so now it seems like okay we're in a position where we can take these matchup charts or selection games and we can compute an optimal strategy for them and hopefully get some information about which characters are gonna get played in the wild we did this here for that Street Fighter 4 chart and you get something like this which is totally utterly wrong if you've ever played Street Fighter 4 you know that first of all more than 9 of the 39 characters get played this was before the recent patch there were 39 more over a third of the players don't play Balrog that is not reality bare legs a fine character but it is not a third of the care players so there's still one problem with our method here and the problem is that perfectly optimal play is not realistic right

players may play to win players may be very good at playing to win and you know despite this they're not going to play perfectly they might play some approximation of perfectly right and beyond that there's some noise in the data we have these matchup charts they're not perfect even if we've taken them from real data from the wild they're still going to be noisy so we can't have this very stringent dependency on you know absolutely perfect optimal play if we want to learn something about our game but we can think about approximately optimal play so the idea is okay we want to know how often you know you can win while playing Balrog some percentage of the time we don't know can't can you play is it possible to be have a very effective community that has 12% balrog in it so we force our strategy to play Balrog 12 percent of the time and then we check can you still win a lot essentially so we modify our linear program you don't need to know the details here but you put one more constraint on it and then you pop out here this this set of play rates it's totally different than the

last one right and this says ok this is the one where we know Balrog is played exactly 12 percent of the time and then we can check at the one where he's played 13 percent of the time and 14 percent of the time it's sort of explored this whole space of what play rates look like when one of the characters appears at some frequency all right and this actually gets us what we want because now we can make a chart like this and let me make sure you really understand what this chart is saying at the bottom we have playwrights that is you know played five percent of the time or twenty percent of your community or whatever and then the two sides of this interval tell you the minimum frequency you should expect this character to occur and the maximum frequency frequency you should expect them to occur so this says Balrogs in any stable strong streetfighter community that wins you know most of the time against any kind of outsider who tries to exploit them you'll see at least you know three percent balrog or something but you'll see at most you know thirty five percent so it's actually a huge range players have a lot of freedom in this game to pick the characters they want to pick and everyone can appear at least you know at some frequency within a sort of

strong competitive meta game so that's great I mean three fighter four is a very balanced game but the real purpose of these bounds is to help us find problems in our in our meta right possible problems so I'm gonna talk about three kinds of characters that these graphs let you find I'll call them always excluded sometimes dominant and always dominate characters all right so I just want to be absolutely sure we understand what this graph means it means if you look at the character at the top left at the laptop then the left point means you have to play Balrog at least 5% of the time in a stable community the right point means you have to play him at most 40 percent of the time all right so finding imbalances here's a matchup chart that I derived from some data again player player made up on smash wiki for super smash brothers melee you don't need a look at the numbers what you do need to see is the matchup charts that it produces so I want to focus your attention first on these entries okay

these are the ones where the right side of the green bar is all the way to the left and what that means is that at most 0 percent of the players in a community can play a young link or link or Yoshi and still have some success ok so that's not good you want a game in which you know players have freedom which players are able to we'll kind of be able to participate in it as any character right and actually contribute and win so this is sort of an immediate problem maybe you want to buff these characters right and you know this is not something you necessarily can easily find in the matchup charts because it depends on the interdependencies on the cap of the characters and who they beat and who beats them another thing we can look for these sometimes dominant characters so fox falco Marth and Samus pop out here these are characters for whom if the players had their druthers eco they could play some enormous frequency what this basically tells us is that if every player in the entire game wanted to play fox they could do so and there would be nothing anyone else could really do to stop them there's no other character that can come in exploit the fact that everybody's playing fox it's like if you

had this rock-paper-scissors community where everybody's playing rock but there's just nothing that actually forces you to play something else now as a designer you basically have your choice it's a matter of taste whether or not you want to do something about this maybe you think it's fine if everybody wants to play fox they won't they will naturally self distribute that's reasonable in our case we had too many players playing Kratos we didn't like in the players didn't like it so I think it would have been really nice to actually know that this was kind of this possibility and find a version of the game in which that wasn't the case which would require essentially giving other characters counters to create us right finding ways that they can force create us out of this dominant position and then after producing those you can actually test them we can you match up charts and see whether you've solved the problem so finally they're always dominant characters now I'm looking at Super Smash Brothers Brawl data which has an infamous problem and you can see it here so Meta Knight has to be played at least 55% of the time in any strong community if you don't play him that much meta Knights will come in and destroy you okay so it's this there's this kind of inevitability that like no

matter what meta Knights go to completely dominate this game obviously you don't want this situation right you may have one criticism which is that yeah which is that if you look at the matchups for Meta Knight they are totally obviously overpowered like all his numbers are ridiculously high he doesn't look anything like the other characters you don't need all this fancy game theory to discover that right but this is an extreme case what about these matchups this is for PlayStation all-stars battle royale this is taken from median skill players but equally informative um now if you look at this again I know you can't really see the numbers the question is is there a character here who totally dominates there one character like you know who just takes over the meta I think it's it's pretty hard to see but when you actually do the computation you see this so it says that sacra has to be played basically half the time half the players have to play sac boy in sort of the convergent one of any of the convergence states of this meta game and this is like really really important to know and I just want to go

back again just to show you this there's nothing obvious here sac boy is the third highest character he is a 5.7 average Mac matchup it's really about this kind of you know cyclical interplay between all these characters right it just so happens that the way his advantages and disadvantages work out this is kind of a necessary consequence and just as some confirmation of this reality here are the frequencies of play for sackboy in the first three weeks of the game this is week one they've already figured out they should play him you know 18 percent of the time week 225 week three he's more than forty percent of the games are played by sac boy okay and his win rates are not changing this is players figuring it out right they're realizing very very quickly the meta is broken and imagine if we had that matchup chart early on and we also had these tools right that would enable us to see where this was all inevitably heading right that sac boy had this kind of inevitable place here now this is high school data so it's a little different from the media and skill data I showed you before but you know just as a consequence of how much data I have but the same principle applies basically

I think we need to try this I think I think it's worth actually applying these methods in the middle of a game early on in a games development you know and it's it's not just about applying the tools or something although you should know I put the code online you can try it yourself this github URL it's really really simple all you do is you take a little CSV of match up charts if you have them how often each character wins and it outputs some graphs like that and you can look at intermediate results too and I really encourage people do this but I want to see how these methods work for different kinds of games you know there are a lot of different ways that we can think about meta game balance and you know we're never going to have just this one true notion of what balance is but the nice thing about these methods is like these sort of vaguely defined here lists you know they start from this really really really reliable source of data these matchups really well-defined data and they produce something that you know is it's kind of vaguely objective right it tells you not how players will play but at least how they should play

and I think there's so much potential to take you know this kind of this kind of data for the game these mashup chart data and learn all sorts of things about the game from it right like really actually step back and take the analysis of our game seriously and not just put games out there and kind of see what sticks and see which players you know completely destroy our game but try to get ahead of them and make a game that actually is good for these players who are now taking them so so seriously alright well thanks so much for listening I have like a few minutes for questions so please oh and also don't forget to put in your ratings on the the radiant email any questions come up to the Meccans yeah over there hi there um I was wondering do you think you could break down the metagame within the actual game into something like this and apply the same methods imagine like tic-tac-toe or something like that we're saying put X in the top left corner and

then the next move and stuff like that I'm so glad you asked because this gets to a point that I meant to mention this is actually pretty key the metagame is this incredibly simple game okay it's just this matrix of numbers at least in the case of street fighting it is more amenable to game theoretic analysis than almost any internals of any games that we play it's a shame that we haven't looked at the meta game through game theory in the past because it is the place where we can learn the most most easily and I encourage other people to do it unfortunately you know take that toe you can do but most games are so complex that they're hard to analyze I think I'm gonna give it a shot with our game I'll tweet you the results this is really really cool the the charts with the matchups and stuff like that can that just be derived from metrics in your game yeah yeah no more type of questions my car says to Freddy said oh yeah that's right I am done I got confused by the time let's go to breakout room wherever want to talk okay thanks a lot

you