http://dbd.game/killswitch
Survivor escape rates vs killer win rates, a bit of math to understand why the devs are right.
Comments
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I'm using a uniform distribution. (And I know a bit of statistics and stochastics, no need to explain that part.)
You draw values, they get distributed on an axis. If it's a bell curve, it's a binomial.
If it's a horizontal line, it's uniform.
I use an uniform one to draw escapes.
Everything else is a result of this.
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You are using a uniform distribution 4 times to simulate the results of a match. Using the same uniform distribution a specific number of times to choose between exactly two choices is exactly what a binomial distribution is used for.
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Wow, I didn't realize I missed a math thread.
@drsoontm I once saw a post, likely in jest, that 40+40+40+40 = 160, thus the survivors must be winning every game. When anyone pointed out how that was wrong, the poster would just say they are disagreeing with basic arithmetic.
The problem here as others have pointed out is you are creating the wrong formula. It's not that the formula is wrong, just like the arithmetic above isn't wrong, it just doesn't actually apply to this game. Being there are two distinct possibilities that can result in what you've set up as a killer win (3k and 4k), two distinct possibilities of a killer loss (0k and 1k), along with draws (2ks), and that those possibilities are not equally likely, you can't create a formula without knowing the likelihood of each scenario.
As @Firellius has pointed out, there are gameplay changes you could make that would radically impact the kill rate but not touch the win rate.
@zarr brings up the issue of Nightlight data. At the time I'm posting this there are 7 killers +/- 1 point of the 60% kill rate. The win rates are: 52.9% (Twins - 259 games), 55.49% (Freddy - 322 games), 52.87% (Hag - 244 games), 54.12% (Pig - 499 games), 54.04% (Chucky - 1038 games), 52.12% (Cannibal - 677 games). There are couple of things to see:
1: Despite thousands of games in total, none of the killers are reflecting your hypothesis. All of them are trending in the same direction as well so it not just a sampling error.
2: Despite having nearly identical kill rates, the win rate can vary by over 3% (Cannibal to Freddy). Because there are reasons behind the numbers. Different killers can arrive at the 60% kill rate via different game breakdowns.
This reminds me of a quote I like from Richard Feynman: “It doesn't matter how beautiful your theory is, it doesn't matter how smart you are. If it doesn't agree with experiment, it's wrong”
Your theory about how the win rates should break down doesn't agree with the real world data (experiment).
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Just to reinforce your statement in draws, draws are also irrelevant because there are no draws in dbd. Each match is 4 simultaneous 1 v 1 scenarios playing out. As a survivor, you win by escaping and lose by not escaping. There is no actual survivor team. There is no "survivors win!" screen. YOU either escape and win, or YOU die and lose. Due to this, there's no situation in dbd where you could draw in that 1 v 1 outside of the server crashing. A draw requires neither side to win nor lose. Even if people aren't aware of what the devs have stated multiple times that the game is 1 vs 4 individual survivors and instead assume it's a team vs team game, a draw would require neither side to win or lose. You cant have the killer fully lose and half of the survivor team win (2 escapes) and declare a draw, because the survivor "team" had winners in it. Draws have neither side winning nor losing. If the killer fully loses and the survivor "team" has a partial win, then clearly the survivors are the winners in that case. Now like I said, there is no survivor team in dbd, but even if someone claims there "actually is", the whole idea that draws exist just doesn't hold any water. There's no draws in 1 v 1 in dbd, and if you subscribe to the idea that the survivors are a team, there's still no draws because you can't draw with one side losing and one side partially winning. Draws require no winners.
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So there's a number of problems with this.
1: The definition of draw is based off the fact that competitions are pretty much always even (synchronous) competitions. Definitions exist for general word usage. Asynchronous games are very rare. It is completely normal to adapt terms from more common activities.
As a community we need a word to refer to 'I killed as many survivors as escaped'. Even, a tie, a draw, etc. all would work, the community has decided on draw.
2: Even if you disregard the above, this whole thread is then pointless. If you can't draw against the survivors (plural) you can't win against the survivors (plural). Kill rate = win rate so a 60% kill rate equals a 60% win rate.
If you want to say survivors aren't a side, okay, but be consistent.
3: On BHVRs views - BHVR has been pretty clear that they are broadly fine with people playing, and viewing, the game however they want. You point out there is no 'survivors win' screen but there is no win screen ever.
Also if we look at game play the idea that BHVR wants each survivor to strictly be out for themselves doesn't look realistic. If one survivor is on hook, and three survivors are in the exit gate, BHVR is fine with them going for the rescue or just leaving. In BHVR's eyes, both are valid ways to play the game. This is a very common situation and over 8 years if they truly thought this was the 'wrong' way to play and that the survivors should just leave, someone would have said so.
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I believe you are correct. And I should never use the word "math", it makes it looks way more complicated than what it is.
@Vishlumbra isn't correct. He's making the same exact false statement you did, only he's not trying to make it seem "scientific".
As I've pointed out, the 40% do not describe the chance of any survivor in any given trial to escape, let alone independent of one another as if the killer is playing a 1V1 one after another. It is simply the amount of survivors that overall escaped in the captured trials. Many of those escapes will come from 3/4-escapes (many more than your simulation predicts), in which case the 40% is not accurate. Many others will also come from solo/hatch escapes, in which again the 40% is not accurate and also not describing what people think of as an actual escape for balance purposes. Either way, any survivor at any point in any match having an average random 40% chance of escaping is not depicting the reality of the game, because the game is not a mathematical system of random chance and because even insofar one would want it to be, it certainly isn't a 1V1, and the escape chances not independent of each other.
With a 50% escape rate, mathematically in a random chance system you would then expect a 33-33-33% split in wins/draws/losses. One doesn't need to be a game intuition genius to realize that real results would certainly not behave that neatly, because some results are simply much more likely than others as per the nature of the game. Specifically, matches where 2 survivors escape are rare because if even only 1 survivor died prior to the endgame, the chances of anyone escaping plummet; and if nobody died prior to endgame, the chances of getting 2 kills aren't high - the game trends toward 3/4-kill and 3/4-escape matches (and between these there is even more weighting, due to hatch and the fact that killers can regularly secure a kill in endgame).
But of course, more than the issue of the model not depicting reality, the issue with this statement also is that draws and survivor winrate is ignored with the bias of presenting misleading results. If we accept the overly simplistic and unrealistic premise that "the killer has to beat the 40% odds three times in order to win", of course the other side of that is that "three survivors have to beat the 60% odds in order for survivors to win" - and what kind of ridiculously low winrate this translates to in your model has been pointed out.
It's all about the perception of the game.
These are the mental gymnastics I was talking about. Even if you genuinely believe a random chance modelling depicts the reality of what happens in this game and its matches, if you were being honest with yourself and others and actually interested in a scientific view, you would simply admit that you deliberately misrepresented the results of that model in order to support your biased narrative that the results are not killer-sided and if anything survivor-sided even with 60% killrates, stating outright false facts ("survivors win about half the time!", "SWF survivors win way more often than killers at high MMR!") and omitting real facts (draws are not killer losses or survivor wins, survivor winrate is ridiculously low in the model).
But sure, let me tackle the gymnastics:
Survivors (plural) win should naturally be the opposite but in practice it isn't. The vast majority of survivors only focus on their own escape: survivor (singular) win. Hence that regular ranting about 60% kill rate. That's why I looked at the win the way they are perceived.
First of all, the assessment that the vast majority of survivors only focus on their own escape and view that as a win is not very scientific. You don't have any objective backing for this and certainly should not use it to evaluate the results of a "scientific" model. More importantly, it doesn't matter what people may or may not subjectively view as a win if we are talking balance logic. That would be game experience discussion (you know, the thing you have to completely ignore to even attempt to mathematically model game results like this). Logically, we can distinguish between killer wins, draws, and survivor wins, and this is what we have to do if we want to objectively quantify balance implications of the results. To discard draws entirely would be absurd. Not only logically, but even from a game experience perspective: I don't actually believe people escaping as the last sole survivor (by hatch or otherwise) actually feel like that's a win, and I do believe in matches where 2 survivors escape neither side will feel like they've lost. Most people view that as a balanced match, and even the game realities that lead to 2 escapes will often make for a rather balanced experience.
Even more notably, this entire line of arguing is you wanting to eat your winrate cake and have the escape rate cake too. But as @crogers271 has also pointed out, you can't look at the one when it suits you and the other when it doesn't: If you actually believe survivors only care about their own escape/that that should be regarded as the "win condition" and that they therefore technically have an average "winrate" of 40%, you have to also acknowledge that they have a lossrate of 60%. Contrasting this to the killer winrate, even if we do entertain the 47% of your model, the lossrate is not 53% because while survivors cannot "half-escape", killers can kill (win against) half of their opponents. That puts the lossrate disparity at 60% for survivors and ~17% for killers. So even when entertaining these gymnastics of killer winrate vs. survivor escape rate, this isn't quite the "balanced" notion you wanted to portray it as. If anything it looks even worse.
But one of the points is that 50% gives a very low rate of win for the killer, which may explain why a while ago when the kill rate was balance for 50% survivor queues went up: it was high-mmr even at the basic killer level.
As per your model, 50% would translate to about an even split between wins, draws and losses for both sides. But regardless, again, I don't remember survivor queue times being bad during that time, or much of any other time in the past 6+ years. Whenever people brought up the queue time bogeyman and I just knew that it didn't agree with my personal queue times, I went and checked out streamers, as well as challenged the people claiming that queue times are so bad to prove it. And the streamers' queue times aligned with my experience (more often than not having longer killer than survivor queue times), and nobody ever took me up on the challenge. Such as here: https://forums.bhvr.com/dead-by-daylight/discussion/comment/2654033/#Comment_2654033
I believed the "infinite queue time" and "killers are leaving" bogeymen had finally been put to rest with the introduction of queue incentives that are on survivor the overwhelming majority of the time (for me, the people I play with and watch, and from impressions of reading around). Of course, the narrative had then shifted to "duh, there are more killers playing because you need 4 survivors for every 1 killer!", which is true, but also means there is no such proclaimed issue of too few players deciding to play killer, more so the opposite.
Draws are irrelevant because they are not a win. I'm not sure in English but in French it's called a "mach nul", one meaning being "the same as if it never happened" (nul et non avenu). They dont really have an equivalent for singular survivor wins as it's kind of all of nothing on that front. Nothing really interesting to take from that.
These gymnastics I already pointed out above. The fact that there is no equivalent for "singular survivor win" in the "overall killer win" metric is not reason to simply ignore a huge chunk of match outcomes, it's reason to question whether drawing equivalence between killer winrate based on team results and survivor "winrate" based on individual results is at all reasonable or logical.
There is something to be taken from the fact that you disregard draws entirely and also pretend they are killer losses/survivor wins: you/your presentation is comically biased.
But if we were to take these gymnastics to their logical conclusion, it would be that killers also "win" against singular survivors by killing them, therefore 60% killrate = 60% winrate.
Yes, I've seen the 17% too, which is interesting, or would be if survivors cared that much about team wins. It's all about perception. (And I realize I've not updated the web app to also draw that curve, I'll do it if I recall tomorrow.)
How you can keep repeating "it's all about perception" and not realize how laughably biased you are being in a thread supposedly concerned with math and logic is beyond me.
No, logic dictates that in order to evaluate game balance based on match outcomes, we can't just ignore any outcome we subjectively don't like or think others don't care about or whatever. 2-kill matches exist, they are balance-relevant. 3-4-escape matches exist, they are balance-relevant. It is balance-logically significant and not irrelevant that survivors according to you only 3-4-escape some 17% of the time, or that killers still kill 2 survivors in the majority of the matches they don't kill 3-4 in.
If it's really all about perception, mine is this: You are using your skewed perception to falsely interpret and present results of a flawed, removed-from-reality model.
But sure, if you want to run with it, do that: add the 17% to your site, edit it into the main post. State that it is "interesting" that survivors as a team only win about 17% of the time. That killers on average only have to worry about not getting 2+ kills in 17 matches out of 100. That's an interesting turn of narrative.
We keep speaking about 40% escape rate mind you but the 48% escape rate in high MMR is also intersting (and explains why that level of play can be so frustrating). I know this detail doesn't escapes you and you expect it to be like that, as do I.
SWFs can obviously be expected to be able to perform much better than solos due to various reasons ("matchmaking" themselves among each other much better than the matchmaking system, build/strategical/tactical/natural coordination, communication), which is why if the balance target for the premise of 4 solos is 40%, we have to accept that SWFs will be more than that. If we wanted 4-SWFs to have 40% instead, the rest would be left behind way too much. Plus full SWFs being able to compete on even terms with killers is reasonable altogether - the overall game experience where the overwhelming majority of the playerbase are solos and duos being on average killer-sided fits its theme and gameplay proposition, but it being a more evenly balanced playing field for 4-SWFs as a team-based tactical multiplayer game fits the more and more competitive proposition the game has also fostered.
And this is ignoring that the escape rates (from a balance purpose perspective) are inflated by the exclusion of matches with disconnects and inclusion of hatch escapes (and sole gate escapes in matches gens had not been finished in, for that matter). And for these high MMR SWF rates specifically, it can also be noted that BHVR (likely) only looked at the survivors' MMR values, and did not filter specifically for the killer also being high MMR, which additionally inflates the rates away from the base balance premise since the matchmaking will often have given them killers of a lower MMR.
I see everything as system, that aside you may have a point directly in relation with mine. Let me think …
Yes, you are right. Hatch escapes are inflating the escape rate somewhat. Win perception on the survivor side may be lower than projected because of that. I'd love to be able to discriminate them out. There is no data about this though. If you can find some BHVR stat about hatch escapes, I'd love to try to include them.
Not everything is a system, or certainly not one that behaves in perfectly predictable, calculable, simulatable patterns. But do let me know if you move on to more important things and figure out, say, the stock market as such a system!
Also pointing out again that "win perception" does not matter if we are logically dealing with balance based on match outcomes. You can't just apply your own feelings of what is a win or not, or your feelings on what other people's feelings are. If we want to objectively quantify balance based on outcomes, we have to look at all outcomes, and also decide on logical, objective terms what they are. For that, win (3-4 kills), draw (2 kills) and loss (0-1 kills) make perfect sense. (Or we can simply do what BHVR does and look at kill vs. escape rate and not concern ourselves with making up emotional win conditions.) And yes, since hatch escapes contribute to the escape rate but almost never the winrate since they typically happen in lost matches where only 1 survivor escapes (or if they happen in won matches the survivor could have usually also simply escaped through the gates), they inflate the escape rate with regards to your flawed way of equating it with escape chances and the derived "winrates".
47/37 I presume you are talking about the measured win rate results of the matches. It's about perception here again. I understand not everybody sees it like that but, for me, if it's not a win, its a loss (I guess I'm extremely competitive).
I fully agree opinion may diverge about this. I've simply provided a tool to have a better idea of what these statistics mean.
If other people draw different conclusions than mine and don't see why I'm only focused on win, it's all the same to me. (Once I believe I've explained myself sufficiently, and I believe I did.)
Opinions are subjective after all. I'd not call either of them biased though.
I'm sorry, but this entire section is a huge cop-out. It's not all about "perception", there are logical incongruencies here, and using these stats (even if we ignore the model being flawed) to make the statements you made and presenting them how you did is nothing but deliberate misdirection or deception. You not only did not explain sufficiently, you intentionally obfuscated crucial aspects to serve a preconceived point. You did not even so much as clarify on your personal (and frankly silly and anti-competition) view that "if it's not a win, it's a loss" (while again ignoring that this would mean survivors lose 60% of the time at best if we biasedly view their escape rate as winrate, or at worst 80+% of the time if we take your model's results and actually compare winrates) and instead made blank false statements such as "killers lose 2/3rds of their matches in high MMR against SWFs!"
Look, I'll lay out my cards: I think what's more likely happening is that you want the game to be seen (by others and yourself) as survivor-sided/not killer-sided even at 60% killrates because you want more killer buffs/survivor nerfs or at least certainly not any killer nerfs/survivor buffs, as well as to be able to tell yourself you are beating the odds if you win because you are good at the game, and game design being at fault if you lose and it not meaning the survivor players played better than you or that you made meaningful mistakes and such. It's a nice bubble to play and experience the game in to think that "not only do I win so much because I'm so good, but the rare times I lose it's not because I'm not good enough", and to not want to be worried that one's "side" or favourite character (especially if that happens to be Nurse) gets changed for the worse. For this, you are willing to disregard reality that 60% is completely obviously killer-sided and sought for by the devs specifically with the intent to make killers stronger, as well as the reality that personal experience with the game indeed does not depend on averages and that the game is in fact abysmally killer-sided for good players (they can win thousands of matches in a row and almost never lose even if they don't streak), with even just competent players winning the overwhelming majority of their killer matches. Not only are 4-SWFs of good or competent players infinitely more rare and will infinitely more often meet a killer that can compete with them (hence survivor winstreaks pale in comparison to killer winstreaks), but some of the killers win most of the time even in tournaments where they exclusively play against good 4-SWFs the caliber of which one would essentially never meet in the actual game.
The reasons why I'm so concerned with threads like this and this narrative at large believe it or not is mostly because I want people to be more competitive, to really evaluate their own gameplay, see and learn from their mistakes, believe that they can improve and do what's necessary to improve. To see the reality that DbD if anything is a game uniquely positioned as one where if you put in the time and effort to improve, you can win against your opponents the vast majority of the time, and that this is all the more so true as killer where you are not at the mercy of the poor matchmaking system or have to find 3 other players around your level that are also just as competitive (playing to win, using the best loadouts to win, etc.) and are willing to play when you do and also use voice chat. The narrative shouldn't be: Killer is so hard and the game so survivor-sided and you can be happy to get 1 kill if the survivors just want to win! - It should be the not-removed-from-reality one of: There is so much room to improve in this game and it's so skill-sided and especially as killer it's so cool and rewarding to see that improvement's effects in any trial because you are always 100% of your side's performance potential, to keep learning and to reach a level where you can beat much of any group you face and become a killer to be feared!
…Anyway, closing yet another entirely-too-long post with saying that I appreciate the work you put into this in and of itself, and that while I do believe even if I were to be more charitable to you and assume that you didn't mean to deceive people and genuinely believed that you were modelling and stating scientifically sound things I still wouldn't see much merit in this way of approaching the stats, I do at least see merit in people putting in more effort to try and understand more things about the game, instead of very anti-knowledge and dismissive reactions like people often have, saying that the stats are "completely meaningless, if not made-up!" and other such nonsense.
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