Greedy Goblin

Wednesday, April 17, 2013

Good players vs bad players: not normal distribution

Tobold reiterated the most harmful socialist doctrine: "most people are average". The doctrine says that the results of a large bunch of people give a Normal distribution, where most people are near the average.

Normal distribution describes the outcome of multiple random choices. If you add N coinflips, the most common result will be N/2, while extremes will be rare. Accepting normal distribution is accepting that the results of people are products of luck, the very opposite of meritocracy. If their results are luck-driven, then bad performers are just unlucky.

This is not true in real life:

It's time to unquestionably prove that every gamer already know implicitly: there are "good" and there are "bad" players and these are distinct groups with little in-between. For that I need data of random or complete sample of player performance results. Performance of selected group members obviously does not work, so I can't use raiding guild parses. I try to put my hands on a complete EVE-kill database, but until then, let's go with WoW LFR data. Let me show a sample, made yesterday by my girlfirend:
The marked people are the tanks and my girlfriend. They will be excluded, tanks because they are under different mechanics and the screenshot maker for not being random (you are always on your screenshots). In this example data, the average damage is 23096339 with standard distribution of 9603079. Below you can see these players classified into seven groups depending on their distance from average:
This data shows what it should: two distinct groups, one for players who read up, gem, enchant and one for those who just "hang out and have fun".

Please send your screenshots (with marked tanks, yourself, groupmembers) from LFR fights where players are all in the same place (no Sha of Fear and such) to gevlon dot freemail dot hu.


silvertemplar said...

I was going to mention it on Tobold's page, but this will do.

There's alot of variance when it comes to Normal Distributions aka "Bell Curves", alot of it is about your data and your measurements. The fact that you're already excluding Tanks implies there are different processes/mechanics in your data already.

When you have this, you will always get a "double hump bell curve" , or even multiple hump curves. Basically a normal distribution for each "mechanic".

Simply put, you will have a hump per class or role in a dungeon scenario (DPS vs. Tank vs. Healer vs. Hybrid) .

Likewise if you're going to look at an MMO as a whole and measure PvP AND PvE performance, you will most likely get 2 humps because you're mixing 2 different processes which can be mutually exclusive (not everyone PvP etc).

I'd say it's a bit of a fallacy (i'm sure there's a term for this in statistics) to assume a distribution WITHOUT ANY DATA and WITHOUT ANY MEASUREMENT and then go further into trying to predict what "average" implies.

I mean first question should be "what are we measuring" ? Are we measuring DPS as a way of telling your MMO performance? You don't need to be a genius to know how flawed this is in MMOs where they Holy Trinity exists.

So in Tobolds case, i'm sure if you somehow have measurements of the exact same process , you most likely will get a normal distribution. I.e. if you measure the DPS of Rogues in the same dungeon.

That said, "average" is a relative term , it does not mean 50% is average. It can mean 10% is average or 90% is average. So it's kinda meaningless to say "most people are average" when you don't actually have a definition of "average" in the context of an MMO.

In a game of Lost Souls, most players might not get past the first level, so what does this it mean if you're saying "most people in lost souls are average" ? Your bell curve would be skewed to the left, and it might make you think everyone is slackers, but we know this would be a lie.

Aziraal said...

I do not agree your comparison between IRL and RL.
What i do agree is that in every game, and it's more noticable in MMO's, there are a pretty big bunch of bad or less than average players. Players, like you describe them, that are nor reading nor optimising their characters.
But what is the point with RL household. Are you really considering that the money income is low for some because they are not interested in "real life mechanics" or "just want to play the life for fun" ? I'm not that sure.
I know you wanted to introduce with the RL example that a Gaussian distribution is good for totally random situation but when peoples are involved everything is different (by the way "This is not true in real life" is not what you should have written as your example with the coin IS real life too).
Anyway your stats with wow are pretty interesting.

Gevlon said...

@Aziraal: indeed. The RL poor can't care less about "real life mechanics", so they don't study in school (despite it's free) and they use lot of "fun" substances: alcohol, tobacco and drugs. Hence they remain poor.

Cathfaern said...

"Are you really considering that the money income is low for some because they are not interested in "real life mechanics" or "just want to play the life for fun" ? I'm not that sure."

are not interested in "real life mechanics":
Example: They don't calculate that if they get $10000 loan, they have to pay back $20000-30000

"just want to play the life for fun"
Dont be arsed to study hard in school, just try to survive. Or they search for easy work, not good payed.

Premier said...

Doesn't this graph massively favor people who AoE in fights over those who do single target damage?

Which of course some fights call for. Not to mention fights where people are doing things that are needed but fairly low damage like smashing orbs or whatever.

Aziraal said...

Please explain your thought process instead of trolling. I gave you a "non trolling comment" please don't be that kind of guy.

You are right but in this very example you cannot considere Horsetail (mage), Exizi (war) participating in any other way than DPS for the raid ... and watch their rank on the list.
You can argue some classes are under other because they give support (heal/offtank/cleanse/ ...) but this example is self explanatory

Anonymous said...

You need to do this sort of dps test on a simple damage fight with one blanket mechanic - like Ultraxion for example - because a lot of fights are very unfriendly for particular classes, like flight and movement phases.

Jim L said...

Gevlon, which do you think has a bigger correlation into which quintile a person will end up in regarding wealth, the person's IQ or the quintile of wealth they grew up in (i.e. for most people the quintile their parents were in)?

Gevlon said...

@Aziraal: I wasn't trolling (maybe simplifying). I honestly believe that poor people are poor because of short term thinking and emotional thinking. They do what feels good (doesn't feel bad) now, ignoring long term gain. Getting loan: I haz stuff now! School is boooring! Let's paaarty!

I understand that you consider it troll, but my point is that these people are a joke.

@Premier: and who choose not to AOE? Who choose bringing a class that can't perform in a fight? The player. Being prepared is first step.

@Jim L: their parents wealth quantile of course. How could they learn proper thinking from a mother who was drank by 10 AM and from a father who was in and out of jail?

Premier said...

It's not that they didn't choose to AOE, it's that not everyone needs to AOE a fight.

Getting top of the DPS charts by using AoE is easy, it'll completely fuck the damage charts for the rest of the run.

They could be of fuck all use for most of the instance and as long as they get picked to AoE down adds or AoE bomb trash packs they're still going to place pretty highly.

This is like looking at the healing charts way back when and assuming Shamans are godly because they could spam chain healing. It's not really a good way to judge it.

DPS Charts do matter, but only in fights where everyone was doing the same things. If there's a fight where everyone has to AoE and then everyone has to Single Target DPS that'd be perfect to judge this, not taking a whole instance and thinking it means anything at all.

Nils Magnus Nilsson said...

If you are really interested in drawing conclusions from facts, consider these figures:

When I see those statistics, two things come to my mind:
1. Many people in their early 20s - for whatever reason - make poor economic decisions, and do not to get a good education.
2. They pay for that mistake themselves by selling their labor cheaply and working long hours for the rest of their lives.

Without a bit of dumb luck, I too would have been a low income worker.
Growing up, my immediate family were loggers and farmers. No drinking, no crimes.
As it happened, I was interested in electronics and my family encouraged education. I enjoyed school; learning was fun. Simple, short term fun.
Now in my late 30s, I no longer have to work full time, but spend more time with my family, thanks to 1)high income and 2)having taxes lowered by our right-wing government.
Meanwhile, many of my childhood friends keep working long hours for low wages.
I have no need to belittle and ridicule those who didn't make the same lucky decision as I did.
I'm glad for myself and my family, but I honestly don't think it's fair.

Anonymous said...

Gevlon, you probably will consider this comment as a troll, but I have to warn that you are about to do something very stupid again:

"I try to put my hands on a complete EVE-kill database"

As people pointed out many times before and you have indirectly proved yourself - KMs are not the way to measure players skills. We have KM whores, we have gankers, we have logi/ewar and we have bait. This combination in reality makes KM are non-measure of skill. Of course we also have staged fights, like those you did some time ago, which further make KMs not the place to look. And there also a lack of direct connection with damage (in isk or hp) dealt and skill - frigate fights are very skill intensive, but they make poor KMs.
In summary - don't do what you want to do or you will just make a fool out of yourself and cause a shitstorm.

Dàchéng said...

Your WoW sample has this flaw in it: in LFR groups, players do not all start at the start and finish at the end. Some leave for various reasons and are replaced by others. This can be clearly seen in your data, making it unable to support your conclusions.

Look at Ruubers' DPS for example. Despite being top DPS, he is only 12th in damage done. There are some possible reasons: he may have joined the raid late, or left the raid early, and so fought less encounters. He may have only fought trash, inflating his DPS. He may have blown all cooldowns at the start of each fight, stolen aggro off the tanks and died early, inflating his DPS at the expense of his damage done. His high DPS might be due to having joined a boss-fight where the Determination buff was already very high. We simply don't know.

As Silvertemplar noted, each class has different DPS mechanics, not just tanks; and each class behaves differently on AoEable trash. They have different distributions.

To provide better data, you must choose data from 1 boss-fight or one pack-fight only, and separate the data by class. To get meaningful data from that, you'll need to look at several runs of the same raid encounter, but with different groups; so the boss-encounter chosen should be only that in which the boss died (or else low damage in a 30 second ninja-pull wipe is hard to compare with high damage done in a full encounter). And he should have been attacked with the same "Determination" buff in each case.

silvertemplar said...


Mage vs. Warrior DPS. I'm 100% certain there will be a debate as to whether these 2 classes are identical in terms of their DPS output. Maybe the one is better at AOE and the dungeon happened to involve alot of trash mobs. Maybe it's better at single target dps, maybe the one can do super spike damage while the other is better at sustained damage.

All of these factors make any conclusion questionable. We know there's a difference, otherwise why have 2 classes in the first place?

To make this more clear, it's like taking the speed of 10 dogs, and the speed of 10 cats, now draw this on a chart and only call this "speed of domestic animals". You will most likely see 2 humps.

Does this mean that "domestic animals" are either very fast or very slow, but rarely "average" ? No way! It would be an entirely wrong conclusion, but this is exactly what i see happening here...

Aziraal said...


You don't get the point.
I'm not comparing Mage vs War. I'm just saying that these classes are almost fully devoted to dammage (if not tank for the war ofc) and some of them are still at the bottom of the chart.

Just pick the first and last mage's DPS or the first and last War's DPS to have a clear comparison. I don't thing their spec + encounter type can justify a 1/2 ratio in terms of DPS.

These guys are really bad players that's it :)

Dàchéng said...

Aziraal, there's no doubt that the top mage, Detemion, does better damage than the bottom mage Horsetaile. The point is that with only three mages in the sample, it's pretty difficult to tell what the distribution is.

Anonymous said...

I disagree with your statement. It's very simplified and incorrect, on multiple levels.

There are fail safe mechanisms in place in both WoW and irl. That is why you do not get a normal distribution. Most countries have some social security and minimum wages. This causes the skew to the right.
Would you agree that the >200k are outliers and that it does not follow the pattern? What are your thoughts on this?

It would be coincidental if you got a normal distribution from LFR with this data. The sample size is too low if you, using 7 groups, to make any analysis. Normal distribution comes from large sample sizes.

This is in my opinion enforced by a few aspects that influence the distribution. Measuring dps brings a lot of complications.

There are for example 11 different classes, that vary in popularity and performance. A hunter who sends in pet and autoattacks will do better than a caster spamming corruption or icelance.
You can include all the classes in one big group. You ideally want the conditions to be similar, you would have to compensate for this variation by increasing the N. You actually give 11 different groups different tools to accomplish the same. This class difference will skew the results.

What do you do with afk (or almost afk) players? Do you include these in the results? No interest to participate in your experiment (or lfr in this case) does not actually say something about their potential performance.
Will you treat these as outliers that should be excluded?
This group should be excluded from the data if you want to maintain the two definitions of your groups.

Do you guys think that the kick system will skew the distribution to the right? I am interested in the results!
Gevlon, would you mind to include raw data as well (like an excel/spss file)?

Anonymous said...

Second post.
I misread the data to some extent. Do you agree that the subclasses with standard deviation of +/-1.25 demonstrate a huge problem? It shows your lack of data.
I assume that you are planning to reduce the size of the intervals when you have received more data.

maxim said...

The more interesting part here is that there are generally very few people who are "just below very good", in comparison to amount of people who are "very good" and "bad".

This is actually a good find, certainly useful for game difficulty curve design. Thanks Gevlon!

Anonymous said...

The last 2 bars on that chars have much larger increments than the other bars, of course the graph will not resemble a bell curve.

Anonymous said...

Raph Koster solved the MMO player distribution with data ten years ago. It is a pareto curve.

The net is that most players suck, and you can't do anything about it.

The real question is how to make a game that is interesting to the few quality players without alienating the feeble masses.

Anonymous said...

All I can say is that I am 19 and have grown up in a house living between 200-250k and I am not looking forward to finishing college and getting thrown into the 55k range lol.

Ruby Porto said...

That RL income graph looks pretty normally distributed (ignoring the distortion on the left caused by the lack of negative incomes and by the minimum wage which is ~$14,500 for full time work).

The spike on the right is caused by the 2 bars covering a far wider range of incomes than any other bar.
The second to last bar is the sum of the next 10 bars in the series if they had kept with the $5000 width bars, and the last bar is the sum of every further bar in the series. Of course they're going to be disproportionately tall.

In other words, what you're seeing is an aberration caused by the method chosen to present the data, not real information.

Anonymous said...

@Anon 18:40
First off. The link that you posted and the information in your post do not match. Your link shows population distribution between MMORPG's. This indeed is a long tailed graphs, showing how the population BETWEEN MMO's follows fixed rules. This however doesn't say (describe) anything about the population itself, except its numbers.

Gevlon wants to learn more about the distribution WITHIN a single MMORPG and in this case within a similar feature.

If what you are saying is true, could you please give me the right post from Ralph Koster that describes the effect that you describe (high % sucky players).

@Ruby Porto
Yes. I completely agree with you, like I said in my post @05:14. It is a right skewed graph. It does follow a normal distribution.

Anonymous said...

>>If what you are saying is true, could you please give me the right post from Ralph Koster that describes the effect that you describe (high % sucky players).

It's in the "Small Worlds" presentation from 2003 and its bibliographical material. Chapter "Talent". Linked to right there on Raph's page. The whole presentation is worth a read in the context of what Gevlon wants to accomplish.

Anonymous said...

Without the outlier at the top, that distribution is the gaussian/normal.
one-25th isn't statistically relevant, especially in a system with exponential runaway scaling.

Grimmash said...

To the graph on RL income, I think there are some other factors you have to consider besides "some people suck, some are awesome".

Real life success is a combination of opportunity, preparation, personal qualities, and the structures of society that influence all these things. Many people making lots of money got those positions due to conditions that had more to do with the social class and structure they inherited than the effort they put into their lives. Yes, some people break these conventions, but most do not, and not all of it is due to people being "bad" at life.

Add to this concentrations of power and wealth, and it becomes more stark. Some portion of those in power often manipulate the system, either intentionally or unintentionally, to favor themselves and their power or wealth controlling group to the detriment of other groups. Look at OTEC in Eve, or the ability of large corporations in the US to manipulate laws and markets to their own advantage.

Many people from average or "bad" groups do everything right, yet still get laid off or marginalized due to factors outside their control.