Win rate and luck

[Ciryonde]

Ohoy people!

 

I don't know if this has been discussed earlier on the forum since you can't search for words shorter than four letters, hence "win rate" is out of the question. Anyways, I was thinking about the connection between luck and win rate and the fact that people often are discussing if it is based on luck or skill. Just for my own amusement I decided to calculate approximately how much luck affects your win rate and I thought I might share the results here.

 

First, a few points, if you plan to just trust me, don't click the spoiler tag:

 

• I assume that you keep a constant expected win rate, which is kinda unrealistic since you probably get better at the game while playing it, higher tiers are more difficult etc. but that would be a pain to model.
• The more games you play the better your win rate will reflect your actual win rate, this is know as the law of large numbers, http://en.wikipedia.org/wiki/Law_of_large_numbers.
• I use a 95% conficende level in my calculations.
• I will add all the calculations i did in a spoiler tag at the end, you can run them yourself at WolframAlpha.com
• Edit: For some of you, especially if you have studied statistics, all this might seem trivial, but please remember that WoWs have players ranging from people with university level statistics education to grade school pupils that only stopped believing in Santa a few years ago.
• Edit 2: There are many ways of increasing your win rate, like playing strong ships or playing in divisions. This is however not based on luck. This post discusses the improbability of lucking your way to a high win rate, and that no-one is going to get a significantly higher win rate than somebody else based on luck. This post does not explain why a player get a specific win rate, only that it is impossible to get a high WR by pure luck.

 

Assuming that you have a true win rate of 50% this table tells you within what area most players (95% percent of the to be exact, 2,5 will have higher and 2,5 will have lower) win rates will end up based on luck alone.

 

Remember that this does not mean that players win rates will be evenly distributed within the given interval, most will cluster around the actual value since this is a normal distribution:

 

Just for even more fun, I decided to assume that win rate actually is based on pure luck, that is that we all actually should have a win rate of 50%, some of us just get good MM and plenty of enemy detonations, and then calculate how lucky you would need to be to achieve some of the win rates we see in game, starting out with my own. I have a win rate of 58,88% in 2218 games, which is on the high side, but in no way extraordinary.

 

The chance of someone winning 1306 games (or more) out of 2218 is approximately 2*(10^-17), or 0,000000000000002%. This might seem improbable compared to winning the jackpot in a large lottery which is 3*(10^-9) or 0,0000003% but it still isn't outside the realm of possibilities, so lets go have a look at someone reaaally good: _FTD_.

 

According to Warships today _FTD_ have played 8010 matches and won 6339 of them. Since we all know that win rate is mere luck and _FTD_ is not better at this game, just luckier, let's calculate exactly how lucky he/she is:

 

The chance for reaching _FTD_'s score just by chance i 7*(10^-623). I won't write that out since its basically a 7 preceded by 623 zeros. To put that in perspective let's say you have a sand box, or better yet, take the Sahara desert. You randomly pick on grain of sand, mark it, throw it back in the desert and let a friend pick a random one, and trust luck that he will get the same one as you. This might seem improbable, but it is child's play compared to _FTD_'s luck. To approximate that, we need to go bigger, MUCH bigger. So assume that you pick an atom somewhere in the observable universe and get _FTD_ (Edit: make sure that his/her luck bringing friends are also there) to guess which one you picked, when he/she has guessed correctly 7 times in a row, that would still be more than a hundred billion times as likely as getting his/her win rate based on pure luck. So _FTD_, if you are reading this, stop playing WoWs and go buy some lottery tickets, you are vasting your time!

 

I now realize that what started out as a fairly serious post kinda went of the rails, but my main point is that after a good number of games, you can expect luck to be responsible for about +-1 percentage point of your win rate. The table can also be used for ballparking the values for other win rates as well even if it wont be exact. For instance, after 3000 games with a 60% WR the probable diff would be 1,75% whilst it is 1,79% for a true WR of 50%. Generally the further away from 50%, the smaller the deviation will be, but as I said, ballpark.

 

And if someone was planning on answering this post with "but there are a lot of players and someone has to be really lucky", then pose yourself the question: There are plenty of people in the world, how many of them do you think would be able to guess the correct grain of sand in the Sahara desert, or a particle in the universe? There are not more players than there are people in the world and if no one in the world can do something that is much much much more likely than lucking their way to _FTD_'s win rate, no player is going to be that lucky.

 

Have a smiley for getting to the end of the post

 

WolframAlpha code:

 

For calculating the interval of win rate where n is the number of games, 0.95 confidence

binomial confidence interval n=50, p-hat=0.50

 

Probability of getting my win rate, or above, by pure luck

P(X>1306) for X~binomial n=2218 p=0.50

 

Probability of getting _FTD_'s win rate, or above

P[X>6339] X~binomial n=8010 p=0.50

 

[Aotearas]

This thread is like the 214% thread's smart little brother.

 

Yay math and statistics!

[xXx_Blogis_xXx]

lol nice work , can give u a +

[Shaka_D]

After reading all that from the OP I can see why most people find it easier to believe in luck.....yep, I have to agree, easier to believe in 4 letters than all that mental stuff. I'll stick with 4 letters.

[Capra76]

_FTD_, if you are reading this, stop playing WoWs and go buy some lottery tickets, you are vasting your time!

 

This public service announcement was brought to you by the World of Warships Association of Battleships captains who are tired and fed-up with being burnt to a crisp.

[Admiral_noodle]

I'm approaching 2000 games with a 60% win rate and yet part of me is still waiting for my luck to "balance out". Even though I did statistics and understand random. And even though I know how MM works.

 

Still can't shake that human feeling

[Stixius]

I dont believe in luck (unless I'm on a losing streak)

 

[robihr]

i only believe in bad luck when i get teammates who cant survive for 5 minutes... when i roflstomp enemy in 5 minutes it is all skill

 

[El2aZeR]

[iJoby]

made me giggle, but fantastic to read, well done OP.

[ParEx]

Well done my friend.

But one point: all written is only valid when it comes to solo randoms. Putting two or three good players into a group and let them act together will screw your model, like _FTD_ who played whooping 625 battles solo with 57,4% WR. His 2 Platoon games where 65,4% WR at 1525 games and 85% at 5800 games in 3 man groups.This still doesnt take his progress into account since I assume he doenst play solo anymore.

But still something to look at when seeing those skyhigh winrates.

[xsmilingbanditx]

Maybe I'll digger into this a little. Will have to check which assumptions you made and why :-)

But well done so far.

As to be fair and add to the poster above: With divisions you have a serious impact on the outcome.

In a random battle with all single-queue guys it's...at least strange. Although I do know it is not totally random (lets just say I got the feeling I may influence the standard derivation :-) ) I can at least understand people who think it is - Because it feels like it. But as we all know, feelings and math don't do well together ^^

[Ciryonde]

But one point: all written is only valid when it comes to solo randoms. Putting two or three good players into a group and let them act together will screw your model, like _FTD_ who played whooping 625 battles solo with 57,4% WR. His 2 Platoon games where 65,4% WR at 1525 games and 85% at 5800 games in 3 man groups.This still doesnt take his progress into account since I assume he doenst play solo anymore.

 

But still something to look at when seeing those skyhigh winrates.

 

A very good point, which I totally missed! But this only really affects _FTD_'s personal skill level and not the win rate vs luck reasoning. I update my advice: _FTD_, when you buy those lottery tickets, don't go alone. Bring two friends since that apparently that makes you incredibly lucky. #NoSkillInvolved

 

Edit: Actually this makes a pretty good case for skill over luck, since there is no reason that I can think of, that would make _FTD_ luckier in divisions than in solo queuing. Unless he/she is queuing with a rabbit's foot or something

[Bongels]

Great Post. So, my 68.83% WR in only 76 games is bob on for a 50% WR later on. Here I was thinking I was doing well. 

 

[Ciryonde]

Maybe I'll digger into this a little. Will have to check which assumptions you made and why :-)

 

Please do, my background is in statistical quality control, which is the art of knowing enough statistics to make other people believe that you know what you are doing without actually really knowing what you are doing yourself

 

Great Post. So, my 68.83% WR in only 76 games is bob on for a 50% WR later on. Here I was thinking I was doing well. 

 

Nah, you should be in the clear, you're win rate is outside what could be expected by chance alone. But there are other caveats, which is why i pointed out that is kinda unrealistic to assume a constant win rate, such as the fact that players are generally better at the higher tiers and depending on your learning curve vs you tier progression that might affect your win rate. So, you are probably above average, but probably not by that much compared to an average player

[ParEx]

 

Edit: Actually this makes a pretty good case for skill over luck, since there is no reason that I can think of, that would make _FTD_ luckier in divisions than in solo queuing. Unless he/she is queuing with a rabbit's foot or something

Again: If you take 2 friends of whom you know are good with you, 3/12 players are sure to be good, or with other words 2/12 = 1/6 less chance to have braindead players around you. This stronly affects the team.

 

[LilJumpa]

So you estimated the probability of a coinflip and added a confidence interval.

 

Gotta love that people are all excited about that.

 

 

[Ciryonde]

Again: If you take 2 friends of whom you know are good with you, 3/12 players are sure to be good, or with other words 2/12 = 1/6 less chance to have braindead players around you. This stronly affects the team.

 

 

Yes, that was my point as well, even though I might have been a little bit less clear about it It would be silly to argue that your personal win rate is based on luck and not your own skill and at the same time say that if you bring skilled people in a division, all of a sudden their skill starts affecting your win rate.

[_ramrus_]

You should try to see how much luck has influence on WR, by doing some real thinking, and then using math to create a model you think holds up.

This is nonsense.

 

[walter3kurtz]

You should try to see how much luck has influence on WR, by doing some real thinking, and then using math to create a model you think holds up.

This is nonsense.

 

 

Why is this nonsense?

[Ciryonde]

So you estimated the probability of a coinflip and added a confidence interval.

 

Don't rain on my parade...

 

Actually, what took the most time was writing the post in an accesible way. For me it would have been a lot easier just to write "Since the deviation from the mean of a binomial distribution is normally distributed, for sufficiently large samples, we will see a convergence towards the mean that will eliminate the factor of luck as the sample size grows, duh..." and be done with it. But the people who would understand that do not need this explained, and the people who do need this explained would not have understood that

 

You should try to see how much luck has influence on WR, by doing some real thinking, and then using math to create a model you think holds up.

 

Nah, I'm not interested in that since my model is robust enough to answer the question posed: "is win rate based on luck or skill?". Accurately modeling the effect of luck on win rate to answer that would be like using a pair of scissors to cut each individual straw in your lawn, effective, but not very efficient... 

[ParEx]

You should try to see how much luck has influence on WR, by doing some real thinking, and then using math to create a model you think holds up.

This is nonsense.

 

Luck is eleminated by large numbers. Everything else is skill in solo randoms.

Your post clearly shows you have not understood what he wrote and what it means.

 

[cracktrackflak]

Luck is eleminated by large numbers. Everything else is skill in solo randoms.

 

 

 

 

Assuming that there is no other factor involved, such as some form of active game management....

[LilJumpa]

 

Don't rain on my parade...

 

Actually, what took the most time was writing the post in an accesible way. For me it would have been a lot easier just to write "Since the deviation from the mean of a binomial distribution is normally distributed, for sufficiently large samples, we will see a convergence towards the mean that will eliminate the factor of luck as the sample size grows, duh..." and be done with it. But the people who would understand that do not need this explained, and the people who do need this explained would not have understood that

 

 

 

So you are saying you described a coinflip for people that have no clue about math.

 

The only thing that is related to WoWs are your examples, which describe that there are other factors involved, one of them being contribution to each game aka skill.

But since there are far more factors than that, I am not sure if you are serious or just trolling.

[Black0rchid]

Great topic ! ! ! 

 

Simplistic analisys for simplistic minds

 

I do believe though that for any serious conclusion to be drawn there would need to be a more deep analysis considering a lot of variables, such as ship classes most played, nation of ships, tier of ships, match making variables, matchmaking changes in the period of time, time spent solo or group playing......there are so many variables to be accounted for that I don't think it would be possible to draw conclusions with any degree of certainty unless you spent one or 2 years analyzing it.

 

As it is, this reminds me of how stupid statistic can be, me and a friend bought 1 chicken, I ate it all ....but statistically speaking between the 2 of us we ate in average 1/2 chicken each....so yeah, keep it up  

 

But for crapand giggles it was worth it