Basic stats to blow your mind

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FIRE!
Posts: 11
Joined: Sat Dec 27, 2014 8:12 am

Basic stats to blow your mind

Postby FIRE! » Tue Sep 08, 2015 1:32 pm

Ok, so the wins, losses, ELO, and ranks are all up on the score board. What happens when you dig into those numbers a little bit?

First, there are 103 names listed on the scoreboard. If you take away all of the players who have played 5 or fewer games, the number of players shrinks to 38.

According to the scoreboard, there have been been 2161 player games. The players ranked in the top 10 have played in 903 of those...which is about 42%. There have been 794 player wins, the players ranked in the top ten have won 429 of them. That means that 10 people of the 103 total players have won 54% of all games. There have been 1211 player losses, and people ranked in the top 10 only account for a third of the losses. So to sum up, the top 10 players win more than half the time and lose about a third of the games they play.

So, how do we explain wins? According to the pretentious people who are ranked in the top 10, they are mystic warriors channeling Ghengis Khan through their router. They are tacticians and strategists. Sometimes they will admit to being lucky, but that is very rare.

The point of playing is to win, and then, it is assumed that wins will increase your ranking. Let's see. If you place rank as your outcome variable and use wins as your only explanatory variable, the regression results show that wins is a statistically significant predictor of rank. The coefficient is negative which means more wins leads to a lower rank. The problem is that this model only explains 4-5% of the variation in rank, and the Root MSE is super high (27). All of those people who only played less than 5 games are causing lots of noise. If we restrict the model to only people ranked in the top 25, the same bivariate model explains around 40% of the variation and the Root MSE goes down to 5.6. So, for the top ranked players, wins does predict a lower rank.

So whet predicts wins? Is it genius? Strategy? Tactics? NOPE. Games played and Wins are correlated at 0.9363. In a simple bivariate regression, the number of games played explains 87% of the variation in wins. F=0.00, and the root MSE - 5.6, p= 0.00. If we control for only the top 25 players, nothing changes. The r-squared goes up to 88% in fact.

To put this is plain english, the number of games you have played is significant predictor of your wins, and your number of wins explains about 40% of your rank. Games and wins are almost interchangeable predictors of rank.

What does this mean? It means that the players with the most experience win the most games. It means that until anyone plays at least 50 games, they are at a drastic disadvantage, and this is illustrated by the number of people who drop out after getting crushed in their first 3 games. The trend still holds even for people with less than 50 games, however. This means that there is a steep steep learning curve the games being played on this site.

If you are a person on this site who has played 116 games in 6 months, please refrain from acting like you are a better "player" than anyone else. You have simply learned the boards better and that gives you an asymmetrical advantage.

The evidence is here and clearly stated. Knowing the boards and how to work through them is experience that makes the difference in winning games. Unless you spend hours playing on this site, you really have no chance. The reason that only 38 of the 103 people still play with any regularity is that people don't like getting their heads caved in all the time. It is frustrating, and people don't have time to learn all the intricacies or the complicated rules on the special boards before they have been curb stomped by -- snip -- no personal attacks please - e_i_pi

The people at the top can continue acting like "hey, sometimes I get lucky," or "hey, you just don't know how to place your forts," but the reality is that this site is set up only for people who can invest an inordinate amount of time playing risk. If you want to broaden the base, you have to change the way the game is played. If the players on this board would like to ever play against someone other than the top 10 people who play in 40% of the games and win half of those, then they should contact eipi and let him know. Otherwise, you have to just accept the fact that the Turkish Horse tribes will continue doing the same thing over and over and over and over and over and over and over...
Attachments
reg rank games & ranl wins.png
reg rank games & ranl wins.png (17.1 KiB) Viewed 7827 times
scatter games wins if games is less than 50.png
scatter games wins if games is less than 50.png (24.35 KiB) Viewed 7827 times
scatter wins games for all players with more than 5 games.png
Evidence
scatter wins games for all players with more than 5 games.png (27.64 KiB) Viewed 7827 times


FIRE!
Posts: 11
Joined: Sat Dec 27, 2014 8:12 am

Re: Basic stats to blow your mind

Postby FIRE! » Tue Sep 08, 2015 1:35 pm

More evidence
Attachments
reg rank wins if rank is less than 26.png
reg rank wins if rank is less than 26.png (8.99 KiB) Viewed 7826 times
reg wins games if rank is less than 26.png
reg wins games if rank is less than 26.png (9.13 KiB) Viewed 7826 times
scatter_games_wins_lfit.png
scatter_games_wins_lfit.png (27.4 KiB) Viewed 7826 times

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e_i_pi
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Re: Basic stats to blow your mind

Postby e_i_pi » Tue Sep 08, 2015 6:40 pm

FIRE! wrote:Ok, so the wins, losses, ELO, and ranks are all up on the score board. What happens when you dig into those numbers a little bit?

You get an inaccurate result set, since the scoreboard only includes people who have taken a turn in the past month.

FIRE! wrote:So, how do we explain wins? According to the pretentious people who are ranked in the top 10, they are mystic warriors channeling Ghengis Khan through their router.

Okay, so this one made me laugh. I used to play at Conquer Club - the top rated people played only against people of lower rank, and foe'd anyone who was any good at the game. ELO is an inherently flawed system, but more on this later.

FIRE! wrote:To put this is plain english, the number of games you have played is significant predictor of your wins, and your number of wins explains about 40% of your rank. Games and wins are almost interchangeable predictors of rank.

Yep yep yep. The proposed scoring system will address this. In essence the scoring will be based on how easy/hard it is to win at a particular metric. That metric may be number of players per team, number of teams, the empire, the faction, etc etc. I have to get cron jobs in before I can start this endeavour, as it will be database intensive.

FIRE! wrote:What does this mean?
...
This means that there is a steep steep learning curve the games being played on this site.
...
It is frustrating, and people don't have time to learn all the intricacies or the complicated rules on the special boards before they have been curb stomped by -- snip -- no personal attacks please - e_i_pi

Please don't personally attack people, that's the first step along the path of bans.

That said, there is a very real problem of players being disheartened by getting flogged in their first few games. There's a few ways we can address this, I was thinking the best way would be to have divisions that players are allotted in, and every 3 months or so there is a promotion/relegation that swaps the top/bottom players between divisions. I think this would be pretty fun, and would corral the inexperienced players in an area where they don't get flogged straight away. The problem is, we don't have that many active players, so unless we want to have games of no more than 8 players or so, we're screwed. I'm open to suggestions here, we really need to solve the dual problems of not enough players and disheartened players.

FIRE! wrote:The people at the top can continue acting like "hey, sometimes I get lucky," or "hey, you just don't know how to place your forts," but the reality is that this site is set up only for people who can invest an inordinate amount of time playing risk. If you want to broaden the base, you have to change the way the game is played. If the players on this board would like to ever play against someone other than the top 10 people who play in 40% of the games and win half of those, then they should contact eipi and let him know. Otherwise, you have to just accept the fact that the Turkish Horse tribes will continue doing the same thing over and over and over and over and over and over and over...

Turkic Horse Tribes aren't the easiest, Moors is I believe. Anyhow, that should change with the new Medieval Era rules which are now live! We can adjust this later on. Also, the proposed scoring system will mean easier empires generate less points. If you specialise in one empire or faction, you'll get diminishing returns as well.

Dinner is ready, I gotta fly, thanks for the posts, wish I listened more in stats at Uni to absorb this properly. If you want replete stats for the scoreboard (not just the past month) contact me and I'll shoot a CSV your way.

Regards,
e_i_pi

Sargon
Posts: 40
Joined: Tue Jan 20, 2015 9:46 am

Re: Basic stats to blow your mind

Postby Sargon » Wed Sep 09, 2015 1:31 am

Fire,

One of the first things I learned in my statistics class over a decade ago (which I got an A+ in, by the way, at the undergraduate level, but I admit I am rusty) was that the data has to be complete, and since the scoreboard has only a portion out of the over 6000 players on the site, you'll have to take up e_i_pi on his offer to send you the entire data set. The "top ten" might not even be in the top 10, which is why I always say that the scoreboard is only a general idea.

It means that the players with the most experience win the most games. It means that until anyone plays at least 50 games, they are at a drastic disadvantage, and this is illustrated by the number of people who drop out after getting crushed in their first 3 games. The trend still holds even for people with less than 50 games, however. This means that there is a steep steep learning curve the games being played on this site.


Unless you spend hours playing on this site, you really have no chance.


This is why I help new players, even if I lose the game. Some players learn faster than others. You cannot assume everyone will learn at the same speed as you.

According to the pretentious people who are ranked in the top 10, they are mystic warriors channeling Genghis Khan through their router. They are tacticians and strategists. Sometimes they will admit to being lucky, but that is very rare.


This is the second time you are misusing that word. Pretentious means "attempting to impress by affecting greater importance, talent, culture, etc., than is actually possessed." Since you admit that some on the board have more experience, and since you've applied that word to myself privately, I/we cannot be pretentious because not only do we have more experience, not only are our arguments valid, they are right (like the discussion we had about the besiege, and I attempting to explain to you that you do not need a cavalry to besiege). You cannot assume people are pretentious because you lack understanding in how things work.

In fact, you were reading from this site's explanation which was in fact incorrect (another reason why I like to help newer people) yet you assumed it was correct, yet I knew better and was trying to help you. I received jabs, name-calling, and insults in return.

So what predicts wins? Is it genius? Strategy? Tactics? NOPE.


Of course experience leads to more wins. I agree with you on that. But there is strategy involved also. Knowing the board is not always enough.

If you are a person on this site who has played 116 games in 6 months, please refrain from acting like you are a better "player" than anyone else. You have simply learned the boards better and that gives you an asymmetrical advantage.


This is obviously a jab at me. I learn quickly and I know how some of the other players play. But there are other factors. Diplomacy, knowing when to strike, knowing when not to strike, etc. are all factors. By your own logic, I have a decent number of wins. That means I have to be doing something right, right? Would you agree with me?

Also, usually winning against eight will yield more points than winning against three, so a player could have a high rating but only a small percentage of wins.

Conclusion: you can't make blanket generalizations; there are too many variables here.

The evidence is here and clearly stated.


You speak with great clarity, but I cannot accept your evidence.

The people at the top can continue acting like "hey, sometimes I get lucky," or "hey, you just don't know how to place your forts," but the reality is that this site is set up only for people who can invest an inordinate amount of time playing risk. If you want to broaden the base, you have to change the way the game is played. If the players on this board would like to ever play against someone other than the top 10 people who play in 40% of the games and win half of those, then they should contact eipi and let him know. Otherwise, you have to just accept the fact that the Turkish Horse tribes will continue doing the same thing over and over and over and over and over and over and over...


This is not a correct conclusion. You control the number of games you are in. You also do not have to join games with players you don't want to play with, although I admit sometimes this cannot be avoided. Actually, perhaps in the future some sort of filter mechanism could be set up to accept only certain players in games, although, in practice, this might not be practical. I like e_i_pi's idea about the divisions.

Sargon

Sargon
Posts: 40
Joined: Tue Jan 20, 2015 9:46 am

Re: Basic stats to blow your mind

Postby Sargon » Wed Sep 09, 2015 1:49 am

e_i_pi wrote: I used to play at Conquer Club - the top rated people played only against people of lower rank, and foe'd anyone who was any good at the game.


Right. I play on another site also (although not as much), and there are tons of gang-ups, cliques, etc. There is actually more luck there, because there is generally only one battle type and it really does come down to luck. That's why this site is better, because experience here plays more of a factor, and there are other variables which offset the luck.

That's my opinion, for whatever it's worth.

e_i_pi wrote: That said, there is a very real problem of players being disheartened by getting flogged in their first few games. There's a few ways we can address this, I was thinking the best way would be to have divisions that players are allotted in, and every 3 months or so there is a promotion/relegation that swaps the top/bottom players between divisions. I think this would be pretty fun, and would corral the inexperienced players in an area where they don't get flogged straight away. The problem is, we don't have that many active players, so unless we want to have games of no more than 8 players or so, we're screwed. I'm open to suggestions here, we really need to solve the dual problems of not enough players and disheartened players.


Personally, that's why I like to play with new players as well as strong players. I would like to think that newer players would feel better about having a teammate who is more experienced; they can benefit and maybe persuade others to join the site. The player that helped me isn't even on the scoreboard! If he hadn't helped me, it would have taken much longer to learn the game.

I really like that division idea. :D

Sargon

FIRE!
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Re: Basic stats to blow your mind

Postby FIRE! » Wed Sep 09, 2015 9:23 am

Good god...the things that come out of your mouth Sargon. You are so convinced that you are right, but the things you type are 90 percent nonsense. The first thing you learned in your undergraduate statistics class was that data has to be complete? Have you ever heard of sampling? Have you ever heard of the central limit theorem? Have you ever heard of confidence intervals? According to your A+ logic any pollster would have to survey a "complete data set" to be able to make predictions about elections or anything else for that matter. It is called SAMPLING for a reason. I guess maybe they didn't cover that in your university class, otherwise you would realize how silly this sounds. Before I address some of the problems with your opinions, we should all just sit here and bask in the glorious way that you opened your critique of my very basic statistical analysis. You began with a completely false statement, but you took on the tone of someone who thinks they have right on their side. Even though you have no idea what my background is, you assume that your limited statistical knowledge gives you some authority to criticize what I wrote, even though there s very little chance you actually looked at the regression results that I posted to verify my claims. Let me see--what word describes a person who "attempts to impress by affecting greater knowledge than is actually possessed?" Oh yes, PRETENTIOUS. You proved it to everyone right here, right now, in public. I would be embarrassed for you, but you bring it on yourself.

Ok, back to sampling. First, Unless there have been drastic changes that either led to a whole new set of people joining the site or a group of people with very similar characteristics leaving at the same time, then there is good reason to believe that the set of observations from the current score board is representative of the entire data set. If those scenarios did happen, however, then there there is reason to believe that this sample is skewed, and that it is not representative of the larger population. Here is the thing...you only use sampling when you are trying to generalize about the greater population. Of course, we would be interested in those types of generalizations about all of the players, but they are not necessary. We can use this set of data, and analyze it as if it is the entire universe of players. The results that I posted show a very strong relationship between games played and wins and wins and ranking, but they only explain what is going on for this sub-set of data, not for the entire universe of people who have ever played on the site. If eipi wants to send me that csv file, I will run the same regressions and post the findings.

The good thing about statistics is that you can calculate how well your model fits the data. I used STATA to analyse these data. The F-score shows how well the entire model reflects reality...and these scores on all of the bivariate regressions are much lower than the 0.05 cutoff. Most of them are actually 0.00. The Root MSE shows how accurate the model is. As the N goes up, the RMSE usually goes down. 103 cases is not that much, and the result is that the RMSE in the best models is around 5-6. That is not great, but it is better than 27. The p-values associated with confidence intervals explain how likely it is that we got these results by accident. All of the p-values in these models are are between 0.002 and 0,000, which means that we did not get these results by random chance. Basically, using a single variable--games played--to explain variation in the number of wins creates a model that is pretty well specified with variables that are highly significant. There is not much way to dispute that.

Finally, there are three scatter plots. The first is only people who have played less than 50 games, and any monkey can see that there is almost a 1 to 1 relationship between games played and wins for beginners. The second is all players with more than 5 games played. The slope is less extreme but the relationship is still very strong and very positive. Finally, the third one is only the top 25 ranked players, and the relationship looks almost exactly the same as the first one. That means, that using 3 different subsets of this data, the relationship between games played and winning holds in all cases.

So here is the thing...I don't care if you accept my evidence because your opinion is based purely on your own inflated sense of self. How many times can you type, "I learn quickly" in one post? The numbers are what they are. All of the statistical checks used to test whether a model is properly specified pass muster. The second model shows that for every 10 games played, a player in the top 25 would expect to win about 4.78 more games. If you compare that to the very basic descriptive statistics I started the first post with, you will see that they both come to the same conclusion. The top players win about 50% of the games. Strictly from a perspective of competitive balance, you have to acknowledge that this number is not positive if the goal is to attract new people to the site.

Sargon
Posts: 40
Joined: Tue Jan 20, 2015 9:46 am

Re: Basic stats to blow your mind

Postby Sargon » Wed Sep 09, 2015 6:09 pm

Fire,

Good god...the things that come out of your mouth Sargon. You are so convinced that you are right, but the things you type are 90 percent nonsense. The first thing you learned in your undergraduate statistics class was that data has to be complete? Have you ever heard of sampling? Have you ever heard of the central limit theorem? Have you ever heard of confidence intervals? According to your A+ logic any pollster would have to survey a "complete data set" to be able to make predictions about elections or anything else for that matter. It is called SAMPLING for a reason. I guess maybe they didn't cover that in your university class, otherwise you would realize how silly this sounds. Before I address some of the problems with your opinions, we should all just sit here and bask in the glorious way that you opened your critique of my very basic statistical analysis. You began with a completely false statement, but you took on the tone of someone who thinks they have right on their side. Even though you have no idea what my background is, you assume that your limited statistical knowledge gives you some authority to criticize what I wrote, even though there s very little chance you actually looked at the regression results that I posted to verify my claims. Let me see--what word describes a person who "attempts to impress by affecting greater knowledge than is actually possessed?" Oh yes, PRETENTIOUS. You proved it to everyone right here, right now, in public. I would be embarrassed for you, but you bring it on yourself.



You're right. My knowledge of statistics is limited. I was simply trying to say that even with sampling incorrect conclusions can be drawn. My apologies for not being more precise.

So what predicts wins? Is it genius? Strategy? Tactics? NOPE. Games played and Wins are correlated at 0.9363. In a simple bivariate regression, the number of games played explains 87% of the variation in wins. F=0.00, and the root MSE - 5.6, p= 0.00. If we control for only the top 25 players, nothing changes. The r-squared goes up to 88% in fact.

To put this is plain English, the number of games you have played is significant predictor of your wins, and your number of wins explains about 40% of your rank. Games and wins are almost interchangeable predictors of rank.

What does this mean? It means that the players with the most experience win the most games. It means that until anyone plays at least 50 games, they are at a drastic disadvantage, and this is illustrated by the number of people who drop out after getting crushed in their first 3 games. The trend still holds even for people with less than 50 games, however. This means that there is a steep steep learning curve the games being played on this site.


At the end of the day, you're trying to prove through the statistics that experience through games played is the primary predictor of wins, and this is not completely correct. It's one factor, I agree 100%, but not the entire factor. There are so many variables here. You are getting so bogged down with the details of the statistics that you are not seeing the forest for the trees. You need to step back and see that the statistics are only one part of the story.

So here is the thing...I don't care if you accept my evidence because your opinion is based purely on your own inflated sense of self. How many times can you type, "I learn quickly" in one post? The numbers are what they are. All of the statistical checks used to test whether a model is properly specified pass muster. The second model shows that for every 10 games played, a player in the top 25 would expect to win about 4.78 more games. If you compare that to the very basic descriptive statistics I started the first post with, you will see that they both come to the same conclusion. The top players win about 50% of the games. Strictly from a perspective of competitive balance, you have to acknowledge that this number is not positive if the goal is to attract new people to the site.


I don't know why someone as intelligent as yourself has to betray that intelligence by resorting to name-calling and character assassination. You've whined and name-called ever since you've been here. Your negativity is quite apparent.

What I find interesting is that you claim that experience predicts wins, yet you have only 9 wins in 39 games and have a rating of 798. I know that others got to the top ten by that point. So your own logic betrays you. If game plays and wins are correlated as you say, you're definitely doing something wrong, compared to what others have done. Experience on the website (which does not not equate to hours spent here) is not the be all and end all. Understanding the interactions/facets of the game is more relevant, which you have not understood yet, evidenced by your troop deployment, for example, your lack of understanding of the battle type besiege setup after 39 games, and your not reading the game logs, to name a few. There might be a steep, steep learning curve for you, but others are getting it more quickly. There's nothing wrong with that, but you cannot spam statistics and get upset at others simply because you haven't understood certain things yet.

I also think that win percentages might decrease as more players are added, but that's a whole other topic.

Sargon

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El Regalo
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Re: Basic stats to blow your mind

Postby El Regalo » Sat Jan 14, 2017 4:33 am

i just started playing, but im confident that it will NOT take me long to start winning, particularly with the more basic versions of the game. and so i expect to start climbing in the rankings in the not too distant future. as a math teacher im not usually one to argue with statistics, but didn't Mark Twain (or was it Benjamin Disreali?) say, "There are three types of lies: lies, damned lies, and statistics"?


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