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#1 bmende

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Posted 04 July 2014 - 11:30 PM

is there no one that has gold or platinum? is it even possible to get that? And once you advance a metal, can you be demoted back to the previous metal?



#2 The Prof

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Posted 05 July 2014 - 01:55 AM

No one is currently gold or platinum.  It is theoretically possible to do but practically it is close to impossible.  Under the current system I would be surprised if there are ever is a gold player.  I would like to see the site realign the point ranges for each rank and league to make use of all levels.  You can get demoted to a lower rank and league if your rating drops enough.



#3 Napoleon 1er

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Posted 05 July 2014 - 08:46 AM

The Prof may correct me but the whole thing is mathematical. Now first ranked silver players like Satan-NL or Sohal, because they are at the top of the leaderboard, when they get a victory they can never get more than 12 points because they play always against lower ranked players. Also the broadest the rank distribution (The Prof let us know if in this case we can call that a standard deviation) the lower the average points they will win in case of victory because the broadest the rank distribution the biggest the rank points difference between them and their opponent. So probably now on average they may win 2 points for each victory while they may loose on average around 20 points for each defeat. So to continue climbing the ranking they need to have a %win >90%, extremely difficult. The other solution is to wait until the breadth of the rank distribution decreases (= until there will  be more players ranked with low number of points difference with them) so their average points won per victory will increase, allowing them to continue climbing the ranking.

Conclusion: Satan-NL needs probably something like ~180 points to reach gold spy level, with his 93%win ratio and considering an average 2 points win for each victory and 20 points loss for each defeat, for each 100 games he will be playing he will make progress of 93x2-7x20=46 ranking points. To reach gold level he will need to play another 180/46= 392 games.

So yes gold is reachable and maybe reached in a not to far future if the number of active high ranked players (with small difference of points from Satan-NL) increases substantially. Platinum level could be removed for time beeing as it is most likely not reachable until very far future and only if the number of gold ranked players will be sufficiently high to enable ranking climbing for the top ranked players. If in 10 or 20 years we reach such situation maybe we can reintroduce the platinum level at this time.

 

...I love mathematics :)

 

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#4 kienzan

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Posted 05 July 2014 - 06:52 PM

As napoleon explained you will need an impossible win ratio to reach gold and platinum.

The only way to realistically make gold or platinum reachable is to inflate the points in the rating system.

 

Lets assume that the number of points is stable.
These points are distributed to all  the players according to their skill.
Satan gets lets say 1000 points which we assume it is  0,01% of the total points.
The platinum threshold is at 10.000 points.
If the number of players remains stable we need 10 times more points in the system so that satan's 0,01% ratio will correspond to 10.000 points and make it realistic for satan to reach platinum.

The way the system is set up right now the only way to introduce new points in the system is when the guys ranked as bronze Spies with 100 points lose a match. When this happens the winner gets 12 points but the loser does not lose any points at all. Thus every time a  bronze spy loses a game the event introduces 12 new points in the system. The rest of us when we play a game we just exchange the points already in the system.

As you can see the system is unsustainable as the amount of points will always increase. Thus as more of these 100 point players lose games, higher ranks will become more reachable for everyone else. Theoretically, given "infinite"  time (long long long long time) reaching the gold marshal status will be something that most of the players will be able to achieve.



#5 The Prof

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Posted 06 July 2014 - 02:32 AM

Both Napoleon’s and Kienzan’s analysis are partly right.  First, it is known from this screen shot http://imagizer.imageshack.us/a/img839/1589/xrve.png that it takes 1208 points to become a silver marshal, and since the point ranges get wider as ranks increase, 1350 seems to be a good estimate for what it would take to become a gold spy.  I think Napoleon’s estimate of an average of 2 points a game is about right.  However, if you get 2 points for a win then you get 23 points deducted for a loss, since the total of these two numbers must be 25.  So assuming a 93% win ratio, S-NL will average 2*(.93) + (-23)*(.07) = 0.25 points per game.  At this rate it would take him over a 1000 games to reach gold spy!   Kienzan makes a very good observation that additional points in the system come into being only when a player with rating of 100 or very close to it loses a game.  However, it is not correct to assume that players who maintain their current level of play will maintain the same percentage of total points as the number of points in the system increases.   The highest number of points a player can reach is limited by the difference in skill between the best player and a player brand new to the game.  This difference will naturally be greater in games of pure skill, like Chess, than in those that involve some degree of luck, like Stratego.  In order to support the number of players in each range of 100 points there needs to be typically more than twice as many players in the range of 100 points below it.   The numbers below show the number of accounts at Stratego.com in various ELO ranges:

 

Range         Number of accounts

1100 to 1199 ………   1

1000 to 1099 ……….  3

900 to 999 …………  12

800 to 899 …………  48

700 to 799 …………  137

600 to 699 …………  332

500 to 599 …………  578

400 to 499 ………… 1090

300 to 399 ………… 2240

200 to 299 ............... 4814

 

As you can see, this factor of two between numbers in consecutive groups is a conservative estimate, as it appears to be higher in the silver ranks.  Thus, in order to produce and maintain a player in the 1200 to 1299 range, we would likely need at least twice as many total players as we have now in order to support the whole pyramid.  To have 1300 to 1399 player we would need more than four times as many total players at all levels.  For every 100 additional points the highest player can achieve, the number players below him at each level should at least double, and likely more than a doubling of players is needed in the silver ranges.   


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#6 tableplay

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Posted 06 July 2014 - 04:21 AM

Xerxes, the histogram you have provided in your most recent post does not take into account multiple aliases for a player and therefore drawing conclusions from it may be problematic (particularly at the silvier/tail end of the discrete probability distribution you provided).Furthermore, in your Expected Value/E(x) calculation using a winning percentage of .93, you assume that the winning percentange is a constant and I'm not sure this is the case (perhaps a confidence interval for the winning percentage could be calculated by assuming a particular probability density function for the winning percentage or creating an empirical pdf by tracking winning percentage via snapshots as a player accumulates games played and then computing E(E(x)) ). In any case, thank you for your efforts.

 

Cheers, tp.

Both Napoleon’s and Kienzan’s analysis are partly right.  First, it is known from this screen shot http://imagizer.imageshack.us/a/img839/1589/xrve.png that it takes 1208 points to become a silver marshal, and since the point ranges get wider as ranks increase, 1350 seems to be a good estimate for what it would take to become a gold spy.  I think Napoleon’s estimate of an average of 2 points a game is about right.  However, if you get 2 points for a win then you get 23 points deducted for a loss, since the total of these two numbers must be 25.  So assuming a 93% win ratio, S-NL will average 2*(.93) + (-23)*(.07) = 0.25 points per game.  At this rate it would take him over a 1000 games to reach gold spy!   Kienzan makes a very good observation that additional points in the system come into being only when a player with rating of 100 or very close to it loses a game.  However, it is not correct to assume that players who maintain their current level of play will maintain the same percentage of total points as the number of points in the system increases.   The highest number of points a player can reach is limited by the difference in skill between the best player and a player brand new to the game.  This difference will naturally be greater in games of pure skill, like Chess, than in those that involve some degree of luck, like Stratego.  In order to support the number of players in each range of 100 points there needs to be typically more than twice as many players in the range of 100 points below it.   The numbers below show the number of accounts at Stratego.com in various ELO ranges:

 

Range         Number of accounts

1100 to 1199 ………   1

1000 to 1099 ……….  3

900 to 999 …………  12

800 to 899 …………  48

700 to 799 …………  137

600 to 699 …………  332

500 to 599 …………  578

400 to 499 ………… 1090

300 to 399 ………… 2240

200 to 299 ............... 4814

 

As you can see, this factor of two between numbers in consecutive groups is a conservative estimate, as it appears to be higher in the silver ranks.  Thus, in order to produce and maintain a player in the 1200 to 1299 range, we would likely need at least twice as many total players as we have now in order to support the whole pyramid.  To have 1300 to 1399 player we would need more than four times as many total players at all levels.  For every 100 additional points the highest player can achieve, the number players below him at each level should at least double, and likely more than a doubling of players is needed in the silver ranges.   



#7 The Prof

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Posted 06 July 2014 - 07:10 AM

Tableplay, I admit that we have an imperfect data set to work with because of the proliferation of multiple accounts, however I believe that my conclusions still are valid because if there were only one account per player then although the numbers of players in each ELO range would be smaller, the ratios of these numbers would likely still be approximately the same.  You're right that in general win percentage is not constant.  It depends on the ratings difference between opponents.  In the special case of S-NL, I think it is fairly constant though, since the pool of opponents he is matched with will not likely change as his points increase or decrease a bit since regardless he is in the number one position.  It would be nice to have a sortable database of all game results to investigate if win percentage is as ELO would predict for games between various levels of opponents. 



#8 Napoleon 1er

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Posted 06 July 2014 - 10:54 AM

the interesting thing with this maths is that with ELO calculation system a top player can continue climbing the ranking only if there is a sufficiently high number of players "close" to him in ranking, so the progression of a top player depends not only on his personal skills but also on the skill level of other players!!! ... in other words if Satan-NL wants to continue climbing the ranking it is his advantage to help other players to improve themselves!!! ... is stratego becoming a "team game"? ... interesting conclusions, right? ;)

 

Regarding the question of the influence of multiple accounts I'm not sure it plays a real role in their as a player with 2 accounts is equivalent (from this purely mathematical consideration) to 2 players having exactly same skill level.

 

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#9 tableplay

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Posted 06 July 2014 - 05:49 PM

Hi Napoleon, the tricky bit is the fact that some aliases of a given player are deliberately sandbagged (to the point that they often have aliases in multiple bands of the histogram) by the player in order to gain intel on setups and playing styles of non-cheating opponents and also to cause other players to lose points when the sandbagged alias is then played at the normal skill level (since setups and playing strategies by the legitimate player are executed with the artificially low rating of the sandbagging opponent's alias' in mind). The true ratio between contiguous bands may be so skewed by these factors that the two to one rule may actually be a fallacy if unique ids could actually be instated. Anyway, the efforts of you and Xerxes are much appreciated.

 

Cheers, tp.

 

the interesting thing with this maths is that with ELO calculation system a top player can continue climbing the ranking only if there is a sufficiently high number of players "close" to him in ranking, so the progression of a top player depends not only on his personal skills but also on the skill level of other players!!! ... in other words if Satan-NL wants to continue climbing the ranking it is his advantage to help other players to improve themselves!!! ... is stratego becoming a "team game"? ... interesting conclusions, right? ;)

 

Regarding the question of the influence of multiple accounts I'm not sure it plays a real role in their as a player with 2 accounts is equivalent (from this purely mathematical consideration) to 2 players having exactly same skill level.

 

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#10 The Prof

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Posted 06 July 2014 - 06:04 PM

It’s kind of funny to talk about S-NL “climbing the rankings”, since he is already at the top.  If his only goal is to stay number one, regardless of his ELO rating, then it is not in his personal interest to help others get better.  Now, if his goal is to become a gold level player then it’s true that there needs to be a group of players ranked in the 1100s and 1200s to support that.  The problem is that if he helps players enough that they can rise to at or near his current level then it is likely that his future win percentage against these players will not be as high as it otherwise would have been.  So a decrease in wins would cancel out the fact that he would be getting a bit more points for each win and we may not see any upward movement.  Thus, helping players is unlikely to have much effect. I just don’t see the top players increasing their rating much more than it is now without a large influx of new players, combined with a reduction (or elimination) of new accounts of current players.  When a new players come to the game, everybody currently playing can expect to get a bit of a ratings increase, as the additional points created are filtered through the system.  However, when an old player starts a new account then it drags down the ratings of all their opponents because until the new account reaches it's true ELO rating, his opponents don’t get as many ELO points as the should for a win against the new account, and they get more points deducted for a loss.


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#11 Napoleon 1er

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Posted 06 July 2014 - 06:33 PM

...in summary we can say then that as long as a player is playing with his second alias below his true skill level it has an effect to "keep down the average ranking of all players who are below his own true ranking", same thing if a player is playing with an alias against some higher ranked player from whom he would know the setup from a prior game with his first alias. On average the aliases have for effect to artificially keep the average ranking of each player lower than it should be if everybody would have only one account. Did I summarize correctly? If it is like that and because this effect is likely to affect on average everybody in the same manner we can conclude that it has no impact on the rank of a player compared to the others, it has only impact on the ranking points (that are on average lower than what it should be).

then I have a question: If a player has played 300 games with alias 1 and 300 games with alias 2, do you think that his highest ranked alias is higher, lower or same ranked as if he would have played 600 games with 1 alias only? For me, if his win ratio is significantly higher than 50%,  his 2 accounts with 300 games each will be ranked far below what he would have reached playing 600 games with one alias only. Why? because as long as his win ratio is higher than 50% it means he is on average winning more games than what he is losing, so he must be on average climbing the ranking the more he plays. This is of course true only when you are not too high ranked and when the matching system has equal probability to match you with a higher or a lower ranked player.

 

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#12 The Prof

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Posted 07 July 2014 - 07:28 AM

The impact of a good player starting over with a new alias reduces the overall average rating of the set of all other players, but it does not affect all players equally.  It primarily affects those who are unlucky enough to be the opponents of the alias account, and to a much smaller extent opponents of these opponents.  It is not likely to hurt at all the main account of the player using the alias, especially if the main account is not being used during this time, so the main account stands to possibly gain relative to others.  An alias account will bring down the ratings of its opponents, up until the time when his rating reaches that of his main account.  This is why in a world without aliases players could achieve a higher amount of rating points that they currently can.   

 

To the second part of your post, if a player maintains a win percentage significantly about 50% for 300 games he will have a high rating and at that point most opponents will be ranked below him, so he will need to have an even higher win percentage than before in order to keep increasing his points.  Because 300 games is plenty to get to one’s true rating commensurate with one’s skill level, playing an additional 300 games is not any more likely to increase one’s rating as to lower it, assuming one’s skill level to be constant.  So 600 games does not necessarily lead to any better rating than 300 games.



#13 Sohal

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Posted 07 July 2014 - 09:03 AM

The impact of a good player starting over with a new alias reduces the overall average rating of the set of all other players, but it does not affect all players equally.  It primarily affects those who are unlucky enough to be the opponents of the alias account, and to a much smaller extent opponents of these opponents.  It is not likely to hurt at all the main account of the player using the alias, especially if the main account is not being used during this time, so the main account stands to possibly gain relative to others.  An alias account will bring down the ratings of its opponents, up until the time when his rating reaches that of his main account.  This is why in a world without aliases players could achieve a higher amount of rating points that they currently can.   

 

 

 

well, i'm not sure with that Xerxes

let see with me, I have 2 accounts (Sohal and Cosinus). If i play the same way with both accounts, i should lose the same game and win the others, or i should have the same win ration against hielco for example

so i agree in the first 100 games you'll give people more losses than they should have, but after that period it should not change anything



#14 kienzan

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Posted 07 July 2014 - 09:49 AM

High ranking players creating double accounts acts like a point sink for the system. Which means there are less points to share

Lets say you create a second account and it reaches 800 points and is stable around that area. That means you have drained 700 points from the system (100 you started with + 700 you leached from others to reach the 800 point mark).

It mistaken  to assume that this effects ony the players you played with. Now we all have 700 points less to share between us which is making it harder for everyone to reach higher rankings.

In order to balance the effect yous second account had 700/12=58 games must be lost from Bronze Spy players in order to counteract the point draining effect of a new 800 point second account.

Imagine now all high ranked players creating multiple accounts. That means thousands of points drained from the system into these accounts.

 


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#15 Napoleon 1er

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Posted 07 July 2014 - 06:02 PM

I like your approach kienzan. So let's assume that sohal would have played all cosinus games with sohal account. He would have increased his sohal ranking by xxx points instead of the 900+ points he got for cosimus. So the difference of 900+ and xxx sould in fact belong to other players.
In fact without aliases there would be much less accounts but with much higher ranking on average. So there would have been more silver which would have allowed sohal to get even more points. Possibly gold level would alreafy been reached. High ranked players with multiple aliases are thus just shootimg a bullet in their own foot.

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#16 Sohal

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Posted 08 July 2014 - 09:33 AM

nope 

 

i would have earn 1 point/victory with Sohal account when i got 25 points with cosinus account in my firsts games



#17 The Prof

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Posted 08 July 2014 - 05:29 PM

well, i'm not sure with that Xerxes

let see with me, I have 2 accounts (Sohal and Cosinus). If i play the same way with both accounts, i should lose the same game and win the others, or i should have the same win ration against hielco for example

so i agree in the first 100 games you'll give people more losses than they should have, but after that period it should not change anything

 

I agree with this, that’s why I said “until the time when his rating reaches that of his main account”.  Before that, Cosinus would have taken more points than usual by beating hielco, even though the win ratio would be the same.  When the alias rating reaches the main rating then things are fine, unless a player uses an alias account to secretly gain information on opponents who he might play on the other account.

 

nope 

 

i would have earn 1 point/victory with Sohal account when i got 25 points with cosinus account in my firsts games

 

Cosinus took all those points from many different players, lowering their ratings.  So if Sohal later plays against some of those players he would get fewer points by beating them than if Cosinus had never existed.  What we are saying is not that alias accounts can't accumulate points quickly, but that the maximum number of points a top player can reach is hindered by the existence of multiple accounts.

 

High ranking players creating double accounts acts like a point sink for the system. Which means there are less points to share

Lets say you create a second account and it reaches 800 points and is stable around that area. That means you have drained 700 points from the system (100 you started with + 700 you leached from others to reach the 800 point mark).

It mistaken  to assume that this effects ony the players you played with. Now we all have 700 points less to share between us which is making it harder for everyone to reach higher rankings.

In order to balance the effect yous second account had 700/12=58 games must be lost from Bronze Spy players in order to counteract the point draining effect of a new 800 point second account.

Imagine now all high ranked players creating multiple accounts. That means thousands of points drained from the system into these accounts.

 

 

Nice work, Kienzan!  The concepts of a point store and point sink that you have introduced, and a method to quantify how many points are created or destroyed, are an excellent contribution to our understanding.   I do agree with you that eventually points lost due to alias accounts do work their way throughout the whole system, although I still maintain that in the short term some players are more impacted than others.  Regarding the introduction of new points, it is a bit more complicated than just 12 points for every bronze spy loss.  Any time a player with at or near 100 points loses, the points created will be equal to the difference between 100 and what his points would have been if there were no lower limit.  For example if a player rated 105 loses to a player rated 200 this difference in ratings would normally result in a loss of 9 points, but since he cannot go below 100 it is only a loss of 5 points, so 4 points are created (since the 200 rated player wins 9 points).  The number of points introduced into the system by a new player varies depending on how fast that player improves.  A player who begins with a long string of consecutive losses could potentially provide a lot of points to the rest of us.  However, keep in mind that, as shown by my analysis in Reply #5, the amount of new points has to grow exponentially to result in even a linear growth of the maximum ELO points top players can get.



#18 GaryLShelton

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Posted 20 July 2014 - 03:59 AM

When the alias rating reaches the main rating then things are fine, unless a player uses an alias account to secretly gain information on opponents who he might play on the other account.

 

 

I am curious how someone is supposed to gain information on another player with a "new" account when they will start at the bottom with said new account.  The computer won't generally pair them with someone they may want to gain information on until they are much farther along with a higher ranking.  At that time they probably shouldn't be taken lightly by their higher opponent anyway.  I suppose it is possible to get a lucky game matchup here and there with someone very high, but it doesn't sound like a dependable way to do scout opponents.

 

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#19 Mitthunder

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Posted 21 March 2015 - 03:57 PM

Is there a way for the mods to find out how many new points are created on a daily basis from losing bronze spies? That would be interesting. While I would like to see a new system that allows silver players to reach gold and platinum, it is pretty obvious who is the best without it. Satan-NL currently has 1176 points, the only silver general, with more than 150 points difference from rank 2, while rank 2 is really close to rank 3. Knowing how difficult it is to do that with the current system, you could say he's the Usain Bolt of Stratego.  :lol: He's in a league of his own...

 

You could introduce a referral system to refer friends to the site. This could speed up expansion of the community and in turn create more points in the system. You could put more ways in the system to create extra points. For example, when a player wins twice or more in a row, on his next loss he will only lose half the points he normally would while the winner gets as much as he normally would. Like a reward for your win streak.



#20 Midnightguy

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Posted 03 April 2015 - 06:06 AM

I have written a few times in the past we should adopt the Chess Federation rating system or at least instead of having tons of titles such as Bronze Captain, Silver Spy or Gold General.... Just have for example:

 

Rating & Rating name

850+ Marshal

751–850 General

651–750 Colonel 

551–650 Major

451–550 Captain

351-450 Lieutenant 

251–350 Sargent 

176–250 Miner

126–175 Scout

below 125 Spy

 

Some of our high silvers under Napoleons clean rating system are already at this 850+ rating system so they would be just rated as a Marshal instead of Silver Colonel or General and as we are seeing right now, Course my chart is just an example of when someone should get a new title.






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