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ELO-scores for all leagues, including Gold and Platinum predictions


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#1 NTactical

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Posted 08 August 2014 - 11:41 AM

Hi everyone,

 

Because I didn't see a post about all ELO-categories on this forum before, I will attempt to explain my analysis about the different ranks and make a prediction for Gold and Platinum Leagues.

 

First of all, let's look at the Bronze league. As most of us have passed through all ranks, we know what the ELO-boundaries for each rank/class are. But if we take a closer look, we can extract a pattern:

stratego_bronze.png

 

If we write down the difference between each class in the Delta-row, and repeat this process, we see that the Delta-Delta row is constant (which indicates polynomial growth of the 2nd order (quadratic)).

 

Now let us look at my calculations for the Silver League:

stratego_silver.png

 

Here we observe the Delta-Delta value to be alternating between 14 and 16, probably because 15 would yield values that would be percieved as 'strange' boundaries by humans. Furthermore, we observe the first Delta-increase to be 8: roughly half the Delta-Delta value. We observed this pattern within the Bronze League too: the first Delta value of 5 was half the Delta-Delta constant.

 

Based on this analysis of the pattern, we can predict the ELO-classes for Gold and Platinum leagues as follows: (I wrote a very simple program that calculated these tables for me :) )

stratego_gold_platinum.png

 

 

Furthermore, we observe the total span of the Bronze league to be 500, Silver to be 750, and according to my predictions Gold to be 1000 and Platinum to be 1250, which also fit another pattern. Therefore, I am pretty confident these values are correct.

 

I hope someone finds this blah-blah interesting  :P


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#2 HardRain_Lenny

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Posted 08 August 2014 - 12:32 PM

I wonder how a player can reach Gold or Platinum.

 

As far as I can see now, the boundaries haven't been changed in Bronze and Silver.

 

If you apply the table above on the current situation, hielco and Sohal are still Silver right?



#3 NTactical

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Posted 08 August 2014 - 12:38 PM

Yes, Hielco is currently Silver General, while Sohal is currently Silver Colonel.
 
However, the boundaries of the top ranked player do shift. I have explained that over a year ago in another thread (you can look it up).
 
See it as one big pyramid as a pile of sand. The pyramid can grow in size by adding sand and thus reach a higher peak, but it needs exponentially more "lower" 'users' (sand) at its base. These players can then propagate points to the top that will be distributed. And that.. is a very slow process.
 
Rankings will always be relative to competitors, and relative to time (not playing for a while decreases your position within the ranking in general, as is the case with this account (not played for 1.3 years, while it was top 15 back then)).
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#4 HardRain_Lenny

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Posted 08 August 2014 - 12:47 PM

From my perspective, the boundaries have to be changed in order to get in place the Gold and Platinum Leagues.

 

Hielco should be the head of Platinum Group up to the moment that he will be beaten by a new top player.



#5 NTactical

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Posted 08 August 2014 - 12:50 PM

Why would you argue the top player be ranked HAS to be platinum head?
 
I just stated rankings will always be relative to competitors and time:

See it as one big pyramid as a pile of sand. The pyramid can grow in size by adding sand and thus reach a higher peak, but it needs exponentially more "lower" 'users' (sand) at its base. These players can then propagate points to the top that will be distributed. And that.. is a very slow process.
 
Rankings will always be relative to competitors, and relative to time (not playing for a while decreases your position within the ranking in general, as is the case with this account (not played for 1.3 years, while it was top 15 back then)).

 
I will argue that this system works best, as it is more robust and time-sustainable, because it can handle 1000's of additional users without changing the system or rankings. ELO is a well thought through system.

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#6 HardRain_Lenny

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Posted 08 August 2014 - 01:01 PM

The ELO system seems to work well. Points will be calculated in a valid way.

 

Only the classification of players into divisions can be changed though.

 

Real Madrid is playing Champions League right? It can't be the case that the Champ league will be empty, because maybe in the future Ajax Amsterdam is going to play much better soccer than RM now in order to allocate the current top teams to lower cup leagues?



#7 NTactical

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Posted 08 August 2014 - 01:08 PM

The ELO system seems to work well. Points will be calculated in a valid way.
 
Only the classification of players into divisions can be changed though.
 
Real Madrid is playing Champions League right? It can't be the case that the Champ league will be empty, because maybe in the future Ajax Amsterdam is going to play much better soccer than RM now in order to allocate the current top teams to lower cup leagues?


Mmm. I get your point, and it seems a valid one.

However, that would introduce the following problem:
Let's say we scale the 4 divisions in such a way that the top ranked player would be platinum. That would mean that with every user joining the system (which happens daily) all (sub-)divisions need to be re-scaled. This would mean you can have a different rank class with every minute without even playing or being surpassed by another. What would the rank class have for meaning left then? Exactly. That's why they are static, and there is enough space in front of us to expand to.

The difference with football classes is that they are propagated top-down since they are not really complete rankings (they are rankings within a division, and they cannot be numerically compared to other divisions), while true rankings are propagated bottom-up.


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#8 The Prof

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Posted 08 August 2014 - 06:06 PM

This analysis, which I posted about a month ago in this thread:  http://forum.strateg...d-and-platinum/

shows that it is very unlikely that we will every get more than a few, if any, gold players.

 

ELO 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, a 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.   

 

I agree wholeheartedly with Lenny that the leagues and ranks should be recalibrated.  About a year ago I suggested the following, and I still think it makes sense:  Bronze 100 to 349, Silver 350 to 599, Gold 600 to 849, Platinum 850 and up.  Each rank within each league would have a fixed 25 point interval.  For example, Gold spy 600 to 624, Gold scout 625 to 649, Gold miner 650 to 674, and so on.  This would make 1075 required for Platinum marshal.  Currently only S-NL would be at this level.  I do think it is fitting that the best player at our site should be able to attain this rank.  Sohal would be a Platinum major, and M2C a Platinum captain.  Some may say that this new system would soon become out dated as player rankings increase and that we would end up with many platinum marshals.  However, that conclusion is not supported by the data.  The analysis above shows that any significant appreciation in the ratings of our top players will occur very slowly, and will require a massive influx of new players to make it happen.   


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#9 bmende

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Posted 08 August 2014 - 06:34 PM

Hi everyone,

 

Because I didn't see a post about all ELO-categories on this forum before, I will attempt to explain my analysis about the different ranks and make a prediction for Gold and Platinum Leagues.

 

First of all, let's look at the Bronze league. As most of us have passed through all ranks, we know what the ELO-boundaries for each rank/class are. But if we take a closer look, we can extract a pattern:

 

Dude that's some deep stuff.

 

In a strange way, I actually don't mind at all that gold and platinum is unreachable. it kind of makes me feel like I could be the first haha, and it makes me wonder how mysterious it would be to actually be gold or platinum.



#10 Napoleon 1er

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Posted 08 August 2014 - 11:14 PM

yes this pyramid phenomenon has already been discussed. The funny thing is that if you look at the scale given by The Prof above you see a more or less constant factor of 2-3 for each 100 points in ranking more, 48 players from 800-899 is approx 1/3 of 137 number of players between 700-799 which is again about 1/3 of 332 number of players in the range 600-699 and so on. So starting from 100 (bronze spy) up to 1100 (Satan-NL) there are 10 ranges of 100 points so to allow the pyramid to continue growing you need approximately 2.5^10=9536 players. and to reach 1200 you need 2.5^11=23842 players. All this assuming the pyramid is regular

 

So to allow Satan-NL continue climbing the ranking he needs that there are a sufficient number of players ranked close to him because now, beeing the first ranked player the maximum number of points he can get for a victory is 12. And because of the ELO system with his 92% win ratio he will progress only if he gets on average more than 2 points for each victory or less than 23 points for each defeat (92*2-8*23= 0) which is his limit for continuing to climb the ranking. If more players get ranked close to him the pyramid can become irregular (boosted on the top) and so there is also a possibility to continue to grow even if there are less than 23842 players

 

...it's close to midnight, I need to sleep, I hope these maths do not make anybody afraid ... lol

 

Napoleon 1er


If you don't know where you go ... you have a lot of chance to arrive elsewhere ...


#11 Midnightguy

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Posted 08 August 2014 - 11:24 PM

We already had our first gold players albeit not official Luckypapa and TheMastros.  This was due to an error with awarding 1000 ranking points instead of 1000 battle coins for 3rd place finishers.  With the current system and still lacking of players to reach that high, not likely we'll see Platinum player anytime soon.  


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#12 maribo

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Posted 10 August 2014 - 04:03 PM

It matters not what they call a group of ranking numbers. #1 is still #1. Just like USA is the best country in the world, who cares if I call it the best of the countries in North America (the number 1 continent), or the best of the countries in the Western Hemisphere (the #1 hemisphere). I agree with TheProf. There are enough groups already. The numbers under 400 are the users who should consider another sport.

Another analysis would also show that there are many duplicate accounts in the groups under 400.

Truly there should be a bell curve, in that there are just as few players who really suck as there are those that are great, but because of true newbies, the 200-299 is always naturally going to be high as true newbies test the waters, but honestly its got to be 4840 because the worst of the worst keep trying new usernames. From 399 down you have to say, they don't stand more than a 1% chance of beating any silver player, but from 400-599, they probably stand a 20% chance.



#13 maribo

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Posted 12 August 2014 - 02:11 AM

I can predict with certainty when scout takes spy on first move, general advances (assumption), general takes 6 and 4 then 1 takes 2, 3rd piece is marshall takes a miner , then bombs out, that with certainty 2:36 is my fastest victory this year.



#14 Javeec

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Posted 12 August 2014 - 09:24 PM

I can predict with certainty when scout takes spy on first move, general advances (assumption), general takes 6 and 4 then 1 takes 2, 3rd piece is marshall takes a miner , then bombs out, that with certainty 2:36 is my fastest victory this year.

 

What?



#15 NTactical

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Posted 13 August 2014 - 02:57 PM

I can predict with certainty when scout takes spy on first move, general advances (assumption), general takes 6 and 4 then 1 takes 2, 3rd piece is marshall takes a miner , then bombs out, that with certainty 2:36 is my fastest victory this year.

 

Why did you have to post this here? And what is the use of your post? It sounds like you are drunk  ;)


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#16 waterfall

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Posted 29 September 2014 - 12:43 PM

Hi everyone,

 

Because I didn't see a post about all ELO-categories on this forum before, I will attempt to explain my analysis about the different ranks and make a prediction for Gold and Platinum Leagues.

 

First of all, let's look at the Bronze league. As most of us have passed through all ranks, we know what the ELO-boundaries for each rank/class are. But if we take a closer look, we can extract a pattern:

stratego_bronze.png

 

If we write down the difference between each class in the Delta-row, and repeat this process, we see that the Delta-Delta row is constant (which indicates polynomial growth of the 2nd order (quadratic)).

 

Now let us look at my calculations for the Silver League:

stratego_silver.png

 

Here we observe the Delta-Delta value to be alternating between 14 and 16, probably because 15 would yield values that would be percieved as 'strange' boundaries by humans. Furthermore, we observe the first Delta-increase to be 8: roughly half the Delta-Delta value. We observed this pattern within the Bronze League too: the first Delta value of 5 was half the Delta-Delta constant.

 

Based on this analysis of the pattern, we can predict the ELO-classes for Gold and Platinum leagues as follows: (I wrote a very simple program that calculated these tables for me :) )

stratego_gold_platinum.png

 

 

Furthermore, we observe the total span of the Bronze league to be 500, Silver to be 750, and according to my predictions Gold to be 1000 and Platinum to be 1250, which also fit another pattern. Therefore, I am pretty confident these values are correct.

 

I hope someone finds this blah-blah interesting  :P

 

Nice schedule, small correction        silver colonel have to be 962.



#17 NTactical

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Posted 29 September 2014 - 06:44 PM

Nice schedule, small correction        silver colonel have to be 962.

 

Well noticed. Strange, as this indicates an irregularity in the pattern while all other values seem to fit. This could indicate that the programmers have set the values hardcoded (handwritten) by hand instead of using a simple deterministic algorithm like I wrote; and they made a mistake/typo on that value.

I cannot think of any other explanation. And using unnecessary hardcoded stuff is bad practice; exactly for this reason. At least precalculate them using code then, instead of making human mistakes by using a calculator. Remarkable how one gets to know the actual system implementation manner due to its bugs. * end of me complaining on stratego-devs *


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#18 NTactical

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Posted 29 September 2014 - 06:54 PM

@MT

Maybe this thread should be merged with Rating System Explained (including a Maribo-cleanup).

If not and you have a different opinion, then please delete this single post.


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#19 trickz

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Posted 29 September 2014 - 07:08 PM

Well noticed. Strange, as this indicates an irregularity in the pattern while all other values seem to fit. This could indicate that the programmers have set the values hardcoded (handwritten) by hand instead of using a deterministic algorithm like I wrote, and made a mistake/typo on that value.

I cannot think of any other explanation. And using unnecessary hardcoded stuff is bad practice; exactly for this reason. At least precalculate them using code then, instead of making human mistakes by using a calculator. * end of my complaint *

 

 

Yo Ntactical,

 

I rhyme this flow

and to see you again has been a long time ago!  ;)

But if you're the bomb with programmin', then it's time that this site would know

so you can take care of all the bugs that cause this site to be dyin' bro!  :D

I'm not lyin' yo,.....we all want proper executions in this lion's zone

so please dude, give us some vital hope cuz' this site is dope,

start a revival show and please implement your matrix like it was a biblecode!  :D


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#20 bmende

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Posted 29 September 2014 - 08:52 PM

This may be kind of silly, but I actually like how there are no gold or platinum players. It makes me feel that the game is not over, there is always more goals to be reached in Stratego. Once gold and platinum levels are reached, it makes me feel like theres not much left to discover in this game. It is less aspiring to become a platinum or gold player if there are already gold or platinum players.

My suggestion is this, instead of recalibrating the points, I suggest platinum just be chopped off ( since at the moment it is clearly unattainable,) so that there are only three leagues: bronze, silver, and gold.

Once points are recalibrated, they can't be re-calibrated back. I don't think you can push every silver player up to gold, and then sometime later, if there's too many higher-ranked players, decide to push every gold player down to silver.

So I suggest for now since it seems a little strange that both gold and platinum leagues are absent of players, I suggest that for now there be no platinum league even existing on this site. And in 100 years if somehow a few people make it to gold marshall status, then instead of recalibrating points you could just add platinum back to the site, and then you have another 100 years of challenge.

But if you recalibrate the points (especially recalibrating them backwards), I think you may receive enough complaints from people who like how the game was, and don't want it to change this much. Also, a recalibration may give the elo system less credibility.



Cheers :)


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