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Difficulty of Achieving/Maintaining ELO Ranks, Has it Changed?


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#21 despy

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Posted 06 June 2017 - 05:20 PM

Inflation is due directly to an increase in the money supply. Increasing prices are the symptom of inflation, not the cause. Increasing prices no more cause inflation than wet streets cause the rain. A loaf of bread is always going to be a loaf of bread, just like a mid range player is always going to be a mid-range player here. That we can say that loaf of bread used to cost 25¢ and now costs $2 doesn't reflect on the loaf of bread, only the amount of money needed to buy it. Likewise, if a mid-range player here used to be 420 ELO (half of Hielco) and now that same player can now objectively be said to be 640 (half of Hielco), then there is clear inflation going on. Of course, malcom.jansen is correct that skill is hard to quantify. But I submit that my Hielco standard for the median player is as good as any for our stratego "loaf of bread".

 

I briefly considered getting into a debate about economics, but I will refrain from doing so as that might be a gateway to a much more heated discussion than this was meant to be.

 

I will say though that I like your proposition of using Hielco as a benchmark for skill. The key to all of this thus lies in finding D_hs (the rate of increase in Hielco skill). Defining D_he as the rate of increase in Hielco's ELO, -inf <= D_hs < D_he would strongly suggest that ELO levels have been easier to obtain over time, whereas D_he < D_hs would suggest the opposite.

 

The above is of course under the assumption that at each point, Hielco had reached his equilibrium ELO. An equally plausible theory, and one I'm sure the conspiracy theorists of the forums would enjoy, is that Hielco's true ELO has always been 1337, and he just hasn't had the time to get there yet.



#22 Yellowhat

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Posted 06 June 2017 - 05:29 PM

The difficulty has changed. I can remember the days when there were no marshal blitzers in gold.


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#23 despy

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Posted 06 June 2017 - 05:39 PM

Comparing the ELO needed to be in the top 250 today with the rating needed to be in the top 250 when the site was in its first year is not the apples-to-apples comparison that it may seem to be.  This is because there are many more players, and aliases, than there were back then - there are about 490,000 accounts today.  A true comparison would be the ELO needed to be in say the 99.9th percentile of ELOs today, with that of the ELO needed to be in the 99.9th percentile back then.  

 

Nice. And Prof takes the lead in the analogy quality contest  ;)

 

But wait....

 

Given the likelihood that alias creation follows a negatively skewed distribution across the ELO space (more gold/plat-level players make aliases than bronze-level players), I propose that as more and more aliases have come about over time, so too has the site's ELO distribution evolved. Starting from what I assume was a very pronounced positive skew due to account creation being at the 100 mark, I think we likely now have a more or less bimodal distribution, peaking perhaps in low silver and mid/high gold.

 

Thus a pctl measure would be inferior still, to the pctl_Prof_adj measure, which I define as the percentile measure adjusted by Prof to account for the evolution of the site's ELO distribution. (Not pctl_Despy_adj since your math is better than mine).



#24 despy

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Posted 06 June 2017 - 05:43 PM

The difficulty has changed. I can remember the days when there were no marshal blitzers in gold.

 

I suppose it depends how you define blitzer, but I think this could also be attributed to a 'marshal blitz' strategy being increasingly refined over time, with guys like Constrictor applying a very aggressive one-sided marsh attack highly effectively.



#25 The Prof

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Posted 06 June 2017 - 05:56 PM

I think we likely now have a more or less bimodal distribution, peaking perhaps in low silver and mid/high gold.

 

 

The data do not show a bimodal distribution, but one that is skewed right:  There are 476,761 bronze accounts, 9131 silver, 2883 gold, and 912 platinum.



#26 TheOptician

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Posted 06 June 2017 - 06:03 PM

My head is scrambled, so are my eggs. It's dinner time.

I would add that there are actually about 700,00 accounts (not 490k). This is because there are 200k accounts which never played a multiplayer game.

#27 Unladen Swallow

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Posted 06 June 2017 - 06:09 PM

The data do not show a bimodal distribution, but one that is skewed right:  There are 476,761 bronze accounts, 9131 silver, 2883 gold, and 912 platinum.

 

 

The number of bronze accounts is definitely skewed. The other data suggests there are 3x fewer people in gold than silver, and 3x fewer people in platinum than gold. 

 

How many dormant accounts would there be in bronze? 



#28 despy

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Posted 06 June 2017 - 06:37 PM

The data do not show a bimodal distribution, but one that is skewed right:  There are 476,761 bronze accounts, 9131 silver, 2883 gold, and 912 platinum.

 

Wow, that is incredible - I see I heavily underestimated the number of accounts that are just made and left alone -


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#29 Napoleon 1er

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Posted 06 June 2017 - 06:56 PM

Let's approach the question otherwise in 3 separate questions:
1) is it easier to reach 800 ELO now or a year ago?
Answer is: it is more difficult because as you have now more players that are ranked higher than 800 than a year ago, a new player reaching 700 will get matched more frequently with higher ranked (more skilled) players than he would have been matched with a year ago. So his probability to win games today is lower than a year ago and his win ratio to move from 700 to 800 will be lower than it would have been a year ago.
2) is it easier for Hielco to increase his ELO now or a year ago?
Answer is: first point to note is that for Hielco above rationale is not applicable because he is only matched against lower ranked players. Secondly it is easier for him because the pyramid of the ranked players has flattened over time. Now he get matched more frequently against players ranked closer to him than a year ago so his own ELO can increase more easily than a year ago. But the reason why this happened is because he didn't play as many games as many of the other players who came closer to him. If he would have played as many games as the average of the following 200 active players his ELO today would be higher but his ability to increase it would have remained as difficult as a year ago.
Morality: if we assume that another player that has exactly the same skills as Hielco would exist , such player can reach or even beat Hielco only by playing more ranked games than him over the same period of time.
3) is it easier to be in the top 250 now or a year ago?
Answer is: it is obviously more difficult today because today you need to reach a higher ELO than a year ago to be in the top 250.
Morality: the only way to increase your ranking (ELO points or effective rank), assuming you are playing at your true level, is to increase your skills faster than the average of the other players. And to do that you need to just play more games than the average of the other players.
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#30 despy

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Posted 06 June 2017 - 08:10 PM

1) is it easier to reach 800 ELO now or a year ago?
Answer is: it is more difficult because as you have now more players that are ranked higher than 800 than a year ago, a new player reaching 700 will get matched more frequently with higher ranked (more skilled) players than he would have been matched with a year ago. So his probability to win games today is lower than a year ago and his win ratio to move from 700 to 800 will be lower than it would have been a year ago.

 

This is an interesting perspective, with a conclusion consistent with what I was thinking (having seen opponents' historical ELOs being higher than I would have expected given current skill level). The argument seems circular though, partly because it's unclear how much of the increase in the number of players ranked over 800 is attributable to a higher availability of points / ease of ELO increase (as you pointed out in a previous post), and how much is attributable to a general increase in skill level. 

 

For the argument to be valid; specifically, the premise that one is now matched more frequently with higher ranked (more skilled) players, it would have to hold that the players ranked 800+ now are at least as skilled as players ranked 800+ previously, which is in fact the very thing we're trying to prove/disprove. Further, this decreased probability of winning games given higher-ranked opponents should be a non-factor, since this is supposedly accounted for by the positive opponent ranking vs ELO-at-risk relationship.

 

I hate to play devil's advocate on a conclusion that I agree with, but alas logic must prevail!

 

2) is it easier for Hielco to increase his ELO now or a year ago?
Answer is: first point to note is that for Hielco above rationale is not applicable because he is only matched against lower ranked players. Secondly it is easier for him because the pyramid of the ranked players has flattened over time. Now he get matched more frequently against players ranked closer to him than a year ago so his own ELO can increase more easily than a year ago. But the reason why this happened is because he didn't play as many games as many of the other players who came closer to him. If he would have played as many games as the average of the following 200 active players his ELO today would be higher but his ability to increase it would have remained as difficult as a year ago.
Morality: if we assume that another player that has exactly the same skills as Hielco would exist , such player can reach or even beat Hielco only by playing more ranked games than him over the same period of time.

 
Again I would similarly argue that if we assume the opponent ranking vs ELO-at-risk relationship is truly representative, it should not be any easier now than previously for Hielco to increase his level. In fact, if we assume that his skill has not changed substantially, one could argue that it's in fact more difficult, since his own ELO has increased and he thus gets fewer points than previously when matched against an opponent at some constant ELO.
 
My stance on Hielco (granted, I've only heard legends and never actually witnessed his skill or its evolution) is that his pursuit of ELO is likely asymptotic; i.e., if he keeps playing, his ELO will continue to increase ad infinitum, never actually reaching his true ELO. The result is that any conclusions underpinned by some assumption of the relationship between his skill and ELO break down, since I would think there be some time-varying delta that persists between his skill and ELO that's difficult to model.

 

3) is it easier to be in the top 250 now or a year ago?
Answer is: it is obviously more difficult today because today you need to reach a higher ELO than a year ago to be in the top 250.
Morality: the only way to increase your ranking (ELO points or effective rank), assuming you are playing at your true level, is to increase your skills faster than the average of the other players. And to do that you need to just play more games than the average of the other players.

 

I agree that it is obviously more difficult to be in the top 250 now, but I don't think ELO is a valid basis for the argument since we haven't yet convincingly concluded whether it's more or less difficult to reach a particular ELO level. Rather, it's obviously more difficult now because there are more and more aliases in the Top 250!

 

If we're talking increasing one's place on the 'clean ranking' though, it's certainly much more complicated than just 'playing more games' than others, since there's clearly a wide variance in players' rates of skill increase. (No offence to a certain "Italian Mountain 4", but 35000+ games and still in silver? Come on.)



#31 The Prof

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Posted 06 June 2017 - 08:20 PM

1) is it easier to reach 800 ELO now or a year ago?
Answer is: it is more difficult because as you have now more players that are ranked higher than 800 than a year ago, a new player reaching 700 will get matched more frequently with higher ranked (more skilled) players than he would have been matched with a year ago. So his probability to win games today is lower than a year ago and his win ratio to move from 700 to 800 will be lower than it would have been a year ago.

 

This argument is flawed.  The skill level of one's opponents does not have an effect on the equilibrium ELO of a player.  This is because a player earns more points by beating higher rated players than lower ones.  In fact, the formulas of the ELO system are specifically designed to take this into account.  For example, if my true skill level is an 800 ELO then my win percentage should be 80% against players with a 560 ELO and it should be 20% against players rated 1040.  But in the first case, I will either win 5 or lose 20 points, depending on the result.  In the second case, I will either win 20 or lose 5.  So my ELO remains constant whether I am winning 80% of my games against the lower rated players or 20% of my games against the higher ones.   


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#32 GaryLShelton

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Posted 07 June 2017 - 02:33 AM

No one would hardly believe this. But in the days of yore, prior to Nortrom and Hielco, when Spaceman Spiff ruled the stratego.com rankings, I remember one time seeing only 27 silvers on the leaderboard...ONLY 27 players were ranked above 600! The leaderboard couldn't even claim 250 yet. Can you imagine?

No matter if you use leaderboard rank or The Prof's 99.9 percentile of ELO approach, things are much different now. I began pretty early at the site (March of 2013, I think), but Midnightguy had me beat by about four months. He told me once how he was on the bronze leaderboard at the time being ranked only a bronze miner!

Things have certainly changed. :)
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#33 Napoleon 1er

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Posted 07 June 2017 - 07:51 AM

This argument is flawed.  The skill level of one's opponents does not have an effect on the equilibrium ELO of a player.  This is because a player earns more points by beating higher rated players than lower ones.  In fact, the formulas of the ELO system are specifically designed to take this into account.  For example, if my true skill level is an 800 ELO then my win percentage should be 80% against players with a 560 ELO and it should be 20% against players rated 1040.  But in the first case, I will either win 5 or lose 20 points, depending on the result.  In the second case, I will either win 20 or lose 5.  So my ELO remains constant whether I am winning 80% of my games against the lower rated players or 20% of my games against the higher ones.


So the conclusion is that today it is neither more nor less difficult to move from 700 to 800?

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#34 despy

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Posted 08 June 2017 - 06:30 AM

So the conclusion is that today it is neither more nor less difficult to move from 700 to 800?

 

I think so far the conclusion is that a conclusion cannot be made :)



#35 josephwhite

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Posted 08 June 2017 - 04:32 PM

The problem with analysing this issue is that we have the variability of skill improvement (or digression) which is hard to measure. If everyone's skill level remained constant, it would be easy to determine if their was ELO inflation. Therefore, it would be interesting to see if it is possible to have a control for this variable in a sample.

 

If we could isolate players whose skill level has not changed but who keep playing, we could get the answer. Although we couldn't probably determine this perfectly, there are possibly ways to do it that would give us a good indicative result.

 

For example, players who only play infrequently, yet consistently might be a good benchmark. I'm thinking of a player who plays maybe twice a month on average. If it could be established that this is all that they play and that they don't put other time in learning the game (e.g. reading strategy, studying videos of others, etc.), then I think one could assume that their skill level would not significantly improve. Maybe another option would be the guys who have played many games and are still at low levels (e.g. Italian Mountain 4). It would be interesting to track his growth or lack thereof. These may not be the best examples, but others might be able to think of better ways for isolating skill improvement. 

 

Finally, I agree with The Prof below, with one exception.

 

This argument is flawed.  The skill level of one's opponents does not have an effect on the equilibrium ELO of a player.  This is because a player earns more points by beating higher rated players than lower ones.  In fact, the formulas of the ELO system are specifically designed to take this into account.  For example, if my true skill level is an 800 ELO then my win percentage should be 80% against players with a 560 ELO and it should be 20% against players rated 1040.  But in the first case, I will either win 5 or lose 20 points, depending on the result.  In the second case, I will either win 20 or lose 5.  So my ELO remains constant whether I am winning 80% of my games against the lower rated players or 20% of my games against the higher ones.   

 

The higher one gets, this balance breaks down when playing low ranked players that give only 1 point. For example, I think I only get 1 point from players around 350 and below. However, Hielco probably gets 1 point from players from about 600 and below. Someone at a 600 level might get 1 point from those at 200 and below. Therefore, if we all played someone at 200, our chances of winning might be:

 

Hielco - 99.99%

Me (say at 850 level) - 98%

600 level player - 95%

 

Therefore, Hielco would improve more on 1 point games than the other of us would. In fact, from an ELO perspective, it is probably in his interest to play as many 1 point players as possible (the lower the rating, the better). Note I said from an ELO perspective, as I'm sure these games are quite boring for him and they take a long time to match up.

 

I'm sure Prof could much more accurately state these percentages and levels, but I think you probably get the point.



#36 Napoleon 1er

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Posted 08 June 2017 - 05:30 PM

I think so far the conclusion is that a conclusion cannot be made :)

of course some additional parameters shall also be kept into consideration to find the right answer. For example how shall the "true" level of a player be defined? Could it be "TOP ELO reached -100" or "TOP ELO reached minus 10%" or something similar?

Secondly how does the presence of a lot of aliases in that range 700-800 ELO affect the ability of a new player to move from 700 to 800? From a pure ELO point of view an alias is an account of a player who is playing below his true level, so how does a high proportion of alias in a given ELO range impact the ranking of a new player in that range?


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#37 tobermoryx

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Posted 08 June 2017 - 06:54 PM

The higher one gets, this balance breaks down when playing low ranked players that give only 1 point. For example, I think I only get 1 point from players around 350 and below. However, Hielco probably gets 1 point from players from about 600 and below. Someone at a 600 level might get 1 point from those at 200 and below. Therefore, if we all played someone at 200, our chances of winning might be:

 

Hielco - 99.99%

Me (say at 850 level) - 98%

600 level player - 95%

 

Therefore, Hielco would improve more on 1 point games than the other of us would. In fact, from an ELO perspective, it is probably in his interest to play as many 1 point players as possible (the lower the rating, the better). Note I said from an ELO perspective, as I'm sure these games are quite boring for him and they take a long time to match up.

 

I'm sure Prof could much more accurately state these percentages and levels, but I think you probably get the point.

 

If Hielco played someone on 200 he would win 0 pts for winning the games ( but lose 25 if he lost)

 

I believe he would win 0 for defeating a player on 700 ELO

 

As i understand it you must be no more than 577 points above the opponent in order to have a point for winning . 

 

As you say though TheProf knows more.



#38 Napoleon 1er

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Posted 08 June 2017 - 08:57 PM

personnally i have never lost or won a game with respectively 0 or 25 points, the maximum is 1:24. According to something that was written somewhere in 2013 but that i was never able to find again the system does not match people if the ELO difference is more than 622. which is the maximum ELO difference for which you would have the 1:24 ratio. As from 623 the ratio should be 0:25 but the system never matches games then.


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#39 The Prof

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Posted 08 June 2017 - 09:42 PM

It's a difference of 677 or more at which the formula would award the winner just under 0.5 points.  Since results are rounded to the nearest whole numbers, my assumption is that the winner would receive zero points under this scenario.  However, it has never been confirmed if this has ever occurred and so Napoleon may be right that the system may have been designed not to match players in this case, or it may have been designed to override the formula and always award at least one point.   This post summarizes the possible outcomes http://forum.strateg...boards/?p=44361  and this one shows how to obtain precise computation of the percentages that josephwhite was estimating:  http://forum.strateg...boards/?p=44362



#40 Hielco

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Posted 08 June 2017 - 09:58 PM

i have had 0 point for a win in the past :lol:


Edited by Hielco, 08 June 2017 - 09:59 PM.

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