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Rating standard deviation chart

#1

I'm unaware if this exists or not but i'd like to see what the standard deviation would look like for ratings on lichess. All players start at 1500 so a reasonable guess would be that that would be somewhere close to the mode, but an entire chart would be interesting to analyze.

I'm unaware if this exists or not but i'd like to see what the standard deviation would look like for ratings on lichess. All players start at 1500 so a reasonable guess would be that that would be somewhere close to the mode, but an entire chart would be interesting to analyze.
#2

Because of how the Glicko-2 rating system works, it's basically a bell curve with 1500 (give or take 100 points) is right at the top and center of the curve and everything scatters out and down from there, with obviously the 2400+ ratings being at the far bottom right and everything under 1000 being far bottom left. That's just how Glicko-2 works. It will be roughly the same for each and every group that is being rated with Glicko-2, whether it's an SD chart for a large chess community, a video game tournament league, a bowling league, it wouldn't matter. The ratings would distribute in this way, I believe.

Because of how the Glicko-2 rating system works, it's basically a bell curve with 1500 (give or take 100 points) is right at the top and center of the curve and everything scatters out and down from there, with obviously the 2400+ ratings being at the far bottom right and everything under 1000 being far bottom left. That's just how Glicko-2 works. It will be roughly the same for each and every group that is being rated with Glicko-2, whether it's an SD chart for a large chess community, a video game tournament league, a bowling league, it wouldn't matter. The ratings would distribute in this way, I believe.
#3

Yes the data would likely look in this way, but i'm more interested in how many points make up a single deviation such that ~68% of players fall into one deviation from the center and ~95% in 2.

Yes the data would likely look in this way, but i'm more interested in how many points make up a single deviation such that ~68% of players fall into one deviation from the center and ~95% in 2.
#4

Ah, I see what you are saying. The problem with this is that Glicko-2 estimates ratings via distribution curves as it is...each rating is fluid and can shift left or right drastically over a small period of time depending on the data that the curve has to draw from.

So I think what would be more interesting would be to only look at distributions of players who are active and have over 100 recent games, so that their deviation curve is very steep (i.e. >90% certainty of skill level vs. <85% chance that they are much stronger or weaker than their rating indicates). You'll notice players who are inactive for a long period of time and then return may gain/lose more points than players who are actively playing daily, and that is what I mean. So the problem with generating a standard distribution for the site is that many of those values change drastically from day to day...some even from hour to hour. It would still be rather interesting I think.

You should really research Glicko-2 and how it works, if you have not. It's quite interesting.

Ah, I see what you are saying. The problem with this is that Glicko-2 estimates ratings via distribution curves as it is...each rating is fluid and can shift left or right drastically over a small period of time depending on the data that the curve has to draw from. So I think what would be more interesting would be to only look at distributions of players who are active and have over 100 recent games, so that their deviation curve is very steep (i.e. >90% certainty of skill level vs. <85% chance that they are much stronger or weaker than their rating indicates). You'll notice players who are inactive for a long period of time and then return may gain/lose more points than players who are actively playing daily, and that is what I mean. So the problem with generating a standard distribution for the site is that many of those values change drastically from day to day...some even from hour to hour. It would still be rather interesting I think. You should really research Glicko-2 and how it works, if you have not. It's quite interesting.

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