Standard Deviation for Rapid

The mean for rapid chess is 822.77 as of the time of this posting.  The standard deviation is not listed, but based on the shape of the bell curve and the percentile of my own rating and ratings of players I have played against, I estimate that it is about 425 rating points.  

So, +1 standard deviation is about 1250 (about 84th percentile), +2 standard deviations is about 1675 (97.5 percentile) and +3 standard deviations is about 2100 (99.85 percentile). 

-1 standard deviation is about  400 and -2 standard deviations is about 100 (I think 100 is the lowest you can get, since you can't actually subtract 425 points from 400).  

I saw a topic about chess and IQ.  I don't have anything to say about that in this post, but with this information, you can estimate your CQ (chess quotient).  All IQ is, is your percentile on the distribution with 100 as the mean and 15 as the standard deviation.  So, rating of 822.77 is a CQ of 100, 1250 is about 115, 1675 is CQ 130 and 2100 is CQ 145.  

Probably most people won't find this interesting, but for those who are interested in more detail in the rating distribution, I think this is a good starting point.  I'd be curious to see if anyone has different estimates for the rapid standard deviation or estimates for the standard deviation of other chess formats.

Very interesting. 

With respects to IQ, theory and practice do not always translate with people.

It is in my personal case,  I am a late bloomer in all things I have succeeded in but it was thru hard work and discipline.

I find “those threads” that imply IQ and chess players to be arrogant and condescending.

I believe that hard work and dedication to chess is a great way to improve your rating. I also believe that there are certain people who are just born with a keen sense of chess ability.  I personally do not find a correlation between IQ and your chess rating. 

Thanks for your responses.  I'm glad people found this thread interesting.

In this thread I'm just interested in the distribution of rapid ratings, not how they relate to IQ.    You can use the IQ scale for anything that falls on a Bell Curve.  CQ is just a different way to say the same thing that the rating percentile says.  In the way I am using this, if someone has a CQ of 100, I don't mean that their IQ is also 100, just that their rating is  average (because average was defined ahead of time to be 100 on the CQ scale).  

Interesting topic. I will be curious to see what other people have to say about this. Thanks for bringing it up! 

Thanks, that's interesting.  I played a 2150 earlier who was 99.9 th percentile.  I guess they don't calculate more precisely than 99.9; if it's more it rounds up to 100th percentile.

After looking up percentiles of more players, I want to update some of the numbers.

We know that a rating of about 823 is about the 50th percentile.  

+1 standard deviation is about the 84th percentile and a rating of 1193 is 83.9 th percentile, while a rating of 1198 is 84.2 percentile.  So, split the middle and say that 1195 is +1 standard deviation.  Then we would have the gap between 823 and 1195 as 372 rating points.  

+2 standard deviations is the 97.5 percentile.  1606 is at the 97.5 th percentile.  In this case, the gap between 1606 and 1195 is 411 rating points.  

+3 standard deviations is 99.85 percentile.  A rating of 2031 is 99.8 percentile and a rating of 2086 is 99.9 percentile, so somewhere in between, say about 2050 is 99.85 percentile.  Then the gap between 1606 and 2050 is 444.  

It's harder to find percentiles for low ratings, but -1 standard deviation is the 14th percentile and 456 is 15.6 percentile.  

So, on average, a standard deviation is about 400 rating points.  I suspect the reason the gaps change is because the distribution is very close to a normal distribution but not quite.  I suspect that going along with what TCSPlayer said, above 2200 or so, it's no longer a normal distribution, more like a positive skew.  

Hikaru was considered 99.99% procentile in blitz when #1 so Id assume you mean 99.99%