I disagree on #69.
There is a bigger gap between 1200 and 1300 than 3000 and 3300.
There are few players having 3000+ rating and therefore their pool is more prone to bigger deviations. 1200's pool is abudant of samples (players) and therefore significantly more accurate. In essence it is basically about better accuracy on the larger pool of samples.
Well known fact says quite opposite to your statement, actually, the stronger the players the difference between their level of chess is more subtle.
Some of the basics about ratings are easy to understand.
But some basics are not so easy to Thoroughly understand ...
For example - at the higher levels of chess ...
a difference of 50 ratings points between two players playing each other ...
is much more significant than at the lower levels.
(Provided established rating systems like FIDE or USCF or Elo are being used)
Example ...
a 2750 plays a 2700.
That 50 points is huge.
Could we call it 'difference dilation'?
Whereas - try instead a 1250 plays a 1200.
It might appear to be the same gap - if you're talking about addition and subtraction on a number line.
But it isn't.
Its a smaller difference in strength.
When I first heard about this ... I thought:
'Hey that's interesting. Why would it become more significant at the higher levels?'
I don't know all the details as to why.
But the first thing to realize is that rating numbers aren't like mile or kilometer markers on a freeway or motorway ...
I thought of a better analogy just now - but it only describes rather than explains ... incidental rather than key.
For example - in the hundred yard dash - as a runner improves he will find it harder and harder to shave tenths of a second off his personal record times.
Describes but doesn't quite explain.
But some of the people here in this forum might both know that differences in rating become more significant in the higher classes - and know Exactly why - including the relevant and technical math too.
Another thing at higher levels of chess ...
Draws happen much more. A a bigger percentage of drawn games.
GM draws for example.
In the ultimate classic chess which is tournaments against each other in over the board chess at slow time controls.
Why?
Because GM's make a much lower percentage of easily exploitable mistakes.
And their mistakes are usually much smaller mistakes too.
Does that connect to 'difference dilation'?