How do age and initial rating correlate to decline in playing strength with age? The current Rausis phone cheating scandal saw a player with an initial rating of about 2500 in his 50's improve by about 200 rating points in 6 years. This improvement was remarkable because older players are expected to get weaker with age. 

It even received attention a couple of week's ago, before the scandal broke, with the suggestion that he was hacking the system by playing mostly much weaker players and taking advantage of the 400 point rule.

Has there been any analysis showing the correlation between age and rating on one hand with expected decline on the other? 

For example, I'm in my 60's and my FIDE rating is about 1700. How much decline can I expect in the next 10 years? Would that be much different for a 2200 master in his 60's? For a 2500 GM? For 1500 player?

There is a chess.com blog article which looks at the data for just one month which is unsatisfactory in many ways. It shows a graph of average rating in 5 year bands but with no analysis following players with similar starting ages and ratings to see what the decline is over a given period.

The data is there. FIDE publish more than 18 years of rating data which is available for download. Olimpbase have data available for download going back another 30 years although then only strong (master level) players had ratings.
I looked at the data briefly and got some interesting conclusions.

I used data from FIDE webpage for january in years 2006-2019.

I calculated each player's rating change in consecutive years and used player's age in the first of the two as the age when this rating change occurred. Then I simply calculated the average. The result is this:


As you can see, players are on average gaining rating only until the age of 27, and afterwards they tend to slowly lose rating. Children gain the most rating per year, which is very intuitive.

Rating range 19-90 from up close:


Rating loss increase looks linear.

Cumulative rating change:


This is of course cumulative change since the age of 10.

Secondly, I did the same thing but separated players into groups. I looked at each of their entry in the data and put them into respective categories according to the maximum rating achieved in it: which might not be their actual peak rating, but should be a good indication of their top strength.


Gains are much larger here. Might be due to the fact that the negative contribution of sub-1500 players isn't included. Intuitively, higher rated players have higher average rating gains, but the decline rate seems to be similar regardless of the strength.


The linear range up close.


Cumulative again.