# 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.

• Excellent answer. You don't mention the development in the 70+ years range (reversal of the trend), which I guess could easily be explained away by a notably decreased number of games per year (thus less opportunity to lose rating). Commented Aug 7, 2019 at 7:40
• Indeed! I definitely haven't thought of that explanation so I conveniently avoided it... Frankly, a lot of more in-depth work could be done on this topic, this is more of a crude overview of the general picture. Commented Aug 7, 2019 at 8:04
– user24344
Commented Aug 30, 2020 at 22:36
• Too much of the first graph seems to me motivation based. Please put bounds on each graph using box plots or confidence interval. I expect the upper bounds to hang above x axis a while after 27. Maximum score over age starting also with bounds (box plot). Growth per time invested by age and rating (animated heatmap?). I would do all these if you gave me the data.
– ran8
Commented Oct 20, 2020 at 4:42
• Interesting. Is there any indication that any (read: most) player's decline can be described by a few parameters? I.e. not averaging out the individual differences. Commented Jun 6, 2021 at 20:52

As suggested in the question I have taken FIDE rating data from 1992 (when active/inactive flags were first introduced) through to September 2019 taken from Olimpbase and FIDE and loaded it into a database which has allowed me to run SQL queries against the data to get some answers for this question. I looked at average decline in playing strength for players in 5 year age bands from 15 through to 85 and in 100 point playing strength bands from 1500 through to 2700.

I shall present my conclusions from looking at the data first, followed by a brief description of my method followed by the data.

Conclusions

First, I should emphasise that here I am talking about averages. Individuals will obviously vary, possibly wildly from the averages.

• Young, weak players improve faster than older, stronger players. Players in the two weakest bands, 1500 - 1700, continued to improve through to their early 30's.
• Mid strength players (1700 - 2200) start declining first, in their late 20's. At this age weaker players are still improving and stronger players are maintaining their level.
• Mid strength players decline faster in middle age and early old age than both weaker and stronger players.
• Weaker players are more variable (have a higher standard deviation) than stronger players until you get to your 80's when I guess it starts falling apart for everybody.
• Finally, to answer the question about my prospects. I am in the 60-65 and 1700-1800 band so I can "look forward" to an expected decline of 139 points over the next 10 years with a standard deviation of 118. Of course I expect this not to happen. I blame my current low rating on getting "mugged" by several very under-rated juniors last year and I promise I will study more (fingers crossed behind my back).

Method

For each age and rating band I selected the average rating decline over a 10 year period and the standard deviation for each player in the band who was active at the beginning and end of the 10 year period. I restricted these calculations to where I had at least 50 data points, hence the gaps in the following data for older age groups. I ran this query over all the data in the database.

For each age/rating point there are two numbers. The first is the average decline. If this is a negative number it indicates an average increase in rating. The second number, in brackets, is the standard deviation. For a normal distribution 95% of the results would fall within a range of +/- 2 standard deviations. However average improvement/decline is almost certainly not normally distributed. Nevertheless this figure gives a useful indication of variability.

For instance, the first data point for the 15-20 age band and the 1500-1600 rating band is -161 (174). This means that the average rating increase over a 10 year period for players in this band is 161 points and the standard deviation is 174. This high standard deviation indicates that some players will be improving by several times as much as the average while some may stay roughly the same or even decline.

Compare this with the figures for the 50-55 age band and 2600-2700 rating band. The average decline is 43 and the standard deviation is only 28. This suggests that most, if not all the players in this band are declining slightly in rating.

Results

``````AgeBand = 15-20
1500 -     1600 -     1700 -     1800 -    1900 -    2000 -    2100 -    2200 -    2300 -  2400 -   2500 -    2600
-161 (174) -137 (169) -123 (152) -99 (141) -87 (132) -84 (118) -94 (112) -94 (107) -94 (9) -103 (8) -101 (65) -93 (47)

AgeBand = 20-25
1500 -    1600 -     1700 -     1800 -    1900 -    2000 -    2100 -    2200 -    2300 -   2400 -   2500 -    2600
-89 (158) -58 (151) -34 (130)   -28 (123) -21 (109) -15 (95) -23 (82)   -32 (79)  -30 (76) -35 (64) -35 (55) -28 (52)

AgeBand = 25-30
1500 -    1600 -     1700 -     1800 -    1900 -    2000 -    2100 -    2200 -    2300 -   2400 -   2500 -    2600
-71 (149) -19 (142)  2 (124)    20 (122)  29 (102) 16 (88)    7 (75)   -2   (69)    -1 (65) -4 (55)   0 (51)    1 (40)

AgeBand = 30-35
1500 -    1600 -     1700 -     1800 -    1900 -    2000 -    2100 -    2200 -    2300 -   2400 -   2500 -    2600
-53 (144) -18 (147)  21 (121)   37 (102)  48 (87)   35 (79)   29 (75)   16 (62)   17 (59)  14 (51)  16 (47)   18 (59)

AgeBand = 35-40
1500 -    1600 -     1700 -     1800 -    1900 -    2000 -    2100 -    2200 -    2300 -   2400 -   2500 -    2600
3 (125)   22 (123)  41 (116)    58 (100)  63 (93)   51 (79)   44 (69)   30 (60)   29 (56)  25 (47)  25 (48)   33 (38)

AgeBand = 40-45
1500 -    1600 -     1700 -     1800 -    1900 -    2000 -    2100 -    2200 -    2300 -   2400 -   2500 -    2600
25 (113)  22 (110)   70 (120)   73 (108)  80 (91)   66 (78)   57 (68)   42 (61)   38 (57)  35 (51)  38 (44)   38 (37)

AgeBand = 45-50
1500 -    1600 -     1700 -     1800 -    1900 -    2000 -    2100 -    2200 -    2300 -   2400 -   2500 -    2600
22 (135)  54 (121)   73 (111)   93 (100)  91 (93)   80 (80)   69 (70)   54 (66)   48 (57)  41 (51)  38 (43)   49 (34)

AgeBand = 50-55
1500 -    1600 -     1700 -     1800 -    1900 -    2000 -    2100 -    2200 -    2300 -   2400 -   2500 -    2600
23 (123)  85 (116)   91 (120)   106 (99)  109 (89)  95 (82)   81 (73)   66 (70)   57 (63)  53 (57)  43 (40)   43 (28)

AgeBand = 55-60
1500 -    1600 -     1700 -     1800 -    1900 -    2000 -    2100 -    2200 -    2300 -   2400 -   2500 -    2600
66 (127)  84 (103)   117 (106)  129 (106) 126 (103) 108 (89)  92 (76)   73 (72)   70 (67)  54 (54)  55 (47)   44 (38)

AgeBand = 60-65
1500 -    1600 -     1700 -     1800 -    1900 -    2000 -    2100 -    2200 -    2300 -   2400 -   2500 -    2600
93 (123)  123 (126)  139 (118)  146 (106) 136 (95)  117 (90)  105 (78)  87 (76)   82 (79)  70 (72)  93 (77)

AgeBand = 65-70
1500 -    1600 -     1700 -     1800 -    1900 -    2000 -    2100 -    2200 -    2300 -   2400 -   2500 -    2600
96 (111)  123 (122)  144 (120)  141 (107) 152 (102) 124 (89)  112 (80)  108 (87)  91 (82)  81 (81)  69 (37)

AgeBand = 70-75
1500 -    1600 -     1700 -     1800 -    1900 -    2000 -    2100 -    2200 -    2300 -   2400 -   2500
96 (115)  119 (131)  147 (128)  153 (124) 161 (104) 135 (93)  125 (84)  115 (91)  93 (74)  63 (65)

AgeBand = 75-80
1500 -    1600 -     1700 -     1800 -    1900 -    2000 -    2100 -    2200 -    2300 -   2400
119 (207) 156 (180)  171 (123)  167 (141) 173 (101) 156 (101) 138 (94)  126 (96)  134 (92)

AgeBand = 80-85
1700 -     1800 -    1900 -     2000 -    2100 -    2200 -    2300
75 (167)   148 (186)  156 (169) 179 (102) 177 (118) 92 (174)
``````
• I should emphasise that here I am talking about averages. Individuals will obviously vary, possibly wildly from the averages. (+1) for pointing out this truth. Commented Jan 24, 2022 at 16:04