Edit: let me add something because this answer seems to be misunderstood. FIDE ratings are based on game scores (see the Mathematics of Elo Ratings. It was created by Arpad Elo as a method for calculating the relative skill levels of players in zero-sum games such as chess. A player's Elo rating is represented by a number which may change depending on the outcome of rated games played. After every game, the winning player takes points from the losing one. So, if chess is a zero-sum game, so are the FIDE ratings!
The question then is: are FIDE ratings a zero-sum game because of pairings of players with different K-factors? A question I reinterpreted in a more provocative way: is chess empirically a zero-sum game?
As stated in Brian Towers' answer:
Not necessarily. My k FIDE factor is 20. If your's is also 20 then,
yes, my loss will match your gain, but if you are a junior or still
haven't played 30 games (I think) then your k factor will be 40 and
you will gain double what I gain. Similarly if you have ever been over
2400 then your k factor will be 10 and your gain will only be half my
In the May 2020 FIDE list of the standard rating (see here), I observe a distribution of K-values for 2,700 players rated with
- a Fide rating in April and May,
- at least one game recorded in the list of of May 2020.
The distribution is as follows:
K Freq. Percent
10 21 0.78
20 1,704 63.11
40 975 36.11
Total 2,700 100.00
Then, I plotted the estimated probability density function of the difference between their rating in April and May (given that the formula for updating a player's rating is based on the expected and the actual scores of the games played). As expected, the difference is centered on zero because the points lost by some players are won by others.
However, the sum of points gained is greater (23,144) than the sum of points lost (-21,564), which represents an average gain of +0.59 per game. However, this average is not statistically different from 0! Conclusion: we cannot reject the hypothesis that chess is (empirically) a zero-sum game!
One caveat: I did not observe the results and matches of these players; I assumed that the points won by some players in this list are lost by others in the same list.
This aside, I like very much the point about the experience gained and the sharing of ideas during and after a game, which suggests that "chess is anything but zero sum"!