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More or less what is asked in the title. I am familiar with how the system itself works, but I am wondering if there would be any issues if most chess tournaments didn't follow the Swiss format and to a lesser extent, round-robin and match formats which all have each player play a similar number of games. However, consider a single-or double-elimination tournament bracket, which would mean that when a system was first implemented, stronger players would be playing more games in those tournaments than the weaker players who would be eliminated sooner.

Also the question is not limited to issues in relation to the accuracy of the ratings in a statistical sense, though that would of course be the main consideration.

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    I think some mathematical issues disappeared when FIDE started to compute expected score game by game instead of expected score in the whole tournament. Then the total number of rating points is conserved (sum of losses = sum of gains), even if the players play different number of games in the tournament. – Dag Oskar Madsen Sep 27 '15 at 15:54
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Theoretically there's no problem. But, for example, if 'parking the bus' approach (a player gets a high level in ranking, then he stops playing) is one of the most known practical issues of Elo ranking, the problem should be with weaker players that play just brackets, with one or few games every tournament.

Many post-Elo ranking systems, as Glicko (for chess), or TrueSkill (for X-box games), or rankade (our multipurpose ranking system) have some 'activity dynamics feature' to avoid this.

Rankade adds the option for different weights for match, due to different tournament format and/or match duration, and more.

While playing one-on-one (as in a chess group) or in symmetrical factions (as in basketball group), the total number of rating points is conserved. as per Dag Oskar Madsen comment.

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i had stats in grad school and my feeling is that the ratings would vary a little by tournament but not enough to be a problem and not as much as other factors that can influence them eg being sick on a given day or having jet lag or whatevr

if they can win a tournament with a draw or several that is more likely to happen and tend to compress the ratings a little

if they have to win as in a knockout format they would be forced to win if they could

i dont know how the current ratings work but they could account for the format differences to eliminate that little bit of noise

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    Did you also have punctuation and capitalisation in grad school? – BlindKungFuMaster Feb 5 '16 at 11:21

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