Are Elo ratings adjusted after each match, or after each tournament?

Question

I'm aware that the FIDE ratings list is only published once per month. I'm interested in how often the ratings are recalculated internally to FIDE without being published.

Are ratings adjusted match after match, or after every tournament? Even if the ratings are updated once a month, does FIDE count every match, or a whole tournament?

An example to make my point clear

Consider a three-player, single round robin tournament.

Player                 Elo

Roanin Novel     2798

Rigi Hains           2745

Dan H. Yvasin     2784

Results

Round 1: R. Novel (1) beat Rigi Hains (0)

Round 2: Rigi Hains (0.5) drew with D.H. Yvasin (0.5)

Round 3: D.H. Yvasin (1) drew with R. Novel (1.5)

My question

If FIDE was calculating the players' ratings, would it first update the players' ratings match by match¹, or would their rating be adjusted by counting the tournament as a whole?²

¹ In this case, rating changes after every match.

² Here we calculate the expected score of each player at the start of the tournament, and compare it with the final score only. No rating changes occur between matches.

The calculations (all assume K=10)

Method 1 [Match by match] (Final ratings in bold)

• After the first match, R. Novel is rated 2802.24 and Rigi is rated 2740.76.

• After the second match, Rigi is rated 2741.38 and Dan is rated 2783.38

• After the last match, Dan is rated 2783.65 and Novel is rated 2801.97

Method 2 [Whole tournament]

1. Roanin Novel

   • Initial expected score = 1.096

   • Actual score = 1.5

   • Hence, new rating = 2802.04

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2. Rigi Hains

   • Initial expected score = 0.868

   • Actual score = 0.5

   • Hence, new rating = 2741.32

---

3. Dan H. Yvasin

   • Initial expected score = 1.036

   • Actual score = 1.0

   • Hence, new rating = 2783.64

---

Conclusion

• In such a short tournament, there doesn't seem to be a significant difference in the results of the two methods, but maybe there could be one in a longer tournament.

• Which of them does FIDE use?

Answer 1

Neither

Elo-ratings are not ajusted for calculation after each game, they are not adjusted after each tournament either. They are adjusted each month.

For all games played during one month, each player is supposed to have his last published elo-rating. If I am 2300 on the 1st of November and we play together November the 29th, your rating will be calculated by considering that you have faced a 2300-player. Whether I have gained 50 points in a previous tournament from 5 to 12 of November, or lost 100 points from novermber 16 to 23, will only be relevant for my rating on December 1st, and for my opponents in December and thereafter.

In your example, the second method applies. But there won't be any ajustment after the tournament if one of your three players plays another tournament within the same month.