: How does the FIFA rankings work ?

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: How does the FIFA rankings work ?

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Anonymous 0 Comments

I guess your question is how are they calculated. The ranking was implemented in 1992, and it was changed several times. I’ll talk about the system used since 2018.

They used an implementation of the Elo rating system. Each national team has a given rating, and at the end of every match, they exchange points (i.e., a team gets X points, and the other one lose the same amount). How many points they exchange is calculated by a formula that uses the ratings pre-match to generate an “expected result”, which is compared with the actual result post-match, and with how important the match is (a friendly gives less points than a World Cup final, for instance).

Let’s use some numbers ([I used this site for the calculations](https://hermann-baum.de/excel/WorldCup/en/FIFA_Ranking.php)). Let’s say we have team A with 1600 points, and team B with 1500. The expected result is 0.59478 for A (1 means A will win, 0.5 means they will tie, 0 that B will win), so the calculation gives a slightly better probability for A, which makes sense because they have a better rating. Let’s also say this is an official friendly, so they would exchange a maximum of 10 points. If we plug all the numbers into the formula, a win by team A gives them 4.05 points, a win by B gives them 5.95, and a tie means B gets 0.95.

Notice how team A wins less points if they win than B, this is because they’re supposed to be the better team, so it’s expected for them to win. This is a main characteristic of Elo-like systems. Another thing to consider is that the formula has two parameters that are arbitrarily chosen by the ranking organizer (FIFA in this case):

– how many points are exchanged in a match, which comes from a table, ranging from 5 to 60 depending on the importance of the match (this is known as K factor in Elo, but as I in the FIFA formula),

– and how to relate each team points with their relative strength. The base Elo system uses 400 points as one order of magnitude of expected result, but FIFA uses 600 (i.e., if a team has 2000 points and another has 1400, the better team has a 10/11=0.90909… chance of winning, vs. 1/11=0.090909… of the other team, which are an order of magnitude apart).

Anonymous 0 Comments

I guess your question is how are they calculated. The ranking was implemented in 1992, and it was changed several times. I’ll talk about the system used since 2018.

They used an implementation of the Elo rating system. Each national team has a given rating, and at the end of every match, they exchange points (i.e., a team gets X points, and the other one lose the same amount). How many points they exchange is calculated by a formula that uses the ratings pre-match to generate an “expected result”, which is compared with the actual result post-match, and with how important the match is (a friendly gives less points than a World Cup final, for instance).

Let’s use some numbers ([I used this site for the calculations](https://hermann-baum.de/excel/WorldCup/en/FIFA_Ranking.php)). Let’s say we have team A with 1600 points, and team B with 1500. The expected result is 0.59478 for A (1 means A will win, 0.5 means they will tie, 0 that B will win), so the calculation gives a slightly better probability for A, which makes sense because they have a better rating. Let’s also say this is an official friendly, so they would exchange a maximum of 10 points. If we plug all the numbers into the formula, a win by team A gives them 4.05 points, a win by B gives them 5.95, and a tie means B gets 0.95.

Notice how team A wins less points if they win than B, this is because they’re supposed to be the better team, so it’s expected for them to win. This is a main characteristic of Elo-like systems. Another thing to consider is that the formula has two parameters that are arbitrarily chosen by the ranking organizer (FIFA in this case):

– how many points are exchanged in a match, which comes from a table, ranging from 5 to 60 depending on the importance of the match (this is known as K factor in Elo, but as I in the FIFA formula),

– and how to relate each team points with their relative strength. The base Elo system uses 400 points as one order of magnitude of expected result, but FIFA uses 600 (i.e., if a team has 2000 points and another has 1400, the better team has a 10/11=0.90909… chance of winning, vs. 1/11=0.090909… of the other team, which are an order of magnitude apart).