The online calculator is also available for ranking women:

▸Online calculator for the FIFA Women's World Ranking

The picture shows the first eight nations of the FIFA World Ranking as of 16 Sep. 2021. A click on the image leads to the current world ranking on the FIFA website.

The rank of each national team is determined by a rating number. In first place (rank 1) is Belgium with a rating number of 1832.33 and in last place (rank 210) is San Marino with a rating number of 791.17.

This rating number changes with each international match of a nation - not only in tournament matches but also in friendly matches. Using the online calculator at the top of the page, you can try out different cases to get a feel for how much the rating number increases or decreases in each case.

Since August 2018, FIFA calculates the ranking coefficient according to a new procedure. In the old method, an average value was calculated from the match results of a certain period. In the new method, the playing strength of a team is indicated by a so-called ELO number, similar to chess. (Arpad Elo had developed this method of calculating playing strength for the American Chess Federation in 1960). This ELO number now determines the rank in the FIFA rankings.

The transition from the old to the new procedure was regulated in such a way that on a certain key date the top of the ranking list (Belgium) received the ELO value 1800. The second in the ranking was given an ELO value of 1796, the third an ELO value of 1792, and so it went on in intervals of 4 points until the last in the ranking. These "starting values" have changed with every game since then according to the formula developed by Arpad Elo. However, this formula is supplemented by some useful special conditions.

Consider an example:

Brazil (hereafter Team A) played against Argentina (hereafter Team B) on July 11, 2021 and lost the Copa América final 0 - 1.

By the way, the amount of the defeat/victory does not matter for the recalculation of the rating number.

In the following I use the same letters for the variables in the formulas as in the ▸description of FIFA to facilitate the comparison with this description.

1. step:

First, a number W is created that expresses a victory in numbers:

W = 1 | a win |

W = 0.5 | half win, i.e. draw |

W = 0 | zero win, i.e. one loss |

2. step:

For Brazil, based on the two ELO numbers (Brazil 1811.73 and Argentina 1725.31), a kind of expected value (W_{e}) for the match result is calculated. This expected value W_{e} is always between 0 and 1. Since Brazil and Argentina are about equal in strength, this number W_{e} will be about 0.5. If Brazil were to play against a much weaker opponent, the expected value W_{e} would be closer to 1.

According to Arpad Elo, the formula for W_{e} is:

Or in linear notation: W_{e} = 1 / (10^((P_{B} - P_{A})/600) + 1)

P_{A}: rating number of Team A (the team whose rating number is recalculated)

P_{B}: rating number of Team B (the opposing team)

Note: When calculating the ▸ELO number in chess, instead of 600, it is divided by 400. Arpad Elo had chosen this number so that the new rating numbers of chess players matched as closely as possible those of Kenneth Harkness's previous rating system.

So for Brazil, in this example, we would have to calculate:

And that gives W_{e} = 0.58216.

The value is slightly greater than 0.5. This was also to be expected, since Brazil's rating number (1811.73) is slightly greater than Argentina's (1725.31). Within certain limits, this number can also be taken as the probability of a Brazilian victory. This probability would therefore be 0.58216 or 58.2%.

3. step:

Calculation of the new rating number P_{A,new} for Brazil according to the formula:

P_{A,new} = P_{A} + I * (W - W_{e})

Factor I (Importance) is a weighting factor, with which friendly matches have less weight than qualifying matches or even knockout matches of a World Cup.
The following weightings are given by FIFA:

5 | Friendly matches played outside of International Match Calendar windows |

10 | Friendly matches played during International Match Calendar windows |

15 | Group phase matches of Nations League competitions |

25 | Play-off and final matches of Nations League competitions |

25 | Qualification matches for Confederations final competitions and for FIFA World Cup final competitions |

35 | Confederation final competition matches up until the QF (quarter final) stage |

40 | Confederation final competition matches from the QF stage onwards; all FIFA Confederations Cup matches |

50 | FIFA World Cup final competition matches up until QF stage |

60 | FIFA World Cup final competition matches from QF stage onwards |

Since the Brazil-Argentina match was the final of a confederation competition (Confederation CONMEBOL), the weighting factor 40 is taken.

The calculation of the new rating number of Brazil then looks like this:

P_{A,new} = 1811.73 + 40 * (0 - 0.58216) = 1788.44

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The Calculation of Argentina's rating number looks like this:

That gives W_{e} = 0.41784.

(It is not a coincidence that the expectation numbers of both teams add up to exactly 1, but a mathematical law.)

The new rating number for Argentina is then:

P_{B,new} = 1725.31 + 40 * (1 - 0.41784) = 1748.60

Additional rule 1:

Matches decided by a penalty shootout are counted as a draw for the defeated team (W = 0.5) and as a "half win" for the winning team (W = 0.75).

Matches in which a penalty shootout is not held for the purpose of deciding the match, but to decide a ranking or whether a player advances to the next round, shall be scored normally.

Additional rule 2:

In knockout matches of final tournaments (e.g. World Cup and European Championship) the rating of the loser does not deteriorate. This is to avoid that a team that has qualified for the knockout round is worse off than a team that has not reached the knockout round.

However, the rating number of the loser can also improve (despite defeat): for example, if a team with a lower rating number loses to a team with a higher rating number after penalty shootout. This improvement will then be credited.

Argentina's rating number improves in our example. Due to the 2nd additional rule, Brazil retains its old rating.

In the online calculator at the top of this page you have to set a checkmark at "KO round". Then you can see the correct new rating numbers:

Brazil: | 1811.73 |

Argentina: | 1748.60 |

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Calculation of ELO number with Excel

If you like to calculate the FIFA rating number in Excel, you can download a corresponding Excel solution here:

▸FIFA Rating Calculator with Excel

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