After losing the opening match against Saudi Arabia, Argentina won the World Cup for the 3rd time. Supporters of Saudi Arabia can comfort themselves by claiming that "we beat the champions. That makes us (Saudi Arabia) champions." By the same logic, any team that has defeated Saudi Arabia before the World Cup can make simialr claims. One may wonder how an individual or team can become a champion by defeating an opponent which wins the championsip (for the first time) at the end of the tournament. Shouldn't the reverse — one becomes a champion by defeating the reigning champion (think of title belts in boxing or MMA) — be true? That got me into thinking how many FIFA member nations can claim to be world champions by defeating a team that has previously won a World Cup. By applying transitivity — A leads to B and B leads to C, thus A leads to C — repeatedly, we can go further and say, if we go far enough, every FIFA member is a world champion.
To date 8 national teams — Argentina, Brazil, England, France, Germany, Italy, Spain and Uruguay — have won the World Cup. In this exercise we consider them Tier 0 champions. Any (current) FIFA member nation that has won a match against any of the Tier 0 teams after the latter won the World Cup would be considered Tier 1 champions. Any team which has defeated any of team in Tier 1 (but has never won a match against any of the Tier 0 teams) would be considered Tier 2 champions, and so forth. The goal is to find how tiers are required before every FIFA member is crowned champions.
Nations may merge, split and be annexed from time to time. In this exercise a FIFA member which was part of a nation that has defeated any of the World Cup winners would be considered Tier 1 champions. (For example, any former Soviet republic.) Similarly, if a FIFA member is formed by merging multiple nations and one of them has defeated any of the World Cup winners, the merged nation would be considered Tier 1 champions. Since 3 of the 4 world Cups won by present-day Germany were won by West Germany before reunification, any nation that has notched a win against West Germany after its first World Cup win in 1954 would also be considered Tier 1 champions.
By applying the above rules, the champions in world football can be separated into the following tiers:
| Tier 0 | |||
| Argentina | Brazil | England | France |
| Germany | Italy | Spain | Uruguay |
| Tier 1 | |||
| Albania | Algeria | Armenia | Australia |
| Austria | Azerbaijan | Belarus | Belgium |
| Bolivia | Bosnia and Herzegovina | Bulgaria | Cameroon |
| Chile | China PR | Colombia | Costa Rica |
| Croatia | Czech Republic | Denmark | Ecuador |
| Egypt | Estonia | Finland | Georgia |
| Greece | Guatemala | Honduras | Hungary |
| Iceland | Indonesia | Iran | Israel |
| Cote D'Ivorie | Jamaica | Japan | Kazakhstan |
| Kosovo | Kyrgyzstan | Latvia | Lithuania |
| Mexico | Moldova | Netherlands | Nigeria |
| North Korea | North Macedonia | Northern Ireland | Norway |
| Paraguay | Peru | Poland | Portugal |
| Republic of Ireland | Romania | Russia | Saudi Arabia |
| Scotland | Senegal | Serbia | Slovakia |
| Slovenia | South Africa | Korea Republic | Sweden |
| Switzerland | Tajikistan | Tunisia | Turkey |
| Turkmenistan | Ukraine | United States | Uzbekistan |
| Venezuela | Wales | ||
| Tier 2 | |||
| Afghanistan | Andorra | Angola | Antigua and Barbuda |
| Bahrain | Bangladesh | Barbados | Benin |
| Bermuda | Botswana | Burkina Faso | Burundi |
| Cambodia | Canada | Cape Verde Islands | Cayman Islands |
| Central African Republic | Chad | Congo | Cuba |
| Curacao | Cyprus | DR Congo | El Salvador |
| Equatorial Guinea | Ethiopia | Faroe Islands | Fiji |
| French Guiana | Gabon | Gambia | Ghana |
| Gibraltar | Grenada | Guadeloupe | Guam |
| Guinea | Guyana | Haiti | Hong Kong |
| India | Iraq | Jordan | Kenya |
| Kuwait | Lebanon | Lesotho | Liberia |
| Libya | Liechtenstein | Luxembourg | Madagascar |
| Malawi | Malaysia | Maldives | Mali |
| Malta | Martinique | Mauritania | Mauritius |
| Mongolia | Morocco | Mozambique | Myanmar |
| Namibia | New Zealand | Nicaragua | Niger |
| Oman | Pakistan | Palestine | Panama |
| Papua New Guinea | Philippines | Qatar | Rwanda |
| Sierra Leone | Singapore | Sudan | Suriname |
| Syria | Taiwan | Tanzania | Thailand |
| Togo | Trinidad and Tobago | Uganda | United Arab Emirates |
| Vietnam | Yemen | Zimbabwe | |
| Tier 3 | |||
| Anguilla | Aruba | Bahamas | Belize |
| Bhutan | British Virgin Islands | Brunei | Comoros |
| Cook Islands | Djibouti | Dominican Republic | Eritrea |
| Eswatini | Guinea-Bissau | Laos | Macau |
| Nepal | New Caledonia | Northern Mariana Islands | Palau |
| Saint Kitts and Nevis | Saint Lucia | Saint Martin | Saint Pierre and Miquelon |
| Saint Vincent and the Grenadines | Samoa | San Marino | Sao Tome and Principe |
| Seychelles | Solomon Islands | Somalia | Sri Lanka |
| Tahiti | Timor-Leste | Tonga | Turks and Caicos Islands |
| Tuvalu | U.S. Virgin Island | Vanuatu | |
Not only does every team can regard themselves champions, every nation (aside than, of course, nations in Tier 0) can only move up — if a nation wins a World Cup in the future, it will rise to Tier 0 and every nation that defeats the new champion would rise to Tier 1 (if they are not already in this tier). There may even be one day (a number of millenia from now) when the tiers would no longer be needed (ie every nation has won the World Cup). (Of course, by then the tournament may be called the Intergalatic Cup.)