World Cup 2026 Elimination "Food Chain"

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World Cup 2026 Elimination "Food Chain"<br>Jul 06, 2026

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Haiti is one of the earliest nations to be eliminated from the 2026 World Cup. After just two matches, they lost 0-1 to Scotland on June 14 and then lost again 0-3 to Brazil on June 20.<br>But if we check the archive, their World Cup journey was actually much longer than those two matches. The qualification stage started in 2024, and they had to endure at least ten matches before securing their place at the World Cup.<br>Before being eliminated by Scotland and Brazil in the group stage, they had actually eliminated several CONCACAF nations during the qualification stage: Saint Lucia, Barbados, Aruba, Honduras, Costa Rica, and Nicaragua.

work in progress

After realizing this, I noticed that there is an implicit “food chain” among nations in the World Cup.<br>Nation B eliminates Nation C, then later Nation A eliminates Nation B, whether in qualification, the group stage, indirectly through mathematical elimination in the third-best group ranking, or later in the knockout rounds such as the Round of 32, Round of 16, and beyond.<br>I want to visualize this “food chain” as a graph.

work in progress (source code)<br>There's plenty of data that I still need to process, and as of this writing, the World Cup is still ongoing. As a result, this dataset remains incomplete and is still a work in progress. Below is the list of (eliminated) nations that I have managed to process so far.

Anyway, what insights have I managed to notice so far?<br>First, there are these “isolated” subgraphs.

Two relatively big subgraphs. Three small, isolated subgraphs.<br>The pattern is obvious: two or three nations manage to push a single nation to the bottom of its group, then get eliminated themselves. This happened to New Zealand, Tunisia, and Turkey.

Then, I found the first “big” subgraph.

very lowres. sorry.<br>Most of it consists of Asian (AFC) nations, but there is also a small connection to South American (CONMEBOL) nations because of two events.<br>First, the intercontinental qualifier between Bolivia and Iraq, where Iraq eliminated Bolivia from World Cup contention with a 2-1 win.<br>Second, Spain (Europe - UEFA) quickly eliminated both Uruguay (South America - CONMEBOL, 1-0) and Saudi Arabia (Asia - AFC, 4-0) in the group stage. As a result, three South American nations—Venezuela, Chile, and Peru—became part of this “Asian subgraph” thanks to Uruguay losing to Spain and Bolivia losing to Iraq.<br>Wait... I just remembered today’s “Hatsune Miku” meme trending on X after Norway eliminated Brazil in the Round of 16.

The meme started after Brazil eliminated Japan in the Round of 32, effectively “taking over” Hatsune Miku from Japan. Now that Brazil has lost to Norway, Miku’s custodianship has passed to Norway.<br>Using that same logic, who is the real “king” of this large, Asian-majority subgraph?<br>I wondered if there was already a mathematical name for this problem: given a directed graph, define the “king” as one or more nodes that sit at the top of the food chain.<br>ChatGPT suggested that if indirect eliminations are taken into account, then the relevant concept is reachability or the graph’s transitive closure. Under that definition, a “king” would be a node that can reach the largest number of other nodes through directed paths.<br>I’m not going to implement that functionality just yet. Instead, I’ll trace it manually using this visualization.<br>Hmm... it seems this subgraph has multiple “kings”: Colombia, Portugal, Canada, Bosnia and Herzegovina, France, Norway, Senegal, Austria, Algeria, and Spain.

And, here’s the second big subgraph that I managed to find.

The real clash between Europe and the Americas.<br>Scotland managed to eliminate Haiti with a 1-0 win. Then, in retaliation (?), South America’s Brazil eliminated Scotland with a 3-0 win. Ironically, Brazil’s assault on Scotland would not have happened without Europe’s Croatia and its advanced 4D chess “remote mathematical elimination” technique. Although Croatia was in Group L and Scotland was in Group C, Croatia still managed to indirectly eliminate Scotland.<br>I jokingly call it a “4D chess” move because the chain of events is so complicated to calculate. Just take a look at this:<br>“Scotland needed Ghana to defeat Croatia by a large enough margin to keep Scotland’s goal difference and ranking among the best third-placed teams alive. Instead, Croatia’s 2–1 victory meant Scotland could no longer finish in the top eight third-placed teams. Before the final Group L matches, Scotland’s qualification scenario required all three of the following: Ghana to beat Croatia by three or more goals; either Uzbekistan to draw with DR Congo or win by fewer than four goals; and either Austria to beat Algeria by at least two goals or Algeria to beat Austria by at least four goals. Instead, Ghana lost 2–1 to Croatia, ending Scotland’s hopes immediately. Even if the other two conditions had been met,...