Elo Rating

The group stage is over, the Round of 32 is set — and the model has changed its mind. ⚽️

When I ran the numbers before kickoff the model had a bold, market-contrarian opinion: 🇪🇸 Spain to win it at 35.3%, 🇦🇷 Argentina second at 23.0% and both dramatically underpriced by the bookies — Spain’s +19.3pp edge over Polymarket was the strongest disagreement between maths and money I’d ever put on this blog. I promised I’d come back on the other side of the trophy ceremony to find out whether the model deserved its confidence.

FIFA is a mafia. Now let’s watch football.

Let’s not beat about the bush: FIFA is a mafia, their Peace Prize a disgrace and a host country so hostile towards the expected guests from all over the world not worthy of that honour. But as soon as the whistle sounds later today and the first ball is kicked, none of this matters anymore and football (or soccer in freedom units) rules everything. ⚽️

A year in the making

The 2026 World Snooker Championship is under way at the Crucible in Sheffield — a natural point to rerun the forecast from last April, when we put Elo on five decades of results and ran ten million tournament simulations. John Higgins led our list at 13.14%; Zhao Xintong was fourth at 10.58% but took the 2025 title and has stayed at or near the top of the ratings since.

At some point this year, I let my laptop run flat-out for almost two weeks just to answer one question: how much of a four-player board game is “skill” and how much is “luck”? That sounds excessive, but there was a catch: before I could even start those simulations, I had to fix a basic problem. Elo – the rating system we’ve been happily using so far – only really knows how to handle one-on-one duels.

Whether a game counts as “skill” or “chance” isn’t just a pub argument — in many countries it’s a legal distinction. Roulette and blackjack live on the “chance” side; tennis and chess are filed under “skill”. Different rules, different taxes, different ways for people to lose money.

The trouble is that this line is usually drawn by tradition and gut feeling. Is poker really “more skill” than backgammon? Is snooker closer to roulette or closer to chess? A group of economists tried to answer that question more systematically: instead of arguing, measure how “skill-heavy” a game is in practice by looking at the Elo ratings of all its players. We’ll meet their work properly in a bit.

Welcome to the Crucible

This blog is usually all about board games, but let’s stretch the definition just a little: snooker is, after all, one of the most widely followed tabletop games in the world. And with the World Championship kicking off at the Crucible Theatre in Sheffield, I couldn’t resist the excuse to dive into something a bit different.

In the last article, we looked at how Elo ratings can be used to measure player strength over time. This time, we’ll take it a step further: using historical match data, a bit of Python, and a lot of simulated tournaments, we’ll try to predict who’s most likely to lift the trophy this year. We’ll also compare our predictions to what the betting markets say – and see whether the wisdom of the crowd agrees with the cold logic of the model.

Chance in games is like seasoning in food — it’s all about the right amount. Just imagine a life without chance, where everything could be planned out strategically. That would get boring over time. In a game, I want to have experiences — I want adventure. A good game is like a miniature life, one where I can make mistakes, enjoy a streak of bad or good luck, and still recover. But you shouldn’t be at the mercy of randomness. There should be ways to compensate — like a friend of mine in CATAN, who always complains about his bad luck, prompting others to treat him more kindly and rarely target him with the robber. In the end, he often wins — to everyone’s surprise.
— Klaus Teuber on the importance of randomness in games in CATAN-News 1/2000 🗄️

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