World Cup fever: insights from the wisdom of crowds

In a recent wire, Markets are wise, but not always, I set out the idea that sits under everything we do at Savana. A crowd’s accuracy is governed by the Diversity Prediction Theorem: collective error equals average individual error minus prediction diversity. The disagreement between forecasters is subtracted from the error. A diverse, independent crowd is accurate not in spite of its disagreement but because of it, and when that diversity collapses, the crowd stops being wise.

That argument was made with more than financial markets in mind. For the next six weeks the world has better things to do than read about equity valuation theory as the World Cup kicks into gear. And so, the team at Savana has read the room and pooled our energies into applying our models to predicting who walks away with it in New Jersey on 19 July.

Five models, one tournament

Using the same principles, we built a small forecasting model for the 48-team tournament. Not one view, but five, each looking at the field through a different lens: long-run Elo ratings, a goals-based model of attack and defence, squad market values, a structural scorecard of pedigree and host advantage, and recent form. Each is reasonable on its own and wrong in its own way. We combined them into a single model, then ran the real draw twenty thousand times to build a picture of how the tournament might pan out.

A word on what this is and is not. Five models is not a crowd, and this is not built to be one. It is a deliberately simple illustration, meant to show the mechanism at work rather than to out-forecast a market with thousands of participants behind it. The point is the principle, not the precision.

One thing was deliberately left out. Prediction markets such as Polymarket are themselves a crowd forecast, so we kept those markets out of the model and used them as the scoreboard. Table 1, below, sets out the win probabilities of the model against Polymarket implied probabilities.

Spain are the clear favourite at one in five, and the market crowns them as well. That agreement is the least interesting part of the table. Spain are the best covered and most analysed team in the field, priced by a deep and diverse crowd, and a model has little to add in the respect. The numbers worth studying are the disagreements beneath the favourite. The sharpest is France. The market has them as a near joint favourite, around 16 per cent, while the combined model puts them fifth, under 10 per cent. That gap of almost six points is the widest in the field. The model leans the other way on Argentina, rating them about 50% higher than the crowd does, with England also substantially above the market.

Where the models disagree

The reason to use five models rather than one is visible only when you take the combined model apart. Table 2 shows what each individual model gives the leading teams, before they are blended. The deeper the shading, the higher that model rates the team.

Look along the England row. The form model, which weights recent results, has England as the most likely winner in the whole field at 37.7 per cent, on the back of a perfect recent run. The structural model, which cares about pedigree, gives them 4.9. Brazil is the mirror image: the structural model loves the five-time champions, while the form model, looking at a patchy run of results, gives them almost nothing.

Taken alone, each of these is a bad forecast. A model that gives Brazil a zero chance based on recent form is obviously too strong, and so is one that crowns England full stop. That is the point of a many models approach, and the one most people find hardest to accept. When a problem is hard, you are better off combining views that think differently, even when each is individually unreliable. The blended column is steadier than any single model feeding it, and it is steadier by a measurable amount.

France is the exception that proves the rule. The five models barely disagree about France, clustering between 8 and 11 per cent. The disagreement there is not among the models. It is between the models and the crowd, which sits at 15.8. When diverse views line up and the market does not, that gap is the only thing worth a second look. The models see a hard group containing Norway and Senegal and mark France accordingly. They hold no loyalty to reputation.

Japan are the model's dark horse, given a 3.8 per cent chance of winning the trophy, more than twice Polymarket's 1.8. Almost all of it comes from one model: the form model, fed a long unbeaten run, rates them among the contenders, while ratings, squad value and history have them nowhere near. No single view would back them, but the blend surfaces exactly the kind of name the crowd has not yet woken up to.

How far they go

Outright odds compress a month of football into one number. For anyone who wants more to work with, the model also gives the chance of reaching each round, which is where most of the interest sits before a winner emerges.

A note for the Socceroos fans. Group D, where Australia sits with the United States, Paraguay and Türkiye, is the most even group in the draw on paper and on the model’s numbers, set out in Table 4. The spread between the strongest and weakest team is the narrowest of any group in the tournament, and on the chance of progressing it is by far the narrowest: 31 points top to bottom, against more than 42 for the next most even group. No team is a passenger and none is a runaway. In the language of the theorem, this is a group with no settled consensus, which is another way of saying it is anyone’s to take.

The same logic prices the market

I am not claiming the model knows better than the betting market. The market is itself a large and capable crowd, and over many tournaments it is hard to beat. The point is the method, and the divergences it surfaces.

The bridge to investing is the one I made in the earlier wire, so I will not rebuild it here. We see a share price as a collective forecast, and the theorem says it is accurate exactly when the views behind it are many, independent and diverse. The favourites in this model are the equivalent of the largest listed companies. They are watched by everyone, priced by a deep and varied crowd, and the model agrees with the market on them. The interesting gaps sit further down the field. You can see them in the first table: the combined model gives Japan more than double the market’s implied chance of winning, and rates Morocco above the crowd too. These are less fashionable names, watched by fewer people and easily defined by a single story, and they are exactly where a thin, like-minded crowd is most likely to misjudge. That is the same place, in markets, where the diversity term is small and prices drift furthest from value. As I set out last week, in equities that describes neglected smaller companies almost perfectly.

This is also why our own investment process is built from many models rather than a single view. It is a rules-based system applied across tens of thousands of global companies, designed to act as one more independent, diverse forecaster, and to add the most where the existing crowd is thinnest and most alike. The World Cup model on this page is a toy version of that same machine.