Model

Why our model can't tell you if Arsenal are better than Flamengo

By FootInsights · Published 29 Aug 2026 · Updated 26 Sep 2026 · 5 min read

A reasonable thing to want from a football model is a single list: every team we cover, strongest to weakest, regardless of competition. Any site could produce that list trivially — ratings are numbers, and numbers sort. What nobody can honestly do is tell you it means anything, and the reason is worth understanding because it applies to every rating system you will encounter, including the famous ones.

The numbers look comparable

Here is what a typical league-anchored rating table looks like. The figures are illustrative, but the shape is universal:

Read that table naively and it says the best team in the Championship (1750) is almost exactly as strong as the best team in the Premier League (1790), and comfortably stronger than the average Premier League side. Nobody who has watched both divisions believes that for a moment.

The table is not wrong. It is being read wrong.

Why every league averages 1500

Elo is a closed, zero-sum accounting system. Every point one team gains, another loses. Run it over a set of teams that only ever play each other, and the total is conserved: the average of the pool stays fixed at wherever it started, which by convention is 1500.

Nine domestic leagues rated this way are nine separate pools. Teams inside each pool play each other and essentially never play across, so nine independent Elo systems each sit anchored at 1500 by construction. A rating of 1750 means “far above average for this league”, and that is the entire content of the number. It carries no information about how the league itself compares to another.

The same problem exists in a different form for the attack and defence ratings a Dixon-Coles model fits. Those are estimated per league, against that league’s own scoring baseline. An attack rating of 0.50 means “scores half a log-goal more than a typical team in this competition” — and a typical team in the Bundesliga, which averages over three goals a match, is not a typical team in the Brasileirão, which averages under two and a half. The units are the same. The zero point is not.

This is why such models are usually fitted per league rather than globally: it makes each league’s numbers internally sharp, at the cost of making them mutually meaningless. That trade is the right one for match predictions inside a competition, which is what most sites actually publish.

What would actually fix it

Cross-league ratings are not impossible. They require matches that cross the leagues — and enough of them.

Continental competitions are the standard bridge. When Premier League clubs play Bundesliga clubs in the Champions League, those results tie the two pools together, and a rating system that ingests them can place both on one scale. This is exactly what the well-known global club rankings do, and why they can say something a domestic-only rating cannot.

FootInsights prices domestic and European football with one model, so it faces this problem directly rather than sidestepping it. That does not make the problem go away, because the bridge is narrow. Only a handful of clubs from each league qualify, they are the strongest ones, and they play a few matches a season against each other. So the connection between two leagues is estimated from a small, non-random sample of their best teams — which tells you about the top of each league and extrapolates, with real uncertainty, to the rest. Even the good cross-league systems are less confident than their tidy numbers suggest, and they are far less confident about the bottom of a table than the top.

Between European and South American club football the bridge is narrower still: a single annual fixture between two continental champions, which is essentially no sample at all. Anyone giving you a confident answer on Arsenal against Flamengo is extrapolating, whether they say so or not.

Why we don’t publish the list anyway

We could take the ratings, apply an offset per league guessed from continental results, and publish a global table. It would get traffic. It would also be a number with far more uncertainty than its presentation implied, and the uncertainty would be invisible to anyone reading it.

That runs against the thing this site is for. Our how our predictions work page states what we publish and why, and a global ranking would be a claim the evidence does not support. The track record settles predictions we can actually check against results; a cross-league rating has no fixture to be settled against, which is precisely what makes it comfortable to publish and impossible to falsify.

What to do with ratings you find elsewhere

Three questions worth asking of any global club ranking:

1. What connects the leagues? If the answer is continental competition, the ranking is only as good as that bridge — strong for elite clubs, thin for everyone else.
2. Is there an uncertainty range? A rating quoted to the integer with no error bar is presenting precision it does not have. This is the same problem as a win rate with no sample size.
3. Is it being used for anything? A ranking that never gets tested against a fixture cannot be wrong, and things that cannot be wrong are not evidence.

Within a competition, our predictions do real work and are settled in public every week. Across competitions that never meet, the honest answer to “who is better” is that nobody knows with nearly the confidence they imply — and we would rather say so than publish a list.