Bundesliga: One Score Matrix, Every Market Read From It

Most people treat the 1X2 market and the goals markets as separate things. In a properly built probabilistic model they are the same object viewed from two angles. This guide explains how.

It starts with two numbers

For every fixture the model estimates two expected scoring rates:

home rate = league average home goals × home attack × away defence
away rate = league average away goals × away attack × home defence

The attack and defence ratios are measured against the league average, with time decay — a weight of 0.0065 per day inside a 730-day window — and shrinkage toward 1.0 when the sample is small.

Both mechanisms matter. Without decay, matches from two years ago carry too much weight. Without shrinkage, a side with a handful of matches receives an extreme ratio and everything downstream inherits the distortion.

From rates to a matrix

From the two rates comes a matrix of every plausible scoreline: 0-0, 1-0, 0-1, 1-1, 2-0 and onward, each with its own probability.

That is the complete picture. Every market is derived from it by summing cells:

Market	Cells summed
Home win	Every cell where home goals exceed away goals
Draw	The diagonal
Away win	Every cell where away goals exceed home goals
Over 2.5	Every cell where the total exceeds 2
Under 2.5	Every cell where the total is under 3
Both teams to score	Every cell where both numbers exceed 0

The important consequence: every market is consistent with every other by construction. There is no configuration in which the home-win probability and the over-2.5 probability contradict each other, because both are read off the same object.

That is a property separating a coherent model from a collection of independent estimates. It is also something you can test on any product: if a source shows a high probability for a dominant home win alongside a very high probability for under 1.5 goals, it is worth asking whether both numbers came from the same place.

Why the low-cell correction affects goals markets too

The correction that re-weights the 0-0, 1-0, 0-1 and 1-1 cells looks like it concerns only the draw. It does not.

All four of those cells sit on the under 2.5 side of the line. Changing their weight necessarily changes the over-2.5 probability, which is the complement.

So a correction designed to improve accuracy in low-scoring results improves the goals markets as much as the match-result market — one of the concrete advantages of producing a matrix rather than estimating each market separately.

When goals markets are withheld

An explicit rule: goals markets are published only when both teams have at least twenty matches of history.

The reason is that the rates are estimated from history. A rate estimated from ten matches carries a wide error bar, and a matrix built on it produces numbers that look precise and are not.

This happens mainly early in a season, and for promoted sides without sufficient history at the current level. In those cases the 1X2 market may appear while the goals markets do not — because the 1X2 probability also leans on strength ratings, whereas the goals markets rest almost entirely on the rates.

What this means for reading a round

1. Cross-market consistency is a check you can run. It costs nothing and it filters out a surprising number of products.

2. Goals markets are not "easier". There is a belief that forecasting goal volume is simpler than forecasting a winner. In practice both come from the same rates, so their uncertainty has the same source.

3. Devig goals markets too. Margins in goals markets are usually tight in major leagues, but in a two-way market the two implied probabilities still sum to more than 100.00%. Comparing a model estimate to a raw implied probability is wrong in a consistent direction there as well.

Data quality and league size

This league sits in the well-covered group: long history, reasonable price depth, xG in recent data files, lineups at a known time. The score is relatively high, so the uncertainty budget is low — the gap required to classify a fixture as actionable is smaller than in a thin-data league.

One detail worth noticing: the number of clubs in a league affects how quickly history accumulates. In a league with fewer teams, each side plays fewer matches per season, so the data quality saturation point — around forty matches per team — is reached later within the season. That is a mechanical effect, not a judgment about the league.

What the backtest says

The Bundesliga is included in the walk-forward backtest shown on the performance page, alongside four other major European leagues. Two findings, published as they stand: roughly 52–53% accuracy on 1X2 across test seasons, and the market's closing price still measuring about 0.02–0.03 better in log-loss.

The figures are pooled across the five leagues, so there is no separate German number.

What to check before a round

1. Whether the goals markets are shown at all. Absence tells you something about history depth.
2. The estimated rates, not just the resulting probability — they explain why the matrix looks the way it does.
3. The data quality score, particularly early in a season and for promoted sides.
4. The decision state, and specifically which PASS reason applies.

Summary

What looks like two separate markets is two readings of one matrix. That is what allows consistency to be verified, and what explains why a correction aimed at four low-scoring cells improves the goals markets as much as the match-result market.

And what does not change: if there is not enough history, the market is not published — because showing nothing is better than showing a number with no basis.

A consistency check you can run on any product

Because every market derives from one matrix, there is a simple test you can apply to any prediction product, even one that does not disclose how it works.

Take a fixture showing a very high probability for a dominant home win. Now look at the over/under probability for the same fixture. If the two numbers do not sit comfortably together — a comprehensive home win alongside a very high probability for under 1.5 — it is worth asking whether they came from the same place.

The test requires no technical knowledge and filters out more than you would expect.

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