Model

Supremacy and total goals: the two numbers behind a football price

By · Published · 7 min read

Ask a trader what they think of a match and you rarely get a probability back. You get two numbers: supremacy and total goals — how far ahead one side is, and how many goals the game holds. That pair is the compressed form of an entire match forecast, and almost every price on the coupon can be rebuilt from it. Understanding the mapping is the difference between reading a market as a list of unrelated bets and reading it as one opinion expressed sixty different ways.

What supremacy and total goals actually mean

Both are expectations, not predictions of a scoreline.

Supremacy (S) is the expected goal difference: expected home goals minus expected away goals. A supremacy of 0.6 does not mean anyone expects the home side to win by 0.6 goals — no such result exists. It means that if the match were replayed many times, the average margin would come out around six-tenths of a goal in the home side’s favour. Supremacy is signed: negative supremacy means the away team is favoured.

Total goals (T) is the expected number of goals in the match, both teams combined. A total of 2.70 means the average across those replays is 2.70 goals, even though no single match ever ends 2.70.

Spread-betting firms quote both directly as markets you can buy or sell. That is a product built on top of the numbers, not what the numbers are for. Their real job is upstream: they are the two parameters a model hands over before any market is priced.

Turning the pair into two goal expectancies

The pair is useful because it inverts cleanly. If λhome and λaway are the expected goals for each side, then by definition:

  • S = λhome − λaway
  • T = λhome + λaway

Two equations, two unknowns. Add and subtract them:

  • λhome = (T + S) ÷ 2
  • λaway = (T − S) ÷ 2

Take S = 0.60 and T = 2.70. Then λhome = (2.70 + 0.60) ÷ 2 = 1.65, and λaway = (2.70 − 0.60) ÷ 2 = 1.05. Two numbers a human can hold an opinion about have become two goal expectancies a model can work with.

The scoreline grid does the rest

Once you have a goal expectancy per side, you can put a probability on every scoreline. The standard approach treats each side’s goals as a Poisson variable, which we walk through in detail in the Poisson distribution in football. Multiply the two distributions together and you get a grid.

Here is that grid for λhome = 1.65 and λaway = 1.05, in percent, home goals down the side and away goals across:

Home \ Away 0 1 2 3 4
0 6.72 7.06 3.70 1.30 0.34
1 11.09 11.64 6.11 2.14 0.56
2 9.15 9.61 5.04 1.77 0.46
3 5.03 5.28 2.77 0.97 0.25
4 2.08 2.18 1.14 0.40 0.11

Every market is now a matter of adding the right cells:

Market Cells summed Probability
Home win everything below the diagonal 51.4%
Draw the diagonal 24.5%
Away win everything above the diagonal 24.1%
Over 2.5 goals all cells where home + away ≥ 3 50.6%
Both teams to score all cells where home ≥ 1, away≥1 52.5%
Home −1 Asian handicap win by 2+ (push if exactly 1) 27.5% win, 23.9% push

The Asian line is worth pausing on. A 23.9% chance of the stake coming back changes what a fair price looks like — with the push removed, home −1 needs about 2.77 to break even rather than the 3.64 the raw 27.5% suggests. That mechanic is covered in Asian handicap explained.

The important part is that all six numbers came from the same two inputs. They cannot contradict each other, because there is nothing for them to contradict — they are six views of one grid.

Why supremacy and total goals, and not any other pair

You could parameterise a match with λhome and λaway directly. The reason the industry uses supremacy and total instead is that the pair separates the questions people actually disagree about.

Watch what happens when total goals is held at 2.70 and only supremacy moves:

S T λh λa Home Draw Away Over 2.5
0.00 2.70 1.35 1.35 37.1% 25.8% 37.1% 50.6%
0.60 2.70 1.65 1.05 51.4% 24.5% 24.1% 50.6%
1.40 2.70 2.05 0.65 70.2% 19.1% 10.7% 50.6%

The result markets swing violently — a home win goes from 37.1% to 70.2%. Over 2.5 goals does not move at all. It sits at 50.6% in all three rows, and that is not a rounding coincidence: if each side’s goals are Poisson, the match total is Poisson with mean T, so the goals markets depend on T alone. Supremacy is invisible to them.

Now move the other lever and hold supremacy at 0.60:

S T λh λa Home Draw Away Over 2.5
0.60 2.70 1.65 1.05 51.4% 24.5% 24.1% 50.6%
0.60 3.40 2.00 1.40 51.5% 21.7% 26.9% 66.0%

The home win barely flickers — 51.4% to 51.5% — while Over 2.5 jumps fifteen points. Raising the total mostly drains the draw, because more goals means fewer level finishes.

That near-orthogonality is the whole point. “I think the home side is stronger than the market does” and “I think this will be a tight, low-scoring game” are separate claims, and this parameterisation lets you hold one while revising the other without accidentally corrupting both.

Both-teams-to-score is the instructive exception: it fell from 54.9% to 41.6% across the first table even though the total never moved. BTTS depends on the split as well as the size, because lopsided goal expectancies make a clean sheet likelier at one end. It is a hybrid market, and treating it as a pure goals market is a common way to misprice it.

Where the mapping breaks down

The arithmetic from S and T to two expectancies is exact — it is just algebra. Everything after that inherits the assumptions of the grid you build, and those assumptions are not free.

The independent-Poisson grid understates draws. Real football has slightly more 0-0s and 1-1s than independence predicts, because goals in a match are not independent events: game state changes how both teams behave. Corrections such as the Dixon-Coles adjustment exist precisely to patch the low-score cells. A grid built without such a correction will quietly under-price the draw and over-price both 1-0 and 0-1.

The pair is also silent on distribution within a match. Two fixtures can share the same S and T while one is a cagey game decided late and the other is end-to-end — identical grids, different in every respect a live trader cares about.

And a compression is still a compression. Squeezing a forecast into two numbers discards how confident the model is in them. A supremacy of 0.6 derived from hundreds of matches of stable data and one scraped together from a handful of fixtures produce the same grid and deserve very different treatment.

Reading a price backwards

The mapping runs in reverse, which is the practical use. Given a market’s 1X2 and Over/Under prices, strip out the margin, then search for the (S, T) pair whose grid reproduces those probabilities. What you recover is the market’s own opinion, stated in the same units as yours — and comparing two supremacies is far more informative than comparing two sets of decimal odds, because the difference is in goals, a quantity you can reason about.

It also imposes discipline. If your view implies a supremacy of 1.4 where the market implies 0.6, you are claiming to know something worth roughly eight-tenths of a goal. That is a large claim about a football match, and stating it that way makes it much harder to talk yourself into.

This is why our published output is a set of probabilities rather than a supremacy line, and why every one of them is scored after the fact on our public track record. Two numbers are a convenient way to carry a forecast around. Whether the forecast was any good is a separate question, and only the record answers it.