Math & ModelsUpdated 21 Jul 20266 min read
Home Advantage
Playing at home lifts a team's expected goals by roughly 15%. That sounds small. In a typical fixture it moves the home win probability by about nine points and the fair price from 2.70 to 2.15.
Home advantage is the largest single non-team effect in football, and it is the first thing any model has to get right. Everything else — form, injuries, motivation — is a rounding error beside it.
How big it actually is#
The blunt version: across league football, home sides collect clearly more than half of all points on offer. That number moves around by country and has trended gently downwards over the decades, but it has never been close to even.
Quoting a single headline percentage is less useful than it looks, though, because it depends on the league, the season and how you count. The version that is actually portable is the one models use: how much does playing at home change a team's expected goals?
Treat it as a multiplier. Suppose two evenly matched sides would each be expected to score 1.35 goals on a neutral ground. Apply a home uplift of about 15% and a matching reduction for the visitors, and you get 1.55 against 1.15 — the same 2.70 goals in the match, distributed differently.
| Expected goals | Home | Draw | Away | Over 2.5 |
|---|---|---|---|---|
| 1.35 v 1.35 (neutral) | 37.1% | 25.8% | 37.1% | 50.6% |
| 1.55 v 1.15 (home ground) | 46.5% | 25.2% | 28.2% | 50.6% |
Two things in that table are worth staring at.
The 1X2 book is transformed. A coin-flip fixture becomes one where the home side is a clear favourite, the away price drifts from 2.70 out past 3.50, and nothing about either team has changed. Nine percentage points of win probability is more than most team-news events are worth.
And the totals book does not move at all. Because the uplift and the reduction cancel, the total expected goals is unchanged, so Over/Under 2.5 sits at 50.6% on both rows. Home advantage is overwhelmingly a distribution effect, not a volume effect — which is why it dominates match-result pricing and barely registers on totals.
Do it yourself rather than trusting the table. In the Poisson calculator, set both sliders to 1.35 and note the three prices, then drag the home rate to 1.55 and the away rate to 1.15 and watch the whole book re-price while the goal total stays put.
Scoreline probability
home ↓ · away →| 0 | 1 | 2 | 3 | 4 | 5 | |
|---|---|---|---|---|---|---|
| 0 | 7.1 | 6.6 | 4.2 | 1.6 | 0.5 | 0.1 |
| 1 | 9.5 | 12.5 | 6.8 | 2.6 | 0.7 | 0.2 |
| 2 | 8.2 | 9.4 | 5.4 | 2.1 | 0.6 | 0.1 |
| 3 | 4.4 | 5.0 | 2.9 | 1.1 | 0.3 | 0.1 |
| 4 | 1.7 | 2.0 | 1.2 | 0.4 | 0.1 | 0.0 |
| 5 | 0.6 | 0.6 | 0.4 | 0.1 | 0.0 | 0.0 |
Percentages, shaded by likelihood. The grid runs to 8-8 behind the scenes; scorelines above 5 are too rare to be worth the ink.
Most likely scorelines
These are fair probabilities — no bookmaker margin. A real price for the same outcome will always be shorter than the fair odds shown, and the gap is the book's fee.
Where the advantage comes from#
Four candidate causes, all plausible, all partly true:
- Travel. Visitors move, sometimes across time zones, sleep in unfamiliar beds and arrive on a coach. The effect is small per match and larger in leagues with real distances or altitude.
- Familiarity. Pitch dimensions, surface, run-up to the stand, warm-up routine, dressing room. Marginal individually, and there are eleven of them.
- The crowd. Direct encouragement of one side and pressure on the other, plus a tactical consequence: home teams attack more, which is visible in shot counts long before it is visible in results.
- Referee bias. Not corruption — ordinary social pressure. Officials in front of a partisan crowd award marginally more of the close calls to the home side, and marginally more stoppage time when the home team is behind.
For decades it was impossible to separate these, because they always arrive together. Then football accidentally ran the experiment.
What the empty stadiums showed#
The behind-closed-doors matches of 2020 removed the crowd while leaving travel, familiarity and everything else intact — across dozens of leagues, in the same season, at the same time. That is about as close to a controlled trial as observational sport ever gets.
Home advantage shrank. It did not disappear, which tells you travel and familiarity are real, but it weakened measurably, and the clearest movement showed up in the referee-mediated numbers: the usual card imbalance against away sides narrowed, and so did some of the stoppage-time asymmetry.
That points at the crowd-and-referee channel doing a meaningful share of the work. It also carries a modelling warning that is easy to miss: a home-advantage term fitted on data from one era is not automatically valid in another. Anything estimated over 2020 and 2021 needs handling with care, and anything fitted before then and applied blindly since is making an assumption it hasn't checked.
How a goals model encodes it#
In a Poisson-family model, expected goals are built multiplicatively: an attack strength for the scoring side, a defence strength for the conceding side, and a home term applied only to the home line.
Roughly, the home team's rate is league average × home attack × away defence × home factor, and the away team's is the same product with a matching away factor. That home factor is fitted from historical results in the same league, not assumed, and it is the same number for every fixture in that competition. Then the whole scoreline grid is built from the two adjusted rates, and every market — 1X2, totals, both teams to score — is read off it. Tofiko's models do exactly this, per league, and refit as results accumulate.
A rating model handles it differently and more simply. Elo just adds a fixed bonus to the home side's rating before computing the expected score, which lands in the same place by another route.
One distinction worth keeping straight: this is a fitted adjustment to expected goals, not something you can read off a team's xG record directly. A side's home xG already contains the home effect. Using it as if it were neutral-ground strength double-counts the advantage.
Why it varies, and why per-team estimates lie#
Home advantage is not one constant. It differs by league — travel distance, altitude, crowd culture and refereeing standards all vary — so a model that fits one number globally will be wrong nearly everywhere. Fitting it per competition is the minimum.
Per team is where it gets treacherous. Some grounds genuinely are harder to visit, and there is no reason in principle why every club's home effect should be identical. But a club plays around nineteen home matches a season, and nineteen matches cannot separate a real stadium effect from noise. A side that happens to win eight at home and lose seven away produces a startling apparent home advantage that means nothing at all — the same sample-size problem that makes a season of betting results uninterpretable. Treat any club-specific home figure quoted from a single season as a story.
Home advantage is the most studied effect in football and it is fully priced. Nobody is winning money by noticing that home teams win more. The value of understanding it is that it lets you read a price properly — and spot when a model, including ours, has applied the wrong adjustment to an unusual fixture such as a neutral venue, a groundshare or a tie played behind closed doors.
Related
- The Poisson Distribution: Turning Expected Goals Into Scorelines
- Expected Goals (xG), Explained Without the Hype
- How Our Models Work: Poisson, Dixon-Coles and Elo
- Elo Ratings in Football: One Number Per Team
- 1X2 Explained: Football's Default Market, and the One Bookmakers Price Best
- Poisson Calculator — Scoreline, 1X2, Over/Under & BTTS Probabilities
- Fair Odds Calculator — Remove the Bookmaker Margin from Any 1X2 Book
- Odds Converter — Decimal, Fractional, American & Implied Probability
Frequently asked questions
How much is home advantage worth in football?
Enough that home sides take clearly more than half of all points in league football. Expressed the way models use it, playing at home raises a team's expected goals by roughly 15% and lowers the visitors' by a similar amount, which is worth around nine percentage points on the home win probability in a typical fixture.
Why do home teams win more often?
Several causes overlap: the visitors travel and sleep away, the home side knows the pitch and the routine, the crowd supports one team, and referees make marginally more favourable calls in front of that crowd. The evidence points at the crowd and referee channel as a large part of it.
Did home advantage disappear during the empty-stadium matches?
It shrank rather than vanished. The matches played without crowds in 2020 gave researchers a natural experiment across many leagues at once, and home advantage measurably weakened, with the clearest movement in referee-mediated measures such as cards and stoppage time.
How do betting models account for home advantage?
A goals model multiplies the home side's expected goals by a fitted factor above one and the away side's by a factor below one. A rating model such as Elo simply adds a fixed bonus to the home team's rating before working out the expected result.