Is home advantage worth a goal?
Fans, pundits and managers all say home advantage is worth a goal. Over 18,000 Scottish league matches since 2000/01 say it is worth about a quarter of one.
Beginner
Contents
The claim
"Home advantage is worth a goal."
You'll hear it from fans, pundits, managers, and your pals at the bar once they're on their third pint.
Why people believe it
It feels true. The home side knows the pitch, sleeps in its own bed, and has thousands of people roaring it on and screaming at the linesman. Everyone remembers the night their team battered someone at home, and the grim away trip where nothing went right. Home advantage is real enough that nobody questions it. The question is how big it is.
The data
Every league game in Scottish football's four divisions since 2000/01: over 18,000 matches, from the Premiership down to League Two. Final scores only, from football-data.co.uk.
The method
For each match, take the home goals minus the away goals. Then take the average across every match.
If the myth is right, that average should be about 1.
The evidence
It's not 1. It's 0.24.
I've watched a lot of Scottish football, and I've never once seen anyone score 0.24 of a goal. Although I've seen a few Celtic efforts that deserved partial credit.
What it means is that over a big stack of games, home teams come out about a quarter of a goal better off. They win about 43% of the time; away sides win about 33%.
The edge is real, and it shows up every season. But it's nowhere near a goal. Not one season in 26 came even close: the best was 0.39.
How sure can we be?
With this many matches, very sure. The top two divisions alone give an average of 0.27, and the 95% range around it is 0.23 to 0.30. A full goal is about 40 standard errors away.
In plain football
- The 95% range is where the true figure almost certainly sits, allowing for the luck in any set of results.
- It is narrow because 10,000 matches is a lot of football. The luck of the odd deflection or penalty evens out.
- A whole goal is miles outside it. This isn't a close call.
Show the mathsStandard error and the 95% range. Optional.
Goal difference varies a lot from match to match: its standard deviation is about 1.83 goals. The uncertainty in an average shrinks with the square root of the number of matches:
$$\text{SE} = \frac{s}{\sqrt{n}} = \frac{1.83}{\sqrt{10471}} \approx 0.018$$
A 95% range is roughly the average plus or minus two standard errors:
$$\begin{aligned} &0.27 \pm 1.96 \times 0.018 \\ &\approx 0.23 \text{ to } 0.30 \end{aligned}$$
The 2020/21 experiment
Covid meant every game in Scotland that season was played behind closed doors. No fans, no noise, no one shouting at the linesman. If home advantage is all about the crowd, that's when it should have vanished.
It didn't really. The home edge dipped to 0.16, down from 0.23 in the seasons around it. But 2016/17 and 2017/18 were just as low, and they had fans in.
So either the crowd matters less than we think, or one season is too small a sample to tell. It's the second one. Take the top two divisions on their own: that season is only 363 matches. Their home edge was 0.18, but the 95% range runs from −0.02 to 0.37, wide enough to include both "no home advantage at all" and a perfectly normal season. Sadly, "let's play another few seasons with no fans" isn't an option I'd recommend.
The bookies, for what it's worth, shaded their home prices down a touch that season: their implied chance of a Premiership home win fell to 41%, from 42 to 43% in the seasons either side. Home sides actually won 38.5%. Close. The bookies usually are.
Verdict
Not supported. Home advantage is real, but it's worth about a quarter of a goal, not a whole one. Good luck finding a striker who can score a quarter of one.
Caveats
- 2020/21 is one season, and the lower leagues played a shortened one.
- Crowds in League One and Two are small anyway, so there wasn't as much noise to take away.
- The Premiership split means fixtures aren't perfectly balanced home and away, though the effect is small.
- An average hides differences between teams. Some clubs may get much more from home than others; this analysis doesn't separate them.
Reproduce the analysis
The results files are published by football-data.co.uk. Download them from there; they aren't rehosted on this site. Then:
import csv, glob, statistics
diffs = []
for path in glob.glob("SC*.csv"): # SC0 Premiership ... SC3 League Two
with open(path, encoding="latin-1") as f:
for row in csv.DictReader(f):
if row.get("FTHG") and row.get("FTAG"):
diffs.append(int(row["FTHG"]) - int(row["FTAG"]))
print(f"{len(diffs)} matches, home advantage {statistics.mean(diffs):.2f} goals")
Spotted a flaw in the method, or have a football claim you'd like tested? Suggest it on LinkedIn, where discussion of these articles happens.