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Research

Longer investigations into football questions, with the data, method and limits laid out.

Do substitutions work? Changes made while losing, like for like

Data
StatsBomb open data: every event in whole seasons and tournaments, men's and women's, 2015/16 to 2025
Sample
3,220 matches; 1,696 changes made while losing, 60th to 80th minute
Method
Chances made and conceded in the 15 minutes before and after, against teams at the same minute and score that hadn't changed yet
Finding
Most of the lift after a change happens anyway; the change adds about one extra goal in 40 to 45 changes, and no points we can measure

Intermediate

Does late money know something? Friday's odds against kick-off

Data
Bet365 prices on Friday and at kick-off, Scottish Premiership and Championship, 2019/20 to 2025/26
Sample
2,710 matches
Method
Log loss of each price; where results landed when a price moved 5 points or more; £1 at Friday's price on what later moved, against bets at the same odds
Finding
Kick-off prices are clearly more accurate in the Championship but not in the Premiership; Championship moves didn't go far enough

Intermediate

Is Scottish football less competitive than the rest of Europe?

Data
football-data.co.uk results and Bet365 odds for nine European top divisions, 2000/01 to 2025/26
Sample
76,154 matches, 234 league seasons
Method
Different champions; the gap from second to third; how spread out each table is against luck, with and without each league's two giants; how often the favourite won
Finding
Scotland's title race is the least competitive by far; the rest of its league is as even as any; other leagues have spread out while Scotland hasn't

Intermediate

Do referees favour the home side?

Data
Scottish Premiership match stats with referees, 2000/01 to 2025/26
Sample
5,877 matches, 152 referees
Method
Yellow cards per foul, home v away; split by which side was outshot; 2020/21 behind closed doors as a natural experiment
Finding
Like for like, away fouls are booked 10 to 20% more often; the gap was lowest in the season without crowds

Intermediate

Do football stats mislead? Five correlations put to the test

Data
Scottish Premiership results and match stats, 2000/01 to 2025/26
Sample
310 team-seasons, 80 manager changes, 11,754 team-matches
Method
Each correlation re-checked like for like: control groups, holding the hidden cause fixed, splitting out the dominant clubs
Finding
In every case most of the headline link disappears once you compare fairly

Beginner

Do the bookmakers get Scottish football right?

Data
Bet365 prices, 2002/03 to 2025/26
Sample
9,646 Scottish league matches, 24 seasons
Method
Implied probabilities, calibration and the bookmaker's margin
Finding
Remarkably accurate in the middle; backing outsiders loses 34.7p per £1

Intermediate

How many points is a goal worth?

Data
Premiership and Championship results, 2000/01 to 2025/26
Sample
572 team-seasons
Method
Regression of points on goal difference
Finding
About 0.63 points per goal; goal difference explains 93% of points

Intermediate

When is the title decided?

Data
Scottish Premiership results, 2000/01 to 2025/26
Sample
25 title races
Method
Simulating the rest of the season from every third round
Finding
Typically 90% sure of the champion by round 12; the table settles it at round 34

Intermediate

How do you know if a football prediction model is any good?

Data
The SPFL Prediction Board's eleven predictors
Sample
5,258 Scottish Premiership matches
Method
Accuracy, log loss, Brier score and calibration
Finding
Picking the most winners is the wrong test; the bookmaker still beats them all

Intermediate