As August gives way to September and the media’s so-called “silly season” winds down, attention shifts to the return of football. With the new season having kicked off, and today’s transfer window now having closed, it can sometimes feel as though a different kind of silly season is only just beginning. Yet football is merely a reflection of our society with its passions, excesses and contradictions. The sport magnifies our tribal instincts, celebrates collective joy and exposes the widening gulf between ordinary fans and the vast sums of money that swirl around the game. It is also – as I have frequently noted – a great test bed for applying economic and statistical analysis.
Some economic reflections on this year’s big stories
While football can provoke great debate, it is just as
likely to be treated with indifference by a large section of the population.
But it is hard to ignore. Even the Financial Times is taking notice, with its
fun online challenge (Can you run a
Premier League football club?) and an article
equating the decline of Manchester United with the fall of the Berlin Wall. I
have long thought that the diminished prowess of the Red Devils speaks more to
the industrial economics literature on why dominant firms decline. Empirical research
conducted by Paul Geroski in the 1980s[1]
challenged the conventional view that dominant firms do indeed decline. Paul is
alas no longer with us, but he did develop a surprising affinity for football, and
he would almost certainly conclude that Manchester United’s recent travails do
not represent a permanent shift in the club’s fortunes.
To the sports journalist or the casual fan, the standoff
between Alexander Isak and Newcastle United, in which the player’s refusal
to train with the team as he tried – eventually successfully – to force a move
to Liverpool, may seem like the petulant actions of a spoiled star. To the
economist, they represent calculated moves in a high-stakes financial
negotiation. Isak’s motivation is clear: moving to one of Europe’s top clubs
will propel him into the footballing elite, generating more trophies and a
higher income. A footballer’s career is short, and could be ended tomorrow by
injury. It is thus rational for him to attempt to maximise his income.
What about the clubs? Newcastle are about to reap the
benefit of Champions League revenues, and must weigh the immediate windfall of
a record-breaking player sale against his value on the pitch, where his
contribution could see the team progress further in the competition thus
generating additional broadcast, matchday and win-related revenue. For their
part, Liverpool must balance ambition with fiscal prudence. A blockbuster
signing is no guarantee of success and the club must be careful that a fee in
the region of £130 million does not undermine their carefully maintained
financial model under the Premier League’s Profit and Sustainability rules
(PSR).
Indeed, one of the features of the transfer window – the
player trading period that closed today – is what it reveals about how modern
football teams manage assets, revenue streams and strategic risk. The economics
of football transfers are increasingly shaped not just by player ability but by
contract dynamics. The Isak case is unusual because he had three years left on
his contract. But when a player has only a year left on his deal, his transfer
value typically falls sharply because the selling club risks losing him for
free under the Bosman
ruling. This shifts bargaining power towards the player and the buying
club: the player can threaten to run down his contract, forcing a cut-price
sale, while suitors know they can secure him on a free the following summer. As
a result, clubs often face a strategic dilemma – cash in now at a reduced fee,
or gamble on retaining the player’s services for another season and risk losing
a valuable asset without compensation. In a financial landscape constrained by PSR
regulations, these contractual time horizons are as important to balance sheets
as the players’ performances on the pitch.
The real action is on the pitch
While much of the economics focuses on the finances, the action
on the field lends itself to statistical analysis. Last autumn, I
took a look at Premier League prospects for season 2024-25 on the basis of
a Poisson simulation model[2].
How did I do? First the bad news: I gave Liverpool only an 8% chance of winning
the title (they won comfortably). More positively, I tipped the five clubs who
would win Champions League places; correctly predicted two of the three
relegated teams and called 8 of the top 10 teams. I will leave it to the reader
to judge whether that was an acceptable performance.
The method has a substantial academic pedigree[3]
and last year’s performance was sufficiently robust that it is worth trying it
again as a means to forecast outcomes for season 2025-26. As a reminder, the
model simulates each game 1000 times and adjusts expected goals (λ) by adding a
random number in the range [-1<n<1] in a bid to capture the element of
luck inherent in any sporting contest. The results are shown in the table
below.
Last word
Applying statistical methods to football outcomes is both fascinating and practically valuable because it allows us to move beyond intuition and anecdote, quantifying the uncertainty inherent in each match and across an entire season. By modelling goals, team strengths and dynamic interactions, we can simulate outcomes that would be impossible to assess reliably by eye. This not only deepens our understanding of the game’s underlying patterns but also provides actionable insights for analysts, coaches and fans. It illustrates how a combination of mathematics, probability, and real-world data can illuminate the complex, dynamic and often unpredictable world of football. This approach is not limited to football: the same principles can be applied to virtually any competitive or stochastic system where outcomes depend on multiple interacting factors, from other sports to business forecasting, financial markets or epidemiology. In all these contexts, statistical modelling enables a deeper understanding of underlying patterns, informs decision-making and helps anticipate outcomes in complex and uncertain environments. Just don’t assume that my model is going to make you rich.
[1]
Geroski, P. A. and A. Jacquemin (1984) ‘Dominant firms and their alleged
decline’, International Journal of Industrial Organization (2) 1, pp. 1-27
[2] The
Poisson distribution – a probability distribution that describes discrete
events – is commonly applied in football analytics to model and predict match
outcomes because goals in a match can be thought of as rare, discrete events
that occur independently over time. In this framework, each team is assumed to
score goals at a constant average rate (λ), and the Poisson distribution gives
the probability of scoring exactly 0, 1, 2, … goals in a match. The probability
mass function for a variable following the Poisson distribution is defined as
[3]
Dixon, M. J. and S. G. Coles (1997) ‘Modelling Association Football Scores and
Inefficiencies in the Football Betting Market’ Journal of the Royal
Statistical Society Series C: Applied Statistics, Volume 46, Issue 2, 265–280
