KAN-CCMVV4037U.
The Economics of Sports
1. Introduction.
February 3
rd
, 2025
Battista Severgnini
Department of Economics-CBS
Plan for Today
Plan for Today
▶ Introduction and Rules of the Game
▶ Why is it important?
▶ What is Sport Economics?
▶ The Business of Sports
▶ Contest Theory
Introduction
2 | 39
Textbook
Introduction and Rules of the Game
4 | 39
Literature for this Class
Roger D. Blair,
Sport Economics
Chapter 1 & 2.
Walter C. Neale,
The Peculiar Economics of Professional Sports.
The Quarterly Journal of Economics (1964) , 78 (1): 1-14.
http://www.jstor.org/stable/1880543
Stefan Szimanski,
The Assessment: The Economics of Sport.
Oxford Review of Economic Policy (2003) , Oxford Review of
Economic Policy (2003), 19 (4): 467-477.
http://oxrep.oxfordjournals.org/content/19/4/467.short
Introduction
Revenues of top US sports and selected
retailers
Berlin water usage during 2014 World Cup
match, Germany v Brazil
Why is this important?
▶ Joseph Ratzinger (1978): Sport becomes a sort of foretaste of
Paradise
▶ Nelson Mandela (1995): Sport has the power to change the
world. It has the power to inspire.
▶ More half of the world watched the 2018 and 2022 World Cup.
Why is it Important?
8 | 39
How Economics can help Sport? (Justin
Wolfers, 2007)
1. Sports shapes broader national debates. Sports is a
microcosm of our broader society and our national narrative on
the important issues, from drugs, to race, to cheating, to
sexual harassment often play out on our sports pages.
2. Professional sports are an important part of the
economy.
3. Sports participation is an important activity. It seems
important to learn whether sports make us happier, healthier
or more productive.
Introduction
Why is it Important?
9 | 39
How Sport can help Economics? (Justin
Wolfers, 2007)
1. Sports provide unique opportunities to test economic
theories
2. Sports provide a useful teaching metaphor.
3. Doing research and teaching on sports is fun.
Introduction
Denition(s) of Sport Economics (1)
It is dicult to nd a clear denition for sport economics or for
sport in general:
▶ Coates: There was less agreement on what sports economics
is. One possibility was that sports economics was the study of
those "sports" that were commercial, though I think there was
unanimous agreement that such a denition was far too
narrow. Another possibility was that sports economics is
dened by the application of price or decision theory. For
example, a study that examines sport using incentives and
objective functions or tries to understand, explain, or predict
choices in a sport context is sports economics.
▶ Blair: all the business and economics related to the activities
covered in the sports section of newspapers. No distinction
between professional and amateur sports.
Denition(s) of Sport Economics (2): Neale
(1964)
Neale (1964) nds 10 dierent peculiar characteristics for dening
rms/players in professional sports. In the original version:
1. Louis-Schmelling Paradox
2. The inverted joint product or the product joint
3. League standing eect
4. Fourth estate benet
5. Multirm plants
6. Diminishing quality returns
7. Input-enthusiasm eect
8. Roger Maris cobweb
9. Bobby Layne rigidity
10. Archie Moore invisibility
1. Neale revised: Feder-Nadal Paradox
What is Sport Economics?
13 | 39
1. Neale revised: Feder-Nadal Paradox
▶ in economics you learned that a rm is better o the smaller
or less important the competition.
▶ monopoly is the ideal market position for a rm
▶ in sport:
▷ rms/players get benets from business monopoly BUT
▷ rms/players get benets from sportive competition
▶ you can nd evidence everywhere, e.g.
▷ in tennis: Federer vs. Nadal vs. Djokovic
▷ in Formula 1: Mercedes vs Ferrari (or Red Bull)
Introduction
2. Neale revised: El Clásico
What is Sport Economics?
15 | 39
2. Neale revised: Real Madrid and
Barcelona (El Clásico)
▶ in economics you learned each rm produces an indivisible
product.
▶ in sport: you need at least two players/teams for producing
an indivisible product
Introduction
3. Neale revised: England vs Denmark
What is Sport Economics?
17 | 39
3. Neale revised: England vs Denmark
If each team in a league plays games against opponents with
relatively equal talent, games have uncertain outcomes and there
will be regular changes in the league standings, generating
additional fan interest in games increasing gate revenues.
Introduction
4. Neale revised: Fourth Estate Benet
What is Sport Economics?
19 | 39
4. Neale revised: Fourth Estate Benet
▶ Sport generates a positive spillover to the media, who can earn
income at no direct cost to themselves.
▶ Positive spillovers can be found in other sectors
Introduction
5. Neale revised: Multirm Plants
1991: O.Marseille vs A.C. Milan. After a blackout, A.C. Milan
director Adriano Galliani refused to put his team back on the pitch.
What is Sport Economics?
21 | 39
5. Neale revised: Multirm Plants
▶ In economics you learned about multi-plant rm.
▶ in sport you have "multirm plants", i.e. the plant cannot be
used without the cooperation of dierent rms.
Introduction
What is Sport Economics?
22 | 39
6. Neale revised: Diminishing Quality
Return
If the league decides to add more teams to the league, the league
will experience diminishing quality returns because the quality of
talent declines as less skilled players are drawn into the league.
Introduction
7. Neale revised: Input-Entusiasm Eect
What is Sport Economics?
24 | 39
7. Neale revised: Input-Entusiasm Eect
▶ Opposite eect with respect to diminishing quality return
▶ As leagues expand into new areas, public attention will be
drawn more to the particular sport and more private
concentration will be put into a development of the skills of
the sport.
Introduction
What is Sport Economics?
25 | 39
8. Neale revised: Lionel Messi's number of
goal
The demand of a player next year depends upon his/her
performance this year.
Introduction
What is Sport Economics?
9. Neale revised: Haaland's Rigidity
Introduction
26 | 39
10. Neale revised: CR7's indivisibility
What is Sport Economics?
10. Neale revised: CR7's indivisibility
You cannot divide CR7 into dierent players.
Introduction
28 | 39
The Business of Sport
Revenue Sources of a Sport Team
1. Ticket Sales
2. Stadium revenues
3. Broadcasting revenues
4. Trademark Licensing Fees
5. Naming Rights
Introduction
29 | 39
The Business of Sport
Cost of a Sport Team
1. Labour Cost
2. Stadium cost
3. Travel cost
Introduction
30 | 39
Real Madrid's Balance Sheet
Real Madrid's Consolidated Budget
33 | 39
The Business of Sport
Prot and Value of the Team
Knowing the amount of prot Π and the interest rate i , we can
compute the value PV of a team as
PV (Π) =
where
▶ t is the time horizon
▶ i is the interest rate
Introduction
PT
πt
v
t=1 (1+i)t + (1+i)t
34 | 39
Contest Theory
How Teams Maximize Their Prot?
Standard Micro Model
The prot Π of a team is given by
Π (Q) = TR (Q) − TC (Q)
where
▶ Q is the quantity (=game) produced
▶ TR is the total revenue
▶ TC is the total cost
and prot are maximized by
∆Π
∆TR
∆TC
∆Q = ∆Q − ∆Q = 0
Introduction
35 | 39
Contest Theory
How Teams Maximize Their Prot?
Including Team Quality
The prot π of a team is now given by
π = P (Q, S) Q − C (Q) − C (S)
where
▶ Q is the quantity (=game) produced
▶ S the quality of the team, number of stars
and prot are maximized by
∆π
∆P
∆C
∆S = ∆S Q − ∆S = 0
Introduction
36 | 39
Contest Theory
How Teams Maximize Their Prot? Contest
Theory (1)
We dene the probability of winning a contest for team i as
xγ
pi = Pn i x γ
j=1 j
where
▶ x is the eort of the team in the contest
▶ γ is the discriminatory power
▶ if γ 7−→ +∞ than the contest becomes an auction
Introduction
37 | 39
Contest Theory
How Teams Maximize Their Prot? Contest
Theory (2)
We dene the prot π of team i as
πi = pi V − ci (xi ) xi
where
▶ c is the marginal cost of eort
▶ V is the prize of winning the contest
Substituting pi :
xγ
πi = Pn i x γ V − ci (xi ) xi
j=1 j
Introduction
38 | 39
Contest Theory
How Teams Maximize Their Prot? Contest
Theory (3)
If we assume that ci (xi ) = c and we maximize π wrt xi :
P
[γxiγ−1 nj=1 xjγ −xiγ γxiγ−1 ]
∂πi
=
V −c =0
P
2
∂xi
[ n xγ]
j=1 j
dividing
by xi and knowing that
Pn γ andPmultiplying
γ
γ
n
j̸=i xj =
j=1 xj − xi , we get
P
γVxi nj̸=i xjγ
∂πi
=
P
2 −c = 0
∂xi
x [ n xγ]
i
j=1 j
Finally, in a symmetric Nash equilibrium xi = xj , we get
and
Introduction
xi∗ = (n−cn1)γV
2
1)]
π ∗ = V [n−γ(n−
n2
39 | 39
Contest Theory
How Teams Maximize Their Prot? Contest
Theory (4)
1)]
π ∗ = V [n−γ(n−
n2
Main results:
▶ if V ⇑⇒ π ∗ ⇑
▶ if n ⇑⇒ π ∗ ⇓
▶ if γ ⇑⇒ π ∗ ⇓
Introduction