TWO TO TANGO
© 2011 John Vrooman Vanderbilt University USA
Competitive balance In pro sports leagues
© 2011 John Vrooman Vanderbilt University USA
John vroomanVanderbilt university, usa
© 2011 John Vrooman Vanderbilt University USA
0 0.5 10
100
200
0
100
200
Team 1 Win PercentTeam 1 Team 2
$M/w2$M/w1
COMPETITIVE PROFIT-MAX EQUILIBRIUM
AcT
MR2
cT
MR1
w1
© 2011 John Vrooman Vanderbilt University USA
COOPERATIVE PROFIT MAX EQUILIBRIUM
0 0.5 10
100
200
0
100
200
Team 1 Win PercentTeam 1 Team 2
$M/w2$M/w1
AcT
MR2
cT
MR1
MR1′
MR2′
w1
A’
© 2011 John Vrooman Vanderbilt University USA
PAYROLL CAP
0 0.5 10
100
200
0
100
200
Team 1 Win PercentTeam 1 Team 2
$M/w2$M/w1
AcT
MR2
cT
MR1
w1
CAP1
C’T C’TB
© 2011 John Vrooman Vanderbilt University USA
0 0.5 10
100
200
0
100
200
Team 1 Win PercentTeam 1 Team 2
$M/w2$M/w1
REVENUE SHARING & Payroll CAP
AcT
MR2
cT
MR1
MR1′
w1
CAP1
BC’T C’T
C’’T C’’T
MR2′
© 2011 John Vrooman Vanderbilt University USA
A’
0 0.5 10
100
200
0
100
200
Team 1 Win PercentTeam 1 Team 2
$M/w2$M/w1
REVENUE SHARING & Payroll MINIMUM
AcT cT
MR1
MR1′
w1
CAP1
BC
MIN2
C’T C’T
C’’T C’’TB’
MR2′
© 2011 John Vrooman Vanderbilt University USA
A’MR2
0 0.5 10
100
200
0
200
Team 1 Win PercentTeam 1 Team 2
w1
AR1
MR2
A
cT AR2
MR1
$M/w2$M/w1
SPORTSMAN WIN-MAX LEAGUE
B cT
© 2011 John Vrooman Vanderbilt University USA
0 0.5 10
100
200
0
200
Team 1 Win PercentTeam 1 Team 2
AR1
AR2’
A
AR1’
$M/w2$M/w1
Win-Max REVENUE SHARING
cT
AR2
P1
P0
P2
© 2011 John Vrooman Vanderbilt University USA
B
0 0.5 10
100
200
0
200
Team 1 Win PercentTeam 1 Team 2
AR1
A
C’TAR2
$M/w2$M/w1
Win-Max PAYROLL CAP
P2
CAP2CAP1
B
P1
© 2011 John Vrooman Vanderbilt University USA
0 0.5 10
100
200
0
200
Team 1 Win PercentTeam 1 Team 2
AR1
AR2’
A
cT
AR2
AR1’$M/w2
$M/w1
PAYROLL CAP & REVENUE SHARING
B cT
CAP2CAP1
C’T P2
C
P1
© 2011 John Vrooman Vanderbilt University USA
0.000
0.500
1.000 wt = wt -1
wt = a + b wt-1 + e t
wt = .500
Win t
Win t -1
b = 0
b = 1
a a = 0
a = .500
Beta Balance
© 2011 John Vrooman Vanderbilt University USA
1970 1975 1980 1985 1990 1995 2000 2005 20100.00
0.25
0.50
0.75
1.00
National Football League
© 2011 John Vrooman Vanderbilt University USA
1970 1975 1980 1985 1990 1995 2000 2005 20100.00
0.25
0.50
0.75
1.00
Major League Baseball
© 2011 John Vrooman Vanderbilt University USA
1970 1975 1980 1985 1990 1995 2000 2005 20100.00
0.25
0.50
0.75
1.00
National Basketball Association
© 2011 John Vrooman Vanderbilt University USA
1970 1975 1980 1985 1990 1995 2000 2005 20100.00
0.25
0.50
0.75
1.00
English Premier League
© 2011 John Vrooman Vanderbilt University USA
fin
© 2011 John Vrooman Vanderbilt University USA
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