TWO TO TANGO © 2011 John Vrooman Vanderbilt University USA

TWO TO TANGO

© 2011 John Vrooman Vanderbilt University USA

Competitive balance In pro sports leagues


John vroomanVanderbilt 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


COOPERATIVE PROFIT MAX EQUILIBRIUM

0 0.5 10

100

200

0

100

200


$M/w2$M/w1

AcT

MR2

cT

MR1

MR1′

MR2′

w1

A’


PAYROLL CAP

0 0.5 10

100

200

0

100

200


$M/w2$M/w1

AcT

MR2

cT

MR1

w1

CAP1

C’T C’TB


0 0.5 10

100

200

0

100

200


$M/w2$M/w1

REVENUE SHARING & Payroll CAP

AcT

MR2

cT

MR1

MR1′

w1

CAP1

BC’T C’T

C’’T C’’T

MR2′


A’

0 0.5 10

100

200

0

100

200


$M/w2$M/w1

REVENUE SHARING & Payroll MINIMUM

AcT cT

MR1

MR1′

w1

CAP1

BC

MIN2

C’T C’T

C’’T C’’TB’

MR2′


A’MR2

0 0.5 10

100

200

0

200


w1

AR1

MR2

A

cT AR2

MR1

$M/w2$M/w1

SPORTSMAN WIN-MAX LEAGUE

B cT


0 0.5 10

100

200

0

200


AR1

AR2’

A

AR1’

$M/w2$M/w1

Win-Max REVENUE SHARING

cT

AR2

P1

P0

P2


B

0 0.5 10

100

200

0

200


AR1

A

C’TAR2

$M/w2$M/w1

Win-Max PAYROLL CAP

P2

CAP2CAP1

B

P1


0 0.5 10

100

200

0

200


AR1

AR2’

A

cT

AR2

AR1’$M/w2

$M/w1

PAYROLL CAP & REVENUE SHARING

B cT

CAP2CAP1

C’T P2

C

P1


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


1970 1975 1980 1985 1990 1995 2000 2005 20100.00

0.25

0.50

0.75

1.00

National Football League


1970 1975 1980 1985 1990 1995 2000 2005 20100.00

0.25

0.50

0.75

1.00

Major League Baseball


1970 1975 1980 1985 1990 1995 2000 2005 20100.00

0.25

0.50

0.75

1.00

National Basketball Association


1970 1975 1980 1985 1990 1995 2000 2005 20100.00

0.25

0.50

0.75

1.00

English Premier League


fin


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TWO TO TANGO © 2011 John Vrooman Vanderbilt University USA