theory of the perfect game © 2008 john vrooman - vanderbilt university usa

THEORY OF THE PERFECT GAME

© 2008 John Vrooman - Vanderbilt University USA

COMPETITIVE BALANCE IN Monopoly SPORTS LEAGUES


John VroomanVanderbilt University, USA


$M/w2$M/w1

LEAGUE EQUILIBRIUM

AcT

MR2

cT

MR1

w1


$M/w2$M/w1

REVENUE SHARING IN PROFIT LEAGUE

AcT

MR2

cT

MR1

B

MR1′

MR2′

w1


CT’

$M/w2$M/w1

OPEN & CLOSED PROFIT LEAGUES

AcT cT

A’CT’

MR1

w1

MRP2

MR1

MRP1

MR2


CT ’

$M/w2$M/w1

INVARIANCE PROPOSITION

AcT cT

A’CT ’

MR1

w1

MRP2

MR1

MRP1

MR2

MR1′

MR2′MRP1’

MRP2’B


$M/w2$M/w1

PAYROLL CAP IN PROFIT LEAGUE

AcT

MR2

cT

MR1

w1

CAP1

C’T C’TB


$M/w2$M/w1

REVENUE SHARING & Payroll cap

AcT

MR2

cT

MR1

C’

MR1′

MR2′

w1

CAP1

BC

C’TC’T


$M/w2$M/w1

REVENUE SHARING & Payroll MINIMUM

AcT

MR2

cT

MR1

MR1′

w1

CAP1

BC

MIN2

C’T C’T

C’’T C’’TB’

MR2′


$M/w2$M/w1

REVENUE SHARING & Payroll MINIMUM

AcT

MR2

cT

MR1

MR1′

w1

MIN1

B

MIN2

C’T C’T

C’’T C’’TB’

MR2′


AR1

MR2

A

cT AR2

MR1

$M/w2$M/w1

SPORTSMAN WIN-MAX LEAGUE

B cT


AR1

AR2’

AcT

AR1’

$M/w2$M/w1

SPORTSMAN REVENUE SHARING

BcT

AR2


AR1

A

C’TAR2

$M/w2

$M/w1

SPORTSMAN PAYROLL CAP

C’T

CAP2CAP1

B

c’T


AR1

AR2’

A

cT

AR2

AR1’

$M/w2$M/w1

REVENUE SHARING & PAYROLL CAP

BcT

CAP2CAP1

C’T C’TC


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


National Football League


Major League Baseball


National Basketball Association


National Hockey League


English Premier League


French Ligue 1


German Bundesliga


Italian Serie A


La Liga Española


Finis


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