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MATHEMATICS - Coggle Diagram
MATHEMATICS
Math model to rank zero-sum sport
ELO rating system
Invented by Arpad Elo around 1950
Used for zero-sum games
Approved by the US Chess Federation in 1960 and published in 1978
Updates player rating based on winning probability
takes into account player strength
Extended to include Margin of Victory (MoV)
Linear method
Joint additive method
Multiplicative method
Logistic method
Higher accuracy than standard Elo system
Entropy Weight Method (EMW)
Decision-making method that takes into account value dispersion
More dispersion, more information extracted
Three-step process
Normalization of decision matrix
Entropy calculation
Weight calculation
FIFA rating system
useful in attracting and keeping the enthusiasm of fans
last 48 months scores with weighs of 0.2, 0.3, 0.5, and 1 every 12 months
factors
outcome
match importance
strength of opposition
confederation strengths