Which of these methods of calculating team rankings using matrices is best?

Sigchi4life
Category:
Mathematics
Price: $15 USD

Question description

 I am trying to work out which method of calculating team rankings when using matrices is best (specifically dominance matrices but If you have a better way please share) 

I have tried it two ways so far (with two calculation variations each): 
Method 1: 
Put the information into a matrix (M) where 0 = Loss 1 = Draw and 2 = Win. Then I add all the elements up per row to get the Vector (V) (sorry if that is not the proper term). Then I square the original matrix(M2) and get the second order vector (V2) of that matrix. Then I do V = V1 + 0.5V2 (for weighting purposes) 

Method Two: 
Instead of only using the win/draw/loss I use the actual amount of goals scored as a ratio. For example if A scored 10 points and B scored 4 points then in row A column B I put 10/3 and in row B column A I put 3/10. 

After that I just continue as I did in method one just using those fractions instead. 

So my first question is which method is better? 

While I was looking around I found a different, more complicated method of getting the result. Instead of just using the vectors (addition of each row for each order matrix) it instead also calculates the vector for the transposed version of the order matrix then subtracts this result from the other normal vector. This results in a a matrix that's elements add up to 0. 

(M^2)x1 - ((M^2)x1)t 

I am sorry if that doesn't make sense It's just difficult to explain in nothing but words. Sorry for the long question, thank you.

Tutor Answer

(Top Tutor) Daniel C.
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School: UIUC
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