# 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.

(Top Tutor) Daniel C.
(997)
School: UIUC
Studypool has helped 1,244,100 students

1831 tutors are online

### Related Mathematics questions

Brown University

1271 Tutors

California Institute of Technology

2131 Tutors

Carnegie Mellon University

982 Tutors

Columbia University

1256 Tutors

Dartmouth University

2113 Tutors

Emory University

2279 Tutors

Harvard University

599 Tutors

Massachusetts Institute of Technology

2319 Tutors

New York University

1645 Tutors

Notre Dam University

1911 Tutors

Oklahoma University

2122 Tutors

Pennsylvania State University

932 Tutors

Princeton University

1211 Tutors

Stanford University

983 Tutors

University of California

1282 Tutors

Oxford University

123 Tutors

Yale University

2325 Tutors