Modelling With Matrices: What are Dominance Matrices?

[@del7920]

This video is so helpful and well made, thank you!

[@charlie3744]

lovely

[@Andrew_Fraser]

Awesome video man. Is it possible to do a dominance matrix for athletic sport seasons and determine a ranking in a similar way? Sports with more than one participant per match. Sprinting, swimming etc.

[@LamyAssassin]

Does it matter what arbitrary values we use?

[@BellCurvedEducation]

It can depend on the context of the problem, but changing the arbitrary values can influence the results. For example, if you were to increase them it could give a different result to decreasing them. If you are using dominance matrices to rank teams in a contest, use smaller arbitrary values for higher order matrices as it is more difficult to draw conclusions (i.e. rank teams) from results that are not direct. In the example I used team A defeated team E who defeated team B. It wouldn't be reasonable if we were to analyse this result equally with the direct result between the first order matrix where team B defeated team A. It is common practice to halve the arbitrary value for each higher order matrix used such that the higher order matrices are not considered equally for ranking. This doesn't mean that you couldn't start with the arbitrary value of 8 and halved it each time, it would give the same result as starting with 1 and halving each time. But starting with 1 and halving is more common practice.

[@LamyAssassin]

Thanks :)

[@zarapopo7442]

i love you