One Step Dominance Matrix

Adding the one step and two step dominance matrices together takes into account both dominances.

One step dominance matrix. Two step dominance scores are found from adding the elements in each row. Now we can rank the players by taking into account one step and two step dominances by calculating a new matrix. Breaking the tie what happens when multiple vertices have the same out degree. The ti nnspire cas calculator is also used in this video.

Sirguy feb 25 14 at 16 48. A has two step dominance over b because a defeated d and d defeated b. Notice that one team can have two step dominance over another in multiple ways.

Team b has two step dominance over team c in two ways. I ve never done anything like this before but i think it would make sense to separate out different sets of games into different results matrices one matrix per round robin as it were and calculate dominance matrix from each separately and then add the two together. Had b lost to a instead the one step two step dominance would have been. B defeated a who defeated c and b defeated e who defeated c.

Dominance matrix of order 2 d 2 as per the match schedule given above we couldn t predict the result of the matches yet because as till the second last round as per matrix d team 1 v s team 6. Step 4 use the combined dominance of a a2 to rank the players. Find all of the two step dominances in the example above. We then look at the next level of dominance which is the number of two stage pathways from one vertex to another this is the matrix 𝐴2 called the two step dominance matrix the overall dominance is found using the matrix 𝐴 𝐴2 add up all the rows of 𝐴.

It eliminates any ties that may occur such as between c and d in not always the case. An introductory video outlining the basics of dominance matrices used in vce year 12 further maths. Team 1 has a total score of 2 and team 6 has the same score so only the last match can decide who will go ahead. To find the two step dominance all you need to do is square the one step dominance matrix using a calculator.

This video gives a brief introduction to dominance matrices which are used to rank teams based on past performance.