Helper to decompose list into pairwise matches

[wdm0006]

If I have 3 competitors with scores: [10, 4, 1], I want to update an arena such that the pairwise comparisons:

competitor 1 vs competitor 2
competitor 1 vs competitor 3
competitor 3 vs competitor 2

are all captured automatically.

[BlankAlmasry]

maybe just
competitor 1 vs competitor 2 ( 2 win)
competitor 2 vs competitor 3 ( 3 win)
is better approach no?
I feel that factorial approach is way more scary than o(n) approach and would scale better
is there any papers talks about how to handles races with elo/glicko etc ?