I was wondering if anyone could help me with what is probably a fairly
basic question.

I want to investigate the significance of head-to-head records of
chess players, versus their ELO rating. In other words, does player A,
who has lost 3 of 10 games to player B and 7 of 10 games to player C,
have more of a chance of beating player B than player C, if their ELO
ratings were all equal?

The counter-theory would I suppose be that the head to head ratings
will already be implicitly accounted for in the ELO ratings (along
with games against all other opponents), and that it is the ELO rating
that is therefore significant rather than the head-to-head rating.

What sort of tests should I look to perform on a database of results
to test this hypothesis?

any help appreciated, with thanks in advance
.
.
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