From
http://www.sole.leidenuniv.nl/content_docs/ConsoleXII2003pdfs/vlachou-2003.pdf ---
More precisely, in (23), the modality is epistemic or, as Condoravdi points out, “the possibility is in view of the epistemic state of the speaker”. In (24), the modality is metaphysical: “we are now located in a world whose past included the (unactualized) possibility of his winning the game”.
(23) He may/might have (already) won the game (# but he didn’t).
(24) At that point, he might still have won the game, but he didn’t in the end.
From
http://www.cs.tcd.ie/publications/tech-reports/reports.02/TCD-CS-2002-39.pdf ---
(1) He might have won.
We can read (1) epistemically as in (2) or metaphysically as in (3).
(2) He might have, for all I know, won.
(3) He might have, at that stage, won, but he didn’t.
The words ‘might’ and ‘have’ are analyzed ... by functions MIGHT and PERF, in terms
of which (1)’s epistemic reading arises from, roughly put,
MIGHT(PERF(he-win))
and (1)’s counterfactual reading from the reversed scoping
PERF(MIGHT(he-win)) .
_______
Personally, I would paraphrase thus:
Epistemic:
It is possible that he won.
(Lack of knowledge about whether he won or not.)
Metaphysical:
It was possible that he [would / was going to] win.
(Knowledge that the potential actually existed for him to win.)
Another example: Supposing a child was playing dangerously close to deep water:
The child might have fallen into the water (and drowned).
Epistemic reading, not knowing where the child is:
The child might have fallen into the water = It is possible that the child fell into the water.
Metaphysical reading, knowing that the child is now safe:
The child might have fallen into the water = The potential existed (then) for the child to fall into the water. (But that potential was unfulfilled.)
At least, that's my interpretation of the terms as used in that article. By the way, it is not, in my opinion, the same as the way "epistemic" is used in other contexts. To me it's a somewhat special use of the word "epistemic".
CJ