In the game Monster Hunter World, the "affinity" is used to describe "the probability of a weapon doing critical hits to a monster".
Is this really an idiomatic usage? Or is it better to just use "Critical Chance"?
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Affinity here appears to be a technical term used in this specific game. This use is not one of the natural meanings of the word, although it may be derived by extension from such a natural meaning. It is not a common term in RPGs in general -- I played several of the early RPGs, including Original D&D, 2nd ed Advanced D&D, Traveler, Top Secret, and several others, and none of them used "affinity" in this sense. So this is a term specific to a particular game -- or possibly a group of related games.
There is nothing wrong with that, but it means that the meaning of the term in this use can only be determined from game rules or documents, or from writings about the game, or the discussions of players. General English meanings won't help much.
Let's check the meaning of affinity according to the Oxford Dictionary
- A natural liking for and understanding of someone or something.
- [Biochemistry] The degree to which a substance tends to combine with another
And let's check also the thesaurus
correspondence, relationship, association, link, analogy, similitude, agreement, compatibility, congruity, parallelism, consonance
You can not translate it as "critical chance". Notice the two synonyms that I've highlighted: compatibility and consonance. Affinity in your context marks the degree of compatibility between a weapon and a monster, meaning that the most compatible weapon is the one that causes more harm - critical hits - to the monster.
Notice the second nuance of affinity: degree to which a substance tends to combine with another. What about the degree to which a weapon combines with a monster? That's affinity.
So I think that it's perfectly idiomatic the usage of affinity in your context. Maybe another good synonym for your context is fitness.
fitness for/to do The quality of being suitable to fulfil a particular role or task.
being that role "killing a specific monster".
UPDATED: OP has indicated that the affinity is the same independently of the kind of monster. Still it got nothing to do with the Japanese gaming culture or a mistranslation. It's a term derived from the original role playing games. If the term is not related to the monsters, probably it applies to your chosen character. For example if you choose an archer, your chances of striking a critical hit with a bow should be greater than the ones that you get using a sword. Affinity is the grade of compatibility between the character and a specific kind of weapon.