No, that would been a question for someone who had loads of "oh sh*t" moments and has been writing that data down.
My impression is that it's not very constant. For example, for hits worth 10k, 12k, and 16k of PvPs, I got Aztec Gold, and Magic Anvils for about 7-8k points, but I also got Kraken's Claw on hits for 17k points and for 38k points, and I got Aztec Gold for a 37k hit and for a 132k hit (so, 10 times more than aforementioned 10-16k). I don't remember if I got another relic soon after that last mentioned hit, but it was a defensive hit. No idea if that plays a role.
Also, if you do several hits in a row, you may not get a relic right away with a big hit, but you'll get one soon after (even for a small hit), almost as if relics have a "points bank" (similar to "res bank" for prizes). For example, I've had 30k hits with no relics won, but then I'd get a relic soon after with very minor hits.
This is just a hunch. I might be completely off, I might be spot on. Probably somewhere in between.
In my opinion, don't bother with relics. Their bonuses are not big, and - with time - you'll end up with those you like without chasing them.
Those you don't need/want, sell them. I suggest selling all the timed ones, plus those you have more than 2 of and those you know you'll never use.