Throwing this out there to see if it lines up with other PVPer's experiences and/or estimates. I came up with this after only succeeding 34% of my raids (46 out of 135 attempts) against a ship with 30% more crew than me (a rare opportunity for me, knowing the number of crew on both sides), which was quite a bit lower than my guesstimate of what is would be. Anyhow, I suspect it's a mirror of the invasion formula:

unmodified raid chance = raider's crew count / (defender's crew count * 3)

i.e. if your crew equals the defender's crew count, you have a 33% chance. In my case that lead to this, the calculation results in a 25% raid chance. Once the Protean Arsenals and Thractti buffs are multiplied in, I get a 36.5% chance, which is close enough to the 34% I achieved to feel reliable. I do suspect there's a similar cap (90%) like there is with invades, but no case studies for that.

Feedback, thoughts, your experiences?

interesting theory .. but can not corroborate without more info on enemy crews ...

Yeah, that's the tricky thing, knowing the other variable. And this all assumes that rank only affects raid payouts, not raid chances, but of course the real raid chance formula could include it in some complicated way...

i suspect there's a curve some how in it ICB.

While I don't normally know the crew counts on ships I raid, there have been a few over the years where I did. On the ones that had a lot more I'd succeed say 1 out of 3 on average.... If your right and all things equal means a roughly 33% chance, shouldn't that had way more crew I should have had less luck.

As I only have the one case, it's entirely possible my guess for the formula is too simplistic. However, if you factor in raiding buffs (keeping in mind the compounding effect they have, e.g. a 10 point gain at 24% base raiding chance, 15 point at 35%) do the numbers still seem off? That being said, anecdotes are slippery fish, but I'm not sure anyone will have the time or patience to spade out the exact formula...