fun one - I also did that at some point with pleikki I think...
Few things that are off:
You calculate in the different attributes part three times - that means you calculate the chance for a wand of a specific attribute (not just getting any q9 20/20 as title suggests.
You say there's 21 possibilities for attr on hct and hsr. Now only 18attr can drop as hsr/hct (estor, sr, fc can't) Furthermore that only applies to multiprofession wands - getting a matching fire wand would be significantly easier since only ele-attributes could come.
You say there are 21 possibilities for the req - that's only 14 for multi profession wands (if I counted properly)
As pyro said 8% and 18% aren't within the available range on todays drop.
Os wands do not necessarily have an "insc" + a "wrap" - doesn't mean any combination is possible, but more than you respect this way. On shields I'm far more into what is and is not a possible combination.
And finally as pyro stated: number of possibilities does by far not say anything considering rarity or rate! Think of os swords - following the logic there's 12 (including nomod) possibilities and you'd deduce a 1:12 ratio for a 15/-1healthreg one - which is by far off.
Long story short - fun project for sure but off on a few assumptions. Just properly deducing all the possibilities is something I would be unable to do since I do not know which combinations of mods are possible. Then deducing the chance is something which is again far off my capabilities - as said: different mods may carry different chances.
Fun idea we followed back then: what about foci? There are all the armor mods, all the +1 attr mods and so on. Compared to all the possibilities on there wand seem easy to get as matching 