I have only one legendary for tanking (and that's only because I got the shield neck as Havoc, which counts for both specs - technically I'm at 0 items dropped as tank spec) and four (again, including the neck) for Havoc. I don't really care about tanking legendaries, but I STILL do not have the Havoc belt and it just kills me.
As the belt is one of the few items that is on the loot table for both Havoc and Vengeance, and is the only potential legendary from a belt-slot token, I have been swapping to Vengeance loot spec before buying/using belt tokens.
My logic has been that with the per-spec bad luck protection that was implemented, I should have a better chance to get the belt as Vengeance, right? Both specs can get that belt, and it's the only belt-slot legendary available to either spec. If Havoc has 4 qualifying legendaries and Vengeance has 1, would it not be better to always go Vengeance before buying and using a belt token?
Here's where it gets a little tricky for me; I *very* rarely play Vengeance anymore, and haven't much at all since the addition of the spec-specific protection in 7.2. At most, I might tank a heroic or low m+ once a week for a quest. Since I play Havoc so much, at what point does my chance as Havoc surpass my chance as Vengeance, even though I have 4x the legendaries as Havoc? As far as I can tell, your bad luck protection only increases as you perform actions that can potentially award a legendary; every cache you open, every boss you kill, etc. If I'm doing nothing on my tank spec and everything on my Havoc spec, how long do you think until an active spec with 4 legendaries surpasses the legendary chance of a spec with only 1 legendary that isn't played often?
I really wish I had a reliably way to determine which is better. On one hand, Vengeance has no spec-specific legendaries, only one shared one. Havoc has four total; three spec-specific, one shared. At one point does the playtime on my Havoc spec contribute enough bad luck protection that it outweigh the flat-out lack of legendaries on my Vengeance spec?
Isn't the bad luck protection incredibly high until you get your first legendary, but STILL higher than normal until you get your second? Isn't the chance to get a second like double the chance of further legendaries after that one? I mean, at LEAST double? This is why I'm having a hard time deciding which spec would be better for a chance at the same item