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The +15% basic effect can be obtained 5 times with the 5 different legendary potions active at the same time. That's then a ×2.01 multiplier to each base potion (1.15^5). As there is 4 base potions of strength, the gain can be 2^4 or ×16 or ~4 areas.
So together those two things can get you a +8 areas. That can indeed make a difference if you miss 5-10 areas to complete a variant.
But there is a lot of other ways to get that 5-10 areas that are effectively far cheaper than that, and kab_reg pointed some of them - using sticky debuffs, aiming for event buffs or using a full legendary dismantle are others (as increasing modron overcharge, buying missing perks, increasing (especially pre-stack) gear, increasing legendaries, etc.). So apart you're a quite rich whale, going that way is probably one of the worst possible ones.
It can be madding to get so close only to stop because some dude has armor you can't break. You can get a potion a week if you want. I don't get stuck that often, and i typically just come back and try again later, but it's just an option to think about, especially when i'm so close. Besides it lasts a day, so theoretically i could knock out a few of those that are just so close.
I got one potion made so far, i guess i'll save it till it happens and i'll let ya know if it works. :)
Just as a reminder 70 plats (which is less than a legendary potion as it is just the vessel "value") is equivalent to $0.52. Is finishing a variant a fifty cents value? The answer is up to each and has no absolute truth. That said, I still have my opinion about it.
Your probably right about using speed to farm, but i don't do that. I either play doing variants, or i run off line.
I mean, it's really not the optimal way to go, but it's absolutely not a critic about it. If you want to use them that way, just do it. But the forum is a public space, and telling it's really not optimal or a wasted way to do sounds important for me. My answer here is general & not personal (and that's quite a close to absolute truth about my answers here on the forum).
The few variants I've had issues are higher lvl patrons stuff and typically when all my heroes with scales are locked. Though i guess one could argue if it's better to offline variants and then spend online time gem grinding. verse background gem groups and actively running variants while i make dinner or watch a game. But that was not my question and a topic for another thread.
edit: that's kind of an answer to your edit ^^
Yea, i've been thinking about doing the patron stuff in the background now that they take well over an hour. the shorter ones i could do 10+ while i was making dinner or watching a game or something using speed potions. Set up the party, click a few potions and in 15 mins i'd set up another. Now unless i watch a couple movies or something i only get a couple in. I stopped doing the background parties for variants because i was getting more gems letting them run verse not for 12+ hours stalled out just past completion.
I've nearly finished all the ones under 1k outside of a few of the most recent additions. I did start adding lvls to a couple speed guys recently as my main party now gets to like 1700+, i added fillers to help with restrictions, and those are nearly done too. I guess at end game there is getting a lot less to do other than pump lvls. I've nearly completed all 4 patrons up to the witchlight, just the newest stuff and elemister left.
The grind continues, this game added 25 bucks a month to my electric bill, so maybe i need to rethink how i'm playing now that i'm so far along that it doesn't need anywhere near the tending it once did. If i can drop it to 10-20 hours a week and get further that would be nice. :)