''Mathematically correct'' build for jungle/top
Disclaimer: I use coachless.gg stats from 16.9 (last patch) and only take into account for items thats have significant sample size . also your playstyle and familiarity with a build/rune also does matter a lot, so yes ''mathematically correct'' is clickbait. I'm a jungle main so I'm lot more confident on what I have to say about jungle build, about top lane I'll just put the stats there for discussion.
JUNGLE BUILD
-Runes : First Strike > Conq
Thats what the stat say, but I'm not convinced after testing, it barely give more gold than triumph and damage wise its fine at best.
-Jg pet: Green smite > Red smite > Blue smite
This had been the trend for multiple patches where green outperform red smite by quite a significant margin. I have tested it and would recommend going green instead of red vs poke comps or 2+ assassins.
-1st item: Voltaic >> Profane > Hubris >> Eclipse (DO NOT GO BRUISER ON JG)
Note that Voltaic is nerfed this patch 16.10 (price increased 100). though the item outperform profane so much last patch, i would still recommend buying it over profane if u can afford it. in cases when you can buy profane but cant buy voltaic, just buy profane, its 150g cheaper.
-2nd item: Serpent fang (when it works) >> axiom > sundered sky
I tested 1 lethality item into sundered sky, it was fine but it seems the stats say otherwise.
-3rd item: Just go Death Dance xd
-Boots : Gluttonous = Steelcap >Merc >>Ionian
note that gluttonous got giga nerfed
-4+ item: build what you need, serylda, mortal reminder, endless hunger, maw, guardian angel (In most cases guardian angel is the best item after your 3 core item, unless you really need that armor pen, magic resist, or the game isnt close to ending and you can buy endless hunger)
TOP BUILD
(I dont have anything to say here, this is up for speculation)
-Runes: Electrocute >> Conq > Grasp (consistent across multiple patches)
-Spells: Flash Ignite >> Flash TP
-Starter: D Blade >> D shield
-1st Item: Profane >> Voltaic >> Eclipse
-2nd Item: Axiom >> Cleaver >> Shojin
-Boots: Steelcap >> Merc
-3rd Item: Death Dance >> Shojin >> Endless Hunger > Maw