Is triple dorans on a 800g back superior than early amp tomes.
I think you seen this before. The dreaded Bjergsen, "lord of the rings" build.
You may have been criticized by your teammates, or been allchatted by your enemy for being batshit insane or being a noob. But lets see this through the maths.
Let's say you are on your first back. With around + 900g in your belt. Is it a wise choice to get a amp tome, and get a straight build path to lost chapter until you generate + 1300g. Or, predict this buildpath and get 2 dorans gaining 30 ap, + 10 mana per sec and 120 health with additional wards and potions, so that your near unlimited early mana and tankiness plus AP stats would overwhelm the enemy?
Your general first back with lost chapter build will be something like this.
+
x2 +
+
= 960g
No gold to buy a additional amp tome, unless you are ballsy enough to face a enemy with their ult up with no pots or pink wards.
The most problematic flaw is of course the mana crystal which is 350g for 250 mana. Which will be generated with triple dorans in JUST 16.6 seconds. And of course there might even be a chance of losing cs against the flood of mana spam so there is even a more larger risk.
x2
=975g (+5 ap efficiency, mana superiority in 16 seconds. +120 health -15 g deficit)
x2
=960g (-5 ap efficiency, mana gain loss in 16 seconds after buy)
The most dreaded part is what will happen if you lose to this build against its incredible block of stats and early mana spam.

+
x2 (85ap + 120 HP)
against the lost chapter side will be...
x2 (55 ap, mana par to triple dorans situationally. Also build will stop progress until it gets a blasting wand)
I think the results are devastating as dynamite. It snowballs hard as hell. Already a 30 ap increase, while lost chapter side has to struggle to make a 850 g blasting wand next. So I want to question again, is triple dorans a tactic superior against people that are not expecting it?