For the love of god dont buy Doran's Ring or Doran's Blade in doombots

TL;DR: the Doran's items are designed and balanced around PvP early game, not doombots early game. So just get a component for your 1st core item instead.

Doran's Ring gives 15 AP, 60 HP, and mana regen. With the exception of mana regen, these stats are not optimal for start.

15 AP is next to useless in doombots laning phase; due to how powerful the bots are even early on, you do not want to trade with them; you would mostly want to use your skills for farming under turret, so the AP is not as useful as it would be in your typical ranked games.

60 HP is somewhat more valuable, as it could mean the difference between surviving enemy attacks with 59 hp remaining or dying. However, it ends up being the difference between spending 7~9 seconds on death timer or spending 4 seconds on recalling, and you still have to walk back from base; you still lose out on gold and exp anyways, which is what your focus should be in doombots laning phase; early game 60 HP is subpar stat for doombots laning phase.

The mana regen is the only stat that's actually arguably useful in doombot laning phase. However most of the champions played in doombot have mana regen between 6 and 8 at lv1, with the regen increase per level being 0.4~0.8. http://leagueoflegends.wikia.com/wiki/List_of_champions/Mana_regeneration Given laning phase lasts 5 minutes, rough estimate would tell you that the 50% mana regen would be equivalent to approximately 450650 more mana to use over the 5 minutes assuming you somehow manage to never have to back. This would let u use your skill about 812 times more than not having Doran's ring on rough estimate. Given that the additional mana lets you last hit 812 more minions than what you'd have gotten without Doran ring, it means that you gain 140g246g (up to 321g if u r soo bad at this game u cant even last hit cannon minions... oh wait u should be using smite for that) in return for the 400g u spent on Doran's Ring. By getting Doran's Ring at the start, you are basically delaying your 1st core item by 154g~260g for an inferior "advantage" in lane. Because you will be poked down anyways and recall/die in lane multiple times, you are not staying in lane for 8 minutes like you would in ranked; mana refill from fountain is going to be very frequent in this game mode so you are not getting much value from mana sustain either.

By purchasing Doran's Ring, you are only making it harder for yourself by delaying your 1st core item by 400g; it's just way more optimal to get a component for your first item or even boots to help dodging more skillshots so that you die less.

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For Doran's Blade , it is a recommended item in our usual ranked PvP matches because we auto attack the minions continuously, allowing us to sustain in lane. However, it's a different story in doombots; we get pushed to our own turret and we can only last hit under tower, so we are not getting much value from the early lifesteal; if it's for covering the lack of AD to last hit under tower, is the better choice as it is cheaper, gives more AD, and is also a component for core items. It is also optimal to get a component for 1st core item such as , or even as explained above.