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Currently there are 3 major support Items: the relic shield, the ancient coin and the spellthiefs edge. I usually use the coin or the shield, because i feel like it's the most secure gold income. However one day I played lulu support with the spellthiefs edge and by playing really aggressive I procced the passive quite often. I think I got more gold on this Item than on any other game where I lasthitted with the shield or stood near a minion when it died. I personally feel like on average i'm getting the most gold with the shield, but mathematically i'm not sure about that.

Let's say there are 6 bot lanes in 3 different games with 3 different Items. Everyone starts with the basic form of the item and goes back whenever they have enough gold to buy the upgrade.

So what is the most efficient gold item when playing perfectly (In a lane, a whole game would be too complex). That means: Standing near as many minions as possible when they die if you have the coin, lasthitting a minion whenever possible (think about cannon minions aswell!) with the shield, and of course keeping the spellthief passive on cooldown with the pick.

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Thanks for asking this question, it was quite interesting to do some research on this :) +1 –  Kevin Feb 5 at 9:57
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2 Answers 2

up vote 3 down vote accepted

This answer was given on 05-02-2014. The current patch is 4.1. The answer will probably get less accurate and/or relevant in future patches.

I'm gonna have to make some assumptions to create a proper example here.

  1. I'm not taking in account any gold increases from masteries.
  2. I'm taking the first ten minutes of the game as 'laning phase', The values may change if the laning phase is longer, but you really can't know that up front so early decision making should not change.
  3. I'm not taking into account any jungle farming
  4. I'm assuming the 'level 1' version of the items, buying the upgrade at some point will ofcourse change the data

Relic shield:

Minions start spawning from 1:30. So at ten minutes the 18th wave will spawn. This means that for the first ten minutes you have 17 waves to farm (the 18th will be underway at ten minutes). A cannon minion spawns in the wave every 3 waves and the Relic shield has a 60 second internal cooldown. So you can last hit the following:
wave 1 (melee minion) +23 +5
wave 3 (cannon minion) +40 +5
wave 5 (melee minion) +23 +5
wave 7 (cannon minion) +40 +5
wave 9 (melee minion) +23 +5
wave 11 (cannon minion) +40 +5
wave 13 (melee minion) +23 +5
wave 15 (cannon minion) +40 +5
wave 17 (melee minion) +23 +5

total 320 gold

Spellthief's edge:

The internal cooldown is 10 seconds per enemy. In a standard game you will be able to start hitting your opponents from about 2:00 when both teams go to their lane after helping their jungler. That means you can hit your opponents 48 times (both of them, as the cooldown is not shared between enemies hit) so 96 procs on the item. It gives you 4 gold per proc. Spellthief's edge also gives a passive 2 gold per 10 seconds. This is 120 gold for ten minutes.

total 504 gold

Ancient coin:

This one is easy, there are 17 waves (as said in the Relic shield part) to be farmed. Four of them have an extra minion. totaling 106 minions. The coin gives 2 gold. It also has the 2 gold per 10 seconds passive.

total 332 gold

Conclusion:

Spellthief's edge is the best item for pure gold gain, but it only grants gold to you. The Relic shield also gives gold to your adc (85). Ancient coin seems like the worst choice gold wise, but it's a lot more passive (and easy, 'safe pick' etc). Depending on when you buy the upgrades this coud change a lot. I think it's too complex to go into that in an answer here, if you really want to know about the upgrades as well, I suggest looking up a support guide that covers these items.

sources:
Relic shield wiki entry
Spellthief's edge wiki entry
Ancient coin wiki entry
Minions wiki entry

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According to the lolwiki a melee minion gives 20 Gold (not 23), also you should take into consideration that the bounty for minions rises all 3 minutes. –  Toby Feb 5 at 10:33
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Good luck hitting both of your opponents 48 times a piece. If you can do half of that, though, it gives 312 gold by minute ten. That means that in order for Spellthief's edge to be worthwhile you must attack an enemy every 10 seconds and hit the other enemy a couple of times - all without missing a beat. –  Bob2Chiv Feb 5 at 12:57
    
@Bob2Chiv The OP specifically said "when playing perfectly". That's why I calculated the values like that. –  Kevin Feb 5 at 13:09
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No problem, I'm just saying that Spelltheif's edge, in practice, is probably the worst LANE gold generating item (for future readers). –  Bob2Chiv Feb 5 at 13:19
    
This answer has excellent methodology but is outdated after patch 4.3 rebalanced gold generation items. As of patch 4.8, using the same calculation technique as Kevin's answer, I figure Spellthief's Edge at 420g, Relic Shield still at 320g, and Ancient Coin at 212g. –  Nelson May 31 at 22:05
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There are 3 build paths (I neglected the final item, since it has no effect on the gold income):

Path: Frost Queen's Claim

Spellthiefs Edge: Autoattack on a champion gives 4 Gold, up to once every 10 seconds. +2 Gold per 10 seconds.

Frostfang: Autoattack on a champion gives 8 Gold, up to once every 10 seconds. +4 Gold per 10 seconds.

Path: Talisman of Ascension

Ancient coin: Being near a minion's death gives 2 Gold

Nomad's Medallion: Being near a minion's death gives 4 Gold. +2 Gold per 10 seconds.

Path: Face of the Mountain

Relic Shield: Killing a minion + 5 Gold - Max. 2 Charges which recharge every 60 seconds.

Targon's Brace: Killing a minion + 10 Gold - Max 3 Charges which recharge every 30 seconds.

Assumptions

Let's say, first minion wave arrives at 2.00 minutes. Minion spawn time is 30 seconds.

  • Caster minions: 15 Gold +0,5/3min
  • Melee minions: 20 Gold +0,5/3min
  • Siege minions: 40 Gold +1/3min (spawns every 3 minion waves)
  • Considering every 3rd wave with siege minion makes + 1/3 minion per wave
  • 2 waves per min = 2*6,3 = 12,6 minions / minute

Some other stuff we assume:

  • First back at minute 6
  • At this base we bux the upgraded version
  • We neglect other items
  • We neglect the time you lose while porting back and walkign down to lane

Some Math:

Path: Frost Queen's Claim

Let's assume first hit on an enemy is also at minute 2. We can trigger the passive 6 times per minute. This means:

  • 6 minutes of gp/10 (12 Gold/Minute) = 6 min * 12 Gold = 72 Gold
  • 4 minutes of passive (6 times/Minute) = 24 times * 4 Gold = 96 Gold

Bonus Gold at 6 minutes: 168

Now we assume to have Frostfang. Since this item doesn't depend on minion gold value we can easily calculate gold per minute.

  • 4 Gold / 10 sec = 24 Gold / Minute
  • 8 Gold / 10 sec (Autoattack passive) = 48 Gold / Minute

Bonus Gold income from 6 minutes on: 62 Gold / Minute

Path: Talisman of Ascension

  • 4 minutes with 12,6 minions / minute = 50,4 minions
  • 50,4 minions * 2 Gold = 101 Gold

Bonus Gold at 6 minutes: 101

After the upgrade we have:

  • 2 Gold / 10 sec = 12 Gold / Min
  • 12,6 minions / min (with 4 Gold for every minion) = 50,4 gold / min

Bonus Gold income from 6 minutes on: 63 Gold / Minute

Path: Face of the Mountain

At minute 2 we can start with killing 2 minions = 30 Gold (15 Gold each)

Then we can hit a minion every 60 seconds. Makes 4 more minions until our first back at the 6 minute mark.

  • 1 Minion for 20 Gold
  • 2 Minions for 20,5 Gold
  • 1 Siege Minion for 40 Gold

So its 81 Gold + 30 Gold from the first two minions.

Bonus Gold at 6 minutes: 111

Now it's getting a bit tricky. We can hit a minion every 30 seconds. This means 90 seconds we can hit two melee minions and a siege minion, which gives us a total of 83 gold. (Regarding the first increase in gold bounty for the minions)

With a bit math: 83 Gold / 90 Seconds = 166 Gold / 180 Seconds = 55,3 Gold / Minute

We also have to pay attention to the rising reward which will be accountable for 6 Gold / 3 minutes.

Bonus Gold income from 6 minutes on: 55,3 Gold / Minute, which increases by 6 Gold every 3 Minutes.

Summary

Frost Queen's Claim:

  • 168 Gold at minute 6
  • From minute 6 it's 62 Gold / minute

Talisman of Ascension:

  • 100 Gold at minute 6
  • From minute 6 it's 63 Gold / minute

Face of the mountain:

  • 111 Gold at minute 6
  • From minute 6 it's 55,3 Gold / minute
  • Increases by 6 Gold every 3 minutes
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