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This is in response to a post earlier that claimed "RS is better than Sickle on EVERY SUPPORT" on the basis that "the gold from relic is far better than sickle stats". But is it actually? Let's find out. (Summary at bottom)
Spectral Sickle
- Grants 25 gold upon poking enemy champions (10s charge)
- Grants 40 AP and 10 Ability Haste at max
Relic Shield
- Grants 120% of kill gold when executing minions (100% split among nearby allies) (20s charge)
- Only 58% of gold counts towards quest completion
- Grants 200 HP and 10 Ability Haste at max
Shared Traits
- Grants identical gold penalties for non-execute last hitting
- Grants 40% boot enchant cd refund on takedown at max
- 1000 gold to upgrade to max level
- Grants 1 gold every 3 seconds at first two tiers, grants 2 gold every 3 seconds at max tier
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1) Time to finish item
Let's assume that perfect play is attained: the player will never sit on 3 unused charges. First, let's calculate how fast each item takes to max out.
Sickle = 25/10s + 1/3s = 28.33 gold every 10 seconds or 2.833 gold every second. 1000/2.833 = 352.983. It takes 353 seconds, or 5 minutes 53, to finish Sickle.
Relic Shield is more complicated. Firstly, only 58% of gold counts towards quest completion. This means you actually need to earn 1724 gold to complete the quest (1724 * 58% = 1000).
Melee minions grant 65 gold, casters (ranged) grant 40 and cannons grant 85. This means that obviously the best method is to solely take melees and cannons.
Here's a little lesson in wave trickery: waves spawn every 25 seconds. The first 3 waves are two caster waves, followed by one cannon wave. The next 3 waves are the same. However, after that, waves alternate between a caster wave and a cannon wave until ~12 minute mark, which is a bit far to actually worry about.
I've gone ahead and worked out that the minimum time to finish Relic Shield is 380 seconds, after 16 minion waves, of which 7 were cannons. A total of 19 Relic Shield charges are used.
Gold (cannon) = 120% * 85 * 7 = 714
Gold (melee) = 120% * 65 * (19-7) = 936
Gold (passive) = 380 * 0.33 = 126.66
Total = 1776.66
While this is above the 1724 gold required, 360 seconds (18 charges) would only give you 1668 gold.
We now add the 17 seconds it takes for the wave to reach lane (Sickle doesn't have this as they only need enemy champions to be there) and it takes 397 seconds, or 6 minutes 37. This is only 44 seconds longer than sickle.
Extra passive gold = 44 seconds * 0.33 (since you get 1 extra gold/3s at max level) = ~15 gold.
This alone is not enough to warrant taking sickle alone. However, I do want to note that it assumes perfect play, and imperfect play is much more likely to happen with Relic Shield than Sickle. You won't be using charges of Shield in a teamfight, and you have to deal with last hitting and your adc instead of the simple poking Sickle wants.
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2) Actual gold earned per item
Spectral Sickle earns you 1000 gold, and 2 gold every 3 seconds after it's fully upgraded.
Now, I know what you're thinking. Skyfire, Relic Shield needs 1724 gold to complete. You earn 724 more gold using it over Sickle! That's huge!
There's just one problem. Relic Shield includes gold that you would have already earned from being close to a dying minion.
You know how someone last-hitting a minion near you gives you half the gold right? THIS IS GOLD YOU EARN ON SICKLE ANYWAY.
Let's go back to that 380 second, 16 minion wave Relic Shield calculation for an example.
Gold (cannon) = 120% * 85 * 7 = 714
Gold (melee) = 120% * 65 * (19-7) = 936
So what about the gold you would have earned with Sickle?
Gold (cannon, no shield) = 50% * 85 * 7 = 297.5
Gold (melee, no shield) = 50% * 65 * (19-7) = 390
True gold earned = 1878.66 - (390+297.5) = 1190.66
Instead of earning ~700-800 extra gold with Shield, you only earn an extra ~200.
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3) Gold in stats
The easiest thing to calculate to be honest. Let's ignore ability haste since both Shield and Sickle grant it.
The going rates, based off base items, is 12 AD for 500 gold, 25 AP for 500 gold and 150 HP for 500 gold.
Gold (Sickle AD) = (20*500)/12 = 833.33 gold
Gold (Sickle AP) = (40*500)/25 = 800 gold
Gold (Shield HP) = (200*500)/150 = 666.67 gold
So Sickle gives 133.33 more gold in stats. This is not even counting the value of ideal stats: basically, the idea that X amount of HP is worth less to an enchanter than it is to a tank support.
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4) Value of earlier completed item
In calculating the times to complete items, I did mention that I assumed perfect play was in use. With imperfect play, the time margins will expand to the point where Sickle can be finished before the second dragon/herald fight whilst Shield can't.
The value of the 40% boot enchant refund, when considering the additional further value for enchanters building enchanter items (like Censer and SOFW) that get triggered by Redemption Enchant, is immeasurable.
Because the refund could potentially turn the tide of a teamfight, I can't calculate a value for it other than suggesting 300-1000 gold extra (I.E. an extra kill or completely flipped teamfight).
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Summary
Having analysed both Sickle and Shield, Sickle will be completed faster and gives more gold in stats, while Shield gives some extra earned gold (though it is nowhere near as much as people think). The extra earned gold margin is only 200.
It is therefore rather absurd to suggest that "every support", including enchanters like Lulu with 5 AP ratios should take a HP item instead of an AP item just to earn 200 more gold.
This suggests that enchanters should take Sickle for the AP and faster item completion, while tanks should take Relic Shield for the HP and because they cannot complete Sickle remotely close to the time I calculated (due to lacking poke). Indeed, this does reflect our actual games.
Tl;dr: there is no mathematical basis to support the idea that Shield > Sickle on enchanter supports.
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