Runes: (+0.25 gold per ten seconds) * (9 seals) + (+1 gold per ten seconds) * (3 quints) = 5.25 gold per ten seconds.
Relic Shield: (+2 gold per ten seconds) + Runes = 7.25 gold per ten seconds
Base gold generation: +19 gold per ten seconds
Now comes the tricky part. Minions start spawning after 90 seconds. There are 6 minions per wave. 3 are caster and 3 are melee. Each wave comes in 30 seconds. Passive gold generations don't begin until 90 seconds into the game when minions spawn. Melee minions are worth more than caster minions so let's assume you go for the melee ones, which will give +22 gold on the first wave and +23 gold on the second one.
You have two charges. This grants you +45 gold. You get another charge after 60 seconds. This is when a siege minion spawns, so save it for then, which will give you +27 gold.
After the first set of three waves:
Relic Shield: +72 gold
Runes: +47 gold
Base: +171 gold
Relic Shield passive: +18 gold
Total: 308 gold is ensured per three waves.
Now let's add things outside your control: Bandit. Let's just assume they're getting 75% of the CS as a baseline. No real reason for that number, other than you're going to get at least that in most cases. Six minions per wave (-2 from relic shield) and 7 minions on the third wave (-1 from relic shield.) That's a total of 18 minions. That's +13 gold per three waves. Also, let's assume you hit each enemy once per wave. Hitting them once every five seconds is just not going to happen and you'll probably hit them more than once per wave, but this is the bare minimum for convenience. That's +10 gold per wave if you're melee. Which is +30 gold per three waves. Which is +60 gold per three waves if you hit both, or one but twice as often.
Now, after three waves you have a grand total of 368 gold. As
, instead of a
I get a
. That + masteries + Relic Shield usually sustains me. What does this mean? You only need 350 gold to upgrade your starter item! Guess how much you have after three waves? It's now been 180 seconds, or three minutes.
Right. So now it recharges every thirty seconds instead of every sixty seconds. That's +23 gold, +23 gold, then +27 gold. Another three waves of
= +73 gold instead of the old +72 gold. It only seems like you're gettting one extra gold, but the real value is in the cooldown of the item. You get one per wave, so let's stay another three waves. +23, +23, +28. It's now been 9 waves and you've gotten +147 gold from
.
After the second set of three waves:
Targon's Brace: +73 gold
Runes: +47 gold
Base: +171 gold
Targon's Brace passive: +18 gold
Total: 309
After the second set of three waves:
Targon's Brace: +74 gold
Runes: +47 gold
Base: +171 gold
Targon's Brace passive: +18 gold
Total: 310
You lost -350 gold from buying the upgrade and had 18 gold leftover. So your grand total is: 637.
Can buy
for -300 gold and can buy a
if you wait 24 seconds. Since backing takes 8 seconds, that's only 16 seconds.
The MASSIVE tl;dr is that the difference of having gold income runes v not having them as a melee support is being able to buy your
and upgrade your starting item and build a
into a
which would later lead to a
. This would happen after 6 minutes. You can't just say "it's .525 gold per second" because the earlier you get gold, the more gold you'll get later. After nine waves, it's a difference of 187 gold. Whereas the math just shows a difference of 141.75 gold. You see an even bigger spike after you upgrade into FOTM but let's not go there.
Is it worth it? No. Don't ever buy gold income runes. But I thought it would be neat to show all the math (in a more realistic light instead of under perfect conditions.)