How much would I have to idle for Steel Plants to be worth it?

A common sentiment seems to be that the Steel Plant upgrade is never good, due to workshop craft ratio not applying to the calciner's steel production...at least not until end-game, when you gain coal so fast that a human can't possibly craft steel by hand fast enough.

But even in mid-game, isn't Steel Plants worth it if I idle? How much would I have to idle for it to be worth it? For instance, let's say my craft ratio is x5 and my coal hits cap in 10 minutes (0.166% coal/sec). Has anyone done the math for what percentage of my time I need to idle in order for the steel production to be worth it?

I attempted to answer this once and completely botched the math. Let me see what I can do this time, since no one else has chimed in.

Let's define some terms, because "Worth it" is a relative term and not useful. Idle time would be any time spent with coal already capped - wasted coal income, where Steel Plants are actually providing value. Active time would be the exact opposite, the ten minutes in your example your coal is filling up. If you want an actual percentage value, you would need to compare rates of Active steel to Idle steel.

Lets assume you always have iron to mix with steel in an Active craft. Safe assumption; Calciners are really really good at making surplus iron. Steel is always made at 1 per 100 units of coal, and in Calciners is 10% of iron output (base .75/s but can be upped) so we get:

Active steel crafting rate = ( (coal/s) / 100 ) * craft-ratio

Idle steel plant rate = (number-of-calciners) * ((0.75 * upgrades) / 1000 )

Percentage of idle time out of total time to render Active steel and Idle steel rates equivalent = 1 / (1 + (idle-rate / active-rate))

which eventually turns into....

Percentage = 1 / ( 1 + ((number-of-calciners * upgrades * 0.075)/(coal-per-s * craft-ratio)))

(this is already very simplified math, as I'm not taking into account that steel plants run during active time, that calciners have an impact on coal-per-s, etc. Even this looks bulky, it'd be easier if we were just looking at a ratio)

The problem is that the only values that make steel plants worth more are number-of-calciners and upgrades to their production, both of which are limited and hard to get. By comparison, the values that makes this percentage higher and steel plants more useless, coal-per-s and craft-ratio, are much easier to increase. To hurt further, global bonuses would count as a calciner upgrade, but have larger effects on the coal-per-s.

The only way to demonstrate this is with game values (I can't figure out charts at this point), so I will try to estimate a few and plug them in.

Your example kinda - craft-ratio=5, coal-per-s=25, calciners=5, upgrades=2.7 (oxidation and kilns are easy to get before steel plants) applied to formula, generates percentage=99.19%

So if coal capped in 10 minutes, as you say, idle time to match that production would be 1,224 minutes, or 20 hours.

Lets try some later game numbers.

craft-ratio=8, coal-per-s=500 (lowball, really), calciners=35, upgrades=10 (roughly all upgrades plus the new partial craft-ratio upgrade comes to 7.4, so lets assume some globals kick in and bring us up to 10 for 7.5iron/s), applied to formula, percentage=99.34%

That's actually WORSE. No one likes this math. Thus the attitude towards the Steel Plants upgrade. The only reason it finds use is that time to cap coal gets so ridiculously short, idle steel is practically guaranteed as soon as you turn your back. Like many other idling mechanisms in this game, Steel Plants are mainly there so you get something when you idle, and not nothing.