Huh. This actually makes sense. (The engineers thing)
Since navies have tenders that heal everything.
I mean steam rams can be healed. Why not steam giants, too?
Maybe they'll be super OP if that happens. Would want some @Abeged 's (AKA battle math master) input if it would be too OP if Steam Giants can be healed.


Doctors are truly practically useless.
The best they can do is reduce damage percentage by a very small percentage.

You know I wasn't planning on doing any math today, but on top of that mad compliment I'm suddenly feeling inspired.

Anyhow, I guess I could calculate the outcome of a standard SG battle with and without doctors, now engineers.

I'll assume both sides are using SG's. One without engineers and one with. This is based on the fact that if one person is waving SG's, the other person almost always mirrors you no matter his skill level.

Anyhow. There's a whole lot of units who would be affected by engineers. Gyros, ballons, mortars/rams and SG's (I don't think I forgot any (relevant) units).

So the lineups will be the following, assuming one full battlefield for each side.

16*7 SG's
40*6 Swords
12*7 Muscets
6*5 Mortars
15*2 Ballons
30*2 Gyro's

(Let me know if I misremember the numbers, as I've stated countless times at this point, I don't battle much on land).


So let's start calculating damage numbers. Luckily I only have to do it once since they're mirrored.

I'll assume all units are fully upgraded and have forge.

Units:
- SG's
HP: 182
Armor: 6
DMG: 45*1.2 = 54
True DMG vs SG's = 54-6 = 48

Swords:
I'm not gonna calculate these. They're going to be the exact same as with doctors. Refer to some of my other posts for calculations on these.

Muscets:
DMG: 29*1.2 = 38.4
True DMG vs SG's = 38.4-6 = 32.4

Mortars:
HP: 32
Armor: 3
DMG: 273*1.2 = 327.3
True DMG vs SG's = 324.3

Balloons:
HP: 40
Armor: 3
DMG: 51*1.2 = 61.2
True DMG vs Mortars = 58.2

Gyro's:
DMG: 20*1.2 = 24
True DMG vs Ballons = 21

Alright, that's the baseline. Now for the damage that is taken, let's start with the easy ones. Balloons and mortars. Gyro's shoot before balloons so we have to account for this first.

As there are 30 units in each stack, both stacks of ballons (should) take damage equally. (I'm aware this isn't always the case, I am unable to explain why this is... Accuracy in a nutshell). I'll calculate based on a logical distribution of damage, as I would any other position.

30*21 = 630 dmg inflicted to each stack of ballons. Let's calculate casualties.

Total hp of balloons: 40*15 = 600. As such all balloons should die in a forge vs forge battle. To my knowledge this is correct.

This means I don't have to calculate for loss of mortars (forgot about this, just saved myself like 10 minutes).


Mortars:

So we know we have a full line of mortars. They're split in 5 stacks with 6 units in each. This means damage will be dealt to 6 different stacks with 5 hits going to each.

5*324.3 = 1621.5 dmg to each of the 6 stacks.

Total health of a stack of SG's: 182*16 = 2912

The loss: 2912-1621.5 = 1290.5/2912 = 44% is left alive (or 1290.5 hp's worth (or 7.09 SG's)).
Remember, this is only of 6 stacks, we have one still on full health.


Muscets:

There are 12 in each stack of muscets. This means that the 2 outer stacks of SG's will take 1 hit, while the 5 inner will take 2 from each stack. This adds up to a total of 7 hits on outer stacks and 14 on inner.

Let's calculate for the inner first.

14*32.4 = 453.6 dmg

All inner stacks have the same amount of health left, this value is 1290.5 as calculated above.

1290.5-453.6 = 836.9/2912 = 28.7% is left alive (or 836.9 hp's worth (or 4.598 SG's)).

Now for the outer.

7*32.4 = 226.8 dmg

These stacks have different amounts of health so I have to calculate seperatly. Let's start with the damaged one.

1290.5-226.8 = 1063.7/2912 = 36.5% is left alive (or 1063.7 hp's worth (or 5.84 SG's)).

The undamaged one:

2912-226.8 = 2683.2/2912 = 92% is left alive (or 2683.2 hp's worth (or 14.74 SG's)).


The frontline:

Now this is going to be a pain to calculate, but then again, I've come this far, may as well finish is properly. Haven't even gotten to the point yet..

We have 3 different kinds of stacks to calculate for, to do so we need the number of SG's alive (which is why I included it above).

Let's start with the 5 inner stacks.

These each have 4 SG's left which can deal damage, meaning they will hit the 4 inner most targets. Since there's 5 stacks, these stacks will be hit 5 times.

48*5 = 240 dmg

To calculate loss we need the exact hp value (which is why I included that above).

836.9-240 = 596.9/2912 = 20.5% is left alive (or 596.9 hp's worth (or 3.28 SG's)).

Remember, this is for the 4 most inner stacks, we still have one stack heavily damaged, one slightly less so, and one even less. Might take a few attempts to get this, I won't judge you, I'm damn concentrated as well.


Now let's calculate the damage the damage the sixth most center stack does.

This stack has 5 SG's alive, which means it will hit the 5 center most stacks once.

48 = 48...

These stacks now have different amount of health. Let's calculate for the 4 we just calculated for above first.

596.9-48 = 548.9/2912 = 18.85% is left alive (or 548.9 hp's worth (or 3.02 SG's)).

And now for the fifth which didn't get hit above.

836.9-48 = 788.9/2912 = 28.09% is left alive (788.9 hp's worth (or 4.33 SG's)).


Last stack, let's calculate the damage dealt by the last and most healthy stack:

This stack has 14 SG's left alive. This means all stacks will be hit twice.

48*2 = 96 dmg

I have to calculate this for each different health stack. The 4 most center stacks have the same hp, the last 3 stacks all have different hp values.
First for the 4 most center stacks.

548.9-96 = 452.9/2912 = 15.55% is left alive (or 452.9 hp's worth (or 2.49 SG's)).


Now for the fifth stack:

788.9-96 = 692.9/2912 = 23.79% is left alive (or 692.9 hp's worth (or 3.81 SG's)).


Now for the sixth stack:

1063.7-96 = 967.7/2912 = 33.23% is left alive (or 967.7 hp's worth (or 5.32 SG's)).


Now the seventh and last stack:

2683.2-96 = 2587.2/2912 = 88.85% is left alive (or 2587.2 hp's worth (or 14.22SG's)).


Hot damn, that's the heavy part. Now for the slightly less heavy but still sort of boring work. We need to figure out how much hp each damaged unit has. Which is another reason why I included the exact unit numbers and hp numbers. It'll make my job easier. Probably is a help to you guys as well. Let me know.



Luckily only SG's have taken damage in our experiment (yes I'm aware some gyro's should have taken damage as well but I honestly can't be bothered. That's a question for another time).

Let's figure out the missing health, starting with the 4 most center stacks.

452.9-2*184 = 84.9 hp which can be healed.

The fifth stack:

692.9-3*184 = 140.9 hp which can be healed.

The sixth stack:

967.7-5*184 = 47.7 hp which can be healed.

The seventh stack:

2587.7-14*184 = 11.7 hp which can be healed.


Total amount of hp that can be healed (excluding gyro's): 84.9*4+140.9+47.7+11.7 = 539.9 hp which can be healed.


So all of that math was for this lonely number, I'm not sure how I feel about this.. Took like an hour.. Anyways..

Let's asses the value were this to be healed. What is it in SG's?

539.9/184 = 2.93 SG's.


Total statistical loss of SG's without "engineers" can be calculated based on their hp.

A full battlefield is 16*7 = 112 SG's.
Total health is then: 112*184 = 20608 hp.
Total loss is: 20608-(452.9*4+692.9+967.7+2587.7) = 14548.1 hp.

The percentage the engineers would do is then:

539.9/14548.1 = 3.71%


The conclusion:

In this specific but very common scenario, a frontline with "engineers" would be 3.71% more effective than a frontline without them. This is in my opinion a pretty large difference, but then again, it would be open to everyone, would't actually make much of a difference in the long run. I would not see it as overpowered, but it would most definitely make SG's the superior frontline unit. And before anyone starts whining "but Abeged, we don't place SG's in while mortars are on the field", I only got one thing to say, I didn't consider I probably should have gone with rams before now. But also the experiment is mirrored, and as such the same (almost) difference would be found. If you don't trust me I do encourage you to do the math yourself. So I guess I had two things to say.

Anyways, that's it for me for now. I'm going to add this to my novel since well, it took way too long not to do so.

i think it would been possible that the engineers should get tired after for example 5-10 rounds so you then need to wave them, it would make sence, it would help the hops to still be a little better because cooks don't need to be waved then and while you sleep you can't be online ofc you can set alarm and so on but still.

It would helped alot to see the difference in gold and damage and so on and see the difference ingame!

what i know it's the following:

to upkeep 1 Giant it cost you 12gold/hour
Hop: 3 gold/hour
@Abeged Can you if you want calculate who would win that battle if they were against each other? and then we can try it in practise to see how a full battle, with hops would work against the same cost in gold against Steam Giants?.

Because i think the gold cost will then decide what unit you gonna use in the future if Gameforge bring Engineers to the game!

Well in war you win by having the lesser losses, and greater damage dealt. As such gold cost is completely irrelevant.
If you're looking for an option to plunder barbarians in the beginning of the game, there's no point in calculating who would win. Of course I could calculate the victor, though I'd prefer not to. That's another hour of work to conclude that SG's that doesn't need waving quite simply are going to be better. They would have the advantage of no waves, like hops, and greater power, since they're SG's.

That said it takes 50 hops to fill a stack = 150 gold
It takes 16 SG's = 192 gold.

An increase of 28%. If you're hoping they will be 28% better than hops I'm sorry to disappoint. But I don't need to calculate anything to tell you this won't be the case.

What i'm talking about is, do we get the same dmg dealt and the same result or even more if we use Hops instead of Steam giants ofc the recourses will be different, because in a long war if you can get better result with Hops than Steam giant you would save ALOT OF gold!

that's why i'm wondering! because the Steam giant don't has 4 times more damage or armor than a hop that's why i'm wondering maybe i'm wrong who knows!
As you can see on your gold calculate it's a 42gold different/stack imagine then in a full battle! with like 100 stacks of Giants or Hops, then it's a 420 gold/hour not much you think but if you have like 4k Hops against 1k Steam giants then it can make a big different or am i wrong? also if you can win the battle with 2-3k instead of 1k Steam giatns it will make a different in gold, that's why i'm wondering, you understand what i'm thinking?

OH MY!

I was just hoping for a mere speculation but you went full out on this!
The amount of thinking you put into this is amazing. Thank you for your time and effort to do this!

I guess if it's a full scale battle, just like you calculated, it won't make much of a difference then.
But I think it would be safe to say that if the SGs weren't dying, only damaged per round, they would make the SGs totally invulnerable as they would be fresh by the start of each round. But to be honest, if anyone is fighting SGs and not even killing them every round, they should just run away. Thus, it would make the winning side win more and the losing side lose more.


Considering your calculations, because it would be available to everyone, it agree that they definitely wouldn't make them OP. Especially since everyone would have access to them anyway.
I can see using SGs against barbarians become a lot easier. But even though if there were engineers, it would not make hoplites obsolete since they would still need cannon fodder.