Intended Mk. Ship Scaling

[TechSY730]

Just a quick question. What is the "toughness multiplier" you are aiming for with Mk. lvls.

Or more formally, if on average takes x Mk. (n-1) ships to take on a Mk. n ship with a 50% chance of winning, what is x (or rather, what are you trying to get x to be)?

[keith.lamothe]

Generally power of an individual unit should scale linearly with mk level.  So a mkII is twice as strong as a mkI, a mkIII is 3x as strong as a mkI and 1.5x as strong as a mkII, etc.

Cap vs cap, it's somewhat less than that because the caps (of most stuff, turrets excluded for example) decrease with higher mk level.

[TechSY730]

Hmm, so the ratio is not a multiplier based on the previous mk. lvl but rather based on mk. lvl 1. I guess that would help prevent the "exponential explosion" a straight multiplier from the previous mk. lvl brings. However, doesn't this system lead to diminishing returns every time you go up the tech tree?

[keith.lamothe]

However, doesn't this system lead to diminishing returns every time you go up the tech tree?

Yes, though significantly slower diminishing than it used to be when stats were typically going up at sub-linear rates.

In general it moderately encourages a "wide" tech strategy over a "deep" one, but this is counterbalanced by the different ship types being, well, different.  Getting MkII fighters might represent a much higher raw dps boost than getting MkIII bombers, but there are tons of things where you don't need raw dps, you need bombers (or stuff with similar bonuses).

Also, the MkIII tech unlocks the MkIV variants too, for when you have an advanced factory, etc.  And going from 2 => (3 + 4) is quite a bit better than going from 1 => 2.  Assuming you have mkIV capability, of course.  And then there's the other weight on the scale of the super-linear increase in m+c cost.

[TechSY730]

Cool, sounds like it's working as you guys want it to. I'm pretty happy with this balance too, but I just wanted to know the math behind it. Thanks.

[Wingflier]

You also have to consider that many times in AI War (especially with the new Eye changes) less = more, and having more firepower packed into less cap can really help the player.

In addition, while higher Marks may have a lower cap, there are many situations that their increased survivability will actually lead to them having a higher sustained DPS, than that of the larger, but less durable, lower MK fleets, which can die quickly to AoE and/or mass target attacks.  That's my experience anyway.

[Rainbow]

In fact, 1 mk 4 ship is better than 4 mk1 ships(that sustained DPS thing), and will actually be able to take out 5 mk1 ships and still survive:  Explanation below, with algebra.

With attack, armour, and health all scaling linearly, the short answer is that a mk n ship will fight evenly with (sqrt(1+8n²) - 1)/2 mk 1 ships, and that a mk n ship will fight evenly with sqrt(1 + 8(n/m)²)2 mk m ships.  To see this, take a mk n ship vs x mk 1 ships:  Armour can be assumed to be zero, and attack and health both 1(dps) at mk 1.  When the first mk1 ship dies, the mk n ship will have taken x/n damage.  At the second death, the mk n ship will have taken (x-1)/n more.  So, to take out the mk n ships, you need (1+2+...+x)/n to be at least n.  This gives the equation x(x+1)/2n = n, or x² + x -2n² = 0, and by the quadratic formula, x = (sqrt(8n^2 + 1)-1)/2, and this generalizes to the mk n vs mk m case.

The +1 actually doesn't make all that much difference at the numbers we are talking about(even mk 5 vs mk 4), and so it's almost the same as 1.4n/m - 1/2.

If you are defeating the enemy piecemeal it gets even better, as a mk n ship can take out n² mk1 ships if it gets to fight them one at a time.

Since this is my first post, hopefully I haven't embarrassed myself too much by making silly errors here.  Also, I really like this game, as can be seen by the effort to calculate this out.  Well done.

[Suzera]

It is still important to unlock higher mk ships for the focused firepower effect, regardless of the scaling.

Mk 4 ships also cost as much as 8 mk 1 ships if I recall correctly, so mk 4 ships are a lot more of an economy drag than losing mk 1 for players. The AI obviously doesn't care at all since their higher mk ships scale much more favorably in economy cost. A mk 4 for the AI costs as much as 3 mk 1s or so. I'm doing a lot of things right now or I'd go get more concrete information.

That's one of the big reasons that high AIP is a lot harder than low AIP, and the late game is harder than the middle, defensively at least.

[BobTheJanitor]

Since this is my first post, hopefully I haven't embarrassed myself too much by making silly errors here.  Also, I really like this game, as can be seen by the effort to calculate this out.  Well done.

Now that is what I call a first post. Don't worry about embarrassing yourself. Worry instead about embarrassing the rest of us newbies whose first posts tend to be more like "HAY GUYS THESE GAEM IS FUN!"