Rebalancing Civ4: RtR Mod

[SevenSpirits]

Just to note, that's because the combat system generally applies situational modifiers (anything besides Combat) to the opposite unit. That 75% applies to the cav's big 15 base strength rather than to the elephant's modest 8. Formation is important for the cavalry because the 25% cancels against some of that 75% that's trying to subtract from the cav's strength.

This is not quite true. Because the relevant number is the ratio between the unit strengths, your reason doesn't make sense. The actual reason is the same reason National Epic is less effective if you're Philosophical - the bonuses are additive.

Take a normal War Elephant (8, +50%) vs a Cav (15). A naive person would think that this is a 12 vs 15 battle. Someone who knows the Civ IV combat system would say it is actually a 8 vs (15/1.5) battle. But those two situations are actually identical, as the strength ratios are identical. Dividing one strength by 1.5 is the same as multiplying the other by 1.5!

But now say this Cav magically got Formation (+25%). Now, a naive observer would calculate the strength ratio as follows:
(8 * 1.5) / (15 * 1.25)
which is the same as
(Original Ratio) * 1.5 / 1.25
which is
(OR) * 1.2

But the way Civ IV actually works, you add the percents together. And you get:
The net modifier is -25%.
8 / (15 / 1.25)
which is the same as
(Original Ratio) * 1.25

As you can see, the system works in favor of the participant with the greater situational percent modifier, if both participants have one.

In practice this is easiest to see with units where one has a higher base strength, but the other has a higher percent modifier and mysteriously has odds, when you'd expect the other unit to have odds. But the base strength has nothing to do with it.

[T-hawk]

You're absolutely right, of course. I basically meant what you said but didn't say it well. From the point of view of the elephant, the cavalry's base strength is high, and to the cavalry the elephant looks small. Which is a really convoluted way of saying the strength ratio.

And what I meant for situational modifiers is the practical outcome. 8 + 50% is better than 10 + 20% for exactly the reasons you describe even though both should equal 12. Why is it better? Because the first 20% of the first unit's bonus cancels out additively against the 20% of the second unit's bonus, instead of modifying the first unit's smaller base strength. 20% of 8 equals 20% of 10, against any sensible rules of mathematics. So it's as if the first 20% of the first unit's bonus is applied to the opposite unit instead. In practice, this effect happens to most modifiers possessed by an attacking unit, since the defending unit most often has higher total percentage modifiers. (This does fall down somewhat for the case of these mounted units, which don't get most defensive modifiers, although a few can exist like river and amphibious penalties.)

[SevenSpirits]

Because the first 20% of the first unit's bonus cancels out additively against the 20% of the second unit's bonus, instead of modifying the first unit's smaller base strength. 20% of 8 equals 20% of 10, against any sensible rules of mathematics. So it's as if the first 20% of the first unit's bonus is applied to the opposite unit instead.

Hmm, I'm still not sure if you understand this right. The unit size is completely tangential. Some background data:

1) A unit with strength A, attacking a unit with strength B, results in a strength ratio A/B.
2) A unit with strength A and % bonus x, attacking a unit with strength B, results in a strength ratio of A/B * (1+x).
3) A unit with strength A, attacking a unit with strength B and % bonus y, results in a strength ratio of A/B / (1+y).
4) A unit with strength A and % bonus x, attacking a unit with strength B and % bonus y, results in
i. If x > y:
* a strength ratio of A/B * (1+x-y).
ii. If y > x:
* a strength ratio of A/B / (1+y-x).

--------------------

The difference between situations 1 and 2 (i.e. the normal case) is that the attacker gains a % bonus x, and this multiplies the strength ratio by (1+x)

--------------------

The difference between situations 3 and 4i is that the attacker gains a % bonux x (which is greater than the defender bonus y), and this multiplies the strength ratio by (1+x-y)*(1+y) = (1 + y + x + xy - yy)

The attacker's % bonus x is more effective here than in the normal case. Proof:
(1 + y + x + xy - yy) > (1 + y + x + xy - xy) [since x > y] > (1 + y + x) > (1 + x)

--------------------

The difference between situations 3 and 4ii is that the attacker gains a % bonus x (which is less than the defender bonus y), and this multiplies the strength ratio by (1+y)/(1+y-x)

The attacker's % bonus x is less effective here than in the normal case. Proof:

(1+y)/(1+y-x) ?= (1 + x)
(1+y) ?= (1 + x) * (1+y-x) [1+y-x is definitely positive, so multiplying will not change the relation.]
1 + y ?= 1 + x + y + xy - xx
0 ?= x + xy - xx
0 < x + xy - xx [x is positive and xy - xx is also positive]

So (1+y)/(1+y-x) < (1 + x)

--------------------

Conclusion:
If you have a % bonus vs a larger % bonus, yours is less effective than normal.
If you have a % bonus vs a smaller % bonus, yours is more effective than normal.
In no case does the strength of the unit matter. It is solely about which unit has the larger % bonus; that unit gets more value out of it.

[Liquidated]

Well seeing as this thread is moving fast, my comment from uh x pages back might have gotten lost.

Am I the only one who would like to see State Property 'nerfed'?

Like the 3+ commerce change for financial btw, one of the best (and boring to play) traits in Civ4.


Cheers!
-Liq

[Cyneheard]

I think Corporations come first. Once we've figured out whether or not something should be done about corporations, and what that should be, then we'll have a better sense of what State Property should provide.

[Ruff_Hi]

re - corporations ... can we make them national wonders? If so, then I have been thinking about how to set them up ... something like ...

• all available at the same tech (corporations?)
  
• require a GP (as per standard)
  
• reduce their benefits
  
• no cost to spread
  
• reduce their dividend and their cost (not sure on this)
  
• only 1 corporation per civ
  

[antisocialmunky]

I like making a national wonder that requires a GP. However it would get confusing wouldn't it especially when the corps go transnational...

IIRC, since I don't usually play with them, the main issue with corporations is that it is very easy to bankrupt the AI with them. Would it be possible to make it so other civs don't have to pay for the corporation but you still get the revenue?


I also think that the main issue the SP balance is that Free Market frankly sucks. And considering that the rise of Capitalism is what gave Europe the ability to colonize the world and that it has pretty much replaced all previous economic systems... it really should be better. Maybe it needs something like +25% gold to Markets and Banks?

[Ruff_Hi]

I was thinking that you cannot spread your own Corp to other civs. Or if you can, it effectively incorporates that Corp as the other civs Corp - so you still don't get any benefits. Naturally, if the other civ has a Corp, then no spread would be allowed.

Thinking about it - you could make it so that you couldn't spread to the other civ (else you could force a Corp on someone), rather you would have to gift your exec away and then the player would have the option to incorporate that Corp (as their 1 and only Corp) or delete the unit.

[plako]

Some thoughts about corporations.

I like the idea of national corporations. I rarely spread/accept foreign corporations unless having a tight alliance where some of the headquarter benefits flow back to me.

Corporations come quite late so they need to be quite profitable compared to founding and spreading corporations. However in current format they feel a bit too good. Headquarters with Wall street + courthouses/rathauses + free market makes most of the corporations goldwise profitable and still provide relatively easily e.g. 10 hammers. I don't know how much this should be changed. Probably minor adjustments could be enough. If spreading the corp doesn't cost gold then larger nerfing would be needed. Either yield or costs or both could be affected.

To lower the random luck factor they could be buildable instead of consuming great person.

I would prefer keeping the option of several corporations per nation.

[Cyneheard]

What about:

National Wonder (GP or not)
No gold cost to spread
No HQ bonus (I think this may be a necessary side effect of National Wonder rules UNLESS we did some serious recoding)
Maintenance can be tweaked down a little if needed. Would have to test that.

Without the HQ bonus, Corps become quite expensive.

If all of the corps only require Corporation tech, then they definitely should require a Great Person each. Otherwise Corp tech becomes way too valuable.

I know that no gold cost, no HQ, and tweaking the tech pre-reqs or maintenance can be done easily in the XML. I'm not sure if the National Wonder set-up will work bug-free, since that requires firing up an MP game with those changes.