Combat stats in relation to stack defense

[SlowThinker]

First of all, read this

http://apolyton.net/forums/showthread.php?s=&postid=2337865&t=6616#post2337865

I thought about ways how to avoid defense is not accomplished by the strongest unit of a stack:

The solution is not to use HP and FP to determine unit strength. But the problem is you may want to use HP and FP to determine if unit will fight more or less predictable. This is determined by the FP/HP ratio, so you should keep unit strength (FP*HP) constant and to change FP/HP only:

an example:
you set normal units 2h, 2f
stable units 4h, 1f
'berserk' units 1h, 4f
(FP*HP is always 4)

But you must be careful since it affects pikemen flag, shore bomardment, ship caught in city and fighter vs. helicopter.

[Alinestra Covelia]

Consider the following:

I have a unit for an evil dictator and his bodyguards. I want this unit to be able to defend itself if attacked, and require a pretty good fight to go down.

BUT I don't want it to defend first if there's a stack of other defenders. Say, the dictator's hiding in a city with plenty of riflemen and a few conscript units.

So can you give me an example of the adm and fh that I should use for these units? I'd want the riflemen defending first, then the conscripts going down, and then only after a long and hard battle with picking them off, would the dictator be exposed.

(And even then, if possible, I'd like him to go down only with a tough fight.)

[Mercator]

Well, if the riflemen and conscripts are good but not too special, especially when compared to the dictator, you should give the dictator a much lower defense, but a much larger FP/HP... Let's see:

The standard Riflemen, for good measure (A/D/M, H/F):
5/4/1, 2/1

Conscripts... slightly worse defense, but the HP and FP mean they'll do twice as much damage, while taking 1.5 times longer to get killed themselves (compared to the Riflemen, that is):
6/3/1, 3/2

Dictator:
10/1/1, 6/4

Um... The defense value (together with the unit's health)is what determines who fights first. In the above case, normally, the Riflemen would fight first, then the Conscript, then the Dictator. If the last Riflemen are wounded, though, it's likely a Conscript will fight instead.
The greater the difference in defense, the more wounded one can get before the others take over.

I'm not sure though, how exactly my examples would turn out in Civ2 "reality"... If you want to test and balance the strength of those units, several people have made Excel calculators that can work out battle outcomes. You can use one of those to test the strength of these three against a few likely attackers.

I'd give you a link to those, but I can't find any right now... Oh wait, there must surely be a few links to them in the combat thread SlowThinker linked to.

[SlowThinker]

Originally posted by Mercator
Conscripts:
6/3/1, 3/2

Dictator:
10/1/1, 6/4

But this way Dictator won't be tougher in defense than Conscripts.
He is 4 times stronger than Conscripts in HP*FP statistic (24 against 6), but he is 5 times weaker if attacker has attack 3, approx. 4 times weaker if attacker has attack 6 etc.
(For more details about theoretical 'power' read this post: Combat math in practice )

So I would suggest to raise Dictator's HP and FP: but don't forget the maximum for HP is 12, and the max. for FP is...?

---

For exact probabilities try Boco's calculator, the link is in the Great Library.

[Mercator]

Originally posted by SlowThinker
But this way Dictator won't be tougher in defense than Conscripts.

Yes, I guess that just had to backfire without thorough knowledge of the whole combat math...

I don't have Excel, by the way, so unfortunately Boco's calculator is lost on me...

I tried to calculate the numbers you came with, but I got something completely different. I'll just trust you then... How does the dictator's performance change with a defense of 2? The problem with raising the Dictator's defense, though, is there is a bigger chance he'll get some action before all the other chaps are killed, right? Um... but nevermind that, you suggest increasing the HP.

The max FP is 127, since the HP max of 12 is because that number is multiplied by 10.

[Boco]

Don't have Excel! Think of it as VB with a spreadsheet attached. Given the cost of the beast, I can't blame you.

Actually this thread brings up what I think is a bug in my calculator. The meat of the calculation is performed by Excel's BINOMDIST function.

BINOMDIST(number_s, trials, probability_s, cumulative)

Number_s is the number of successes in trials.

Trials is the number of independent trials.

Probability_s is the probability of success on each trial.

Cumulative is a logical value that determines the form of the function. If cumulative is TRUE, then BINOMDIST returns the cumulative distribution function, which is the probability that there are at most number_s successes; if FALSE, it returns the probability mass function, which is the probability that there are number_s successes.

First two arguments must be integers. From the GL thread, I assigned these as [(Att_HP/Def_FP) - 1] and [(Def_HP/Att_FP) + (Att_HP/Def_FP) - 1], respectively. Since these ratios must be integers, I used the ROUNDUP function on them. All in all, it agrees with the examples in the GL.

The problem arises when you increase Def_FP relative to Att_HP. As soon as Def_FP > Att_HP, the value rounds up to 1. So additional increases in Att_HP have no benefit in the calculator. There's an analogous situation with the Def_HP:Att_FP ratio.

Does this make any sense to you, SlowThinker?

In short, the calculator works well until you try using it to predict highly unbalanced HP and FP values. Then you're on your own.

[SlowThinker]

Mercator, what is the problem with the math?

Originally posted by Boco
The problem arises when you increase Def_FP relative to Att_HP. As soon as Def_FP > Att_HP, the value rounds up to 1. So additional increases in Att_HP have no benefit in the calculator.

I suppose this is OK. If FP=9 strikes to HP=10, you need 2 hits to kill all hitpoints. If you increase FP to 10, you need 1 hit to kill all 10 hitpoints. But if you increase FP even more, you get no advantage, those 10 hitpoints are killed by 1 hit again.

...
[(Def_HP/Att_FP) + (Att_HP/Def_FP) - 1], respectively. Since these ratios must be integers, I used the ROUNDUP function on them.

You should use
[Roundup(Def_HP/Att_FP) + Roundup(Att_HP/Def_FP) - 1]
shouldn't you?

[Boco]

That logic makes sense. I was overlooking the overkill excessive fp's would give. Whether you hit a bug with a flyswatter or napalm makes little difference from its perspective.

I use ROUNDUP on each ratio before summing them and subtracting 1 (see cells D7, I7, and G18). Are you suggesting summing first then rounding up?

Btw what modifiers are missing? I know there's no sneak attack bonus in the calculator.

[SlowThinker]

Originally posted by Boco
I use ROUNDUP on each ratio before summing them and subtracting 1 (see cells D7, I7, and G18). Are you suggesting summing first then rounding up?

No. ROUNDUP on each ratio before summing is OK.

There may be some other things (besides the sneak attack) missing - I suppose anything in the Info:Combat thread that is newer than your spreadsheet.
(Anyway Info:Combat should cover all new findings.)