Hit Points and Firepower

[DaveV]

quote: Originally posted by Edward on 04-20-2001 04:01 PM DaveV, I think I understand your unmodified attack and defense strengths. They seem to be just the debeest method and seem to include every factor I can think of. How are you getting your "modified" defense strengths?

The stronger unit, the defender in all my examples, receives a bonus equal to the difference between the units' unmodified strengths. So the modified strength for the phalanx is 6.75 + (6.75-6) = 7.5. Modified strength for the pikemen is 10.125 + (10.125-6) = 14.25.

[airdrik]

I am using that complicated sumn(comb) formula of marquis' and go those results. As for who is closer, the results I got were: vet elephant vs. vet fort phalanx (6:6.75), phalanx wins about 72%. For vet elephant vs. vet fort pike (6:10.125), pikeman wins about 98.5%! And for vet elephant vs. non-vet fort musketeer (6:6.75 w/2hp), musketeer wins about 99.5%! So my general rule of thumb would be to just don't attack cities on high defencive terrain with elephants.

[Marquis de Sodaq]

Debeest, your formula will usually give an accurate indication of which unit will win the battle, but is terribly inaccurate about the odds. If what you want to know is: "Will my unit win, yes or no?," it works fine. If you want to know the likelihood, it falls short.

DaveV's formula resembles the true odds calculation for each combat round, but not for the total battle. As such, it also reflects the likely winner, and tends more strongly in the direction of the odds.

The maddeningly complex looking formula is actually workable with a calculator, it just takes a large amount of key punching to finish. What is great about it is that it stands up to playtesting, time and again. A good bonus is that it also accounts for wounded units.

I will soon include in the Combat thread MarkoPolo's example comparing artillery and armor versus riflemen. First I'll try to put together either an Excel spreadsheet or a VB macro to do the number crunching (I've contacted Eggman about getting his, but have not yet heard back). If that is successful, I'll take the time to make an actual combat odds matrix. Like a multiplication table, but civ units in place of numbers. Then nobody will need to think at all, they can just peek at the odds posted next to their Oedo year list...

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"There is no fortress impregnable to an ass laden with gold."
-Philip of Macedon

[Edward]

IMHO, debeest's formula works well enough to be a rough heuristic to use during game play. Anything more complicated than his formula would be too much for my little brain to handle an the fly!

Is it possible for that SUMn(COMB) thing to reduce to something more understandable if you assume the units are ancient (10 hitpoints, 1 firepower, default to the most common situation - both units at full health). It'd be neat if there were a heuristic that said For ancient units, your strength is roughly (modified combat value)^1.5 or some such thing. Maybe it'd reduce to a chart: For modified combat values of 2 to 3 add .5 to estimate the "real" strength. For modified combat values of 3.25 to 6 add 1 ...

[SlowThinker]

quote: Originally posted by Marquis de Sodaq If what you want to know is: "Will my unit win, yes or no?," it works fine.

I don't agree. See my example a warrior with 10HP attacks a vet warrior with 6HP. here (posted April 19, 2001 18:43)

quote: DaveV's formula resembles the true odds calculation for each combat round, but not for the total battle.

DaveV's method gives the stronger unit (or army) precisely IMHO. If the outcome is close, then you have to estimate the chance to win.

In other words, the SUMn(COMB)formula is needed for practical purposes only if the outcome of DaveV's method is close.
But a simple table for the SUMn(COMB)formula would be useful (for example with ah and dh united.
[This message has been edited by SlowThinker (edited April 21, 2001).]

[debeest]

"Debeest, your formula will usually give an accurate indication of which unit will win the battle, but is terribly inaccurate about the odds. If what you want to know is: "Will my unit win, yes or no?," it works fine. If you want to know the likelihood, it falls short."

Yes, that's exactly what I'm saying. If you just want to know which unit is stronger, my formula is quick, easy, and functionally accurate; if you want to know the odds precisely, you have to do complicated statistics. Have I not stated emphatically enough that the relative strength of the units is not the same as their relative frequency of winning a battle? The stronger unit has a disproportionately greater likelihood of winning the battle, because multiple rounds reduce the effects of random variation. Therefore, for practical purposes, I will choose to fight battles where I have any substantial edge (say, 3:2, where I might win 90%), and avoid battles where I have any disadvantage or even a very small advantage (say, 8:7, where I would lose nearly half). How often would I really need to know the precise odds?

My formula does'nt take into account the tie-goes-to-the-defense advantage, and that does seem to matter more than I had thought. I wonder if multiplying the defender's strength by 9/7 would balance that?

"A good bonus is that it also accounts for wounded units."

My formula can also account for wounded units. Just plug in an estimate of the unit's remaining % strength as a multiplier for its HP. So simple.

[SlowThinker]

quote: Originally posted by debeest I wonder if multiplying the defender's strength by 9/7 would balance that?

No. It would work for two warriors only.
For example 5 vs. 5 must be adjusted do 5+1/8 vs. 4+7/8

Sorry , I must repeat my disagreement. I will aim attention to your former post here:

quote: Originally posted by debeest, posted April 19, 2001 01:49 For example, horsemen attacking warriors will, on average, lose 1/2 of their strength.

In fact, the horsemen will lose 1/3 of strength.

Formerly, I thought same things as you. See http://www.apolyton.net/forums/Forum1/HTML/001761.html , my post dated January 27, 2001 06:12, and the following debate.
[This message has been edited by SlowThinker (edited April 21, 2001).]
[This message has been edited by SlowThinker (edited April 23, 2001).]

[debeest]

ST, I think your last post should read "5 1/8 vs. 4 7/8," right? That makes sense to me, and what it means is that the tie-to-the-defender advantage is pretty significant for low-strength units but shrinks dramatically for stronger units. So, with really flimsy units you need to pay attention to the attacker/defender distinction; with units that you'd actually choose to go into battle with, the distinction becomes minor. Right?

DaveV, I can't see how you derived your formula. As a representation of the likelihood of winning the BATTLE, it seems fairly good, but I don't see the specific logic behind it. Is it calculated based on theoretical calculation, or is it estimated based on observation?

I note that several people in this thread have identified the pikeman-versus-mounted bonus as 1.5, whereas someone else gave it as 2, which is what the Civilopedia says and what I've always assumed to be true. (I almost never build them, so I haven't had much opportunity to evaluate their strength.) (I tried cheat-testing by giving all the units 10-fold HP, and reached the conclusion that the bonus didn't actually exist at all; then I realized that it only applied against 1-HP units. The perils of modifying any condition at all....) Is the Civilopedia wrong on the 2-fold pikemen bonus, as it is on so many other points?

[DaveV]

quote: Originally posted by debeest on 04-23-2001 02:35 AM DaveV, I can't see how you derived your formula. As a representation of the likelihood of winning the BATTLE, it seems fairly good, but I don't see the specific logic behind it. Is it calculated based on theoretical calculation, or is it estimated based on observation?

I didn't derive it; I'm indebted to Xin Yu, who pointed it out and convinced me of its validity. The stronger unit bonus is mathematically based on the battle odds formula, not just an empirical estimate.

quote: I note that several people in this thread have identified the pikeman-versus-mounted bonus as 1.5, whereas someone else gave it as 2, which is what the Civilopedia says and what I've always assumed to be true. (I almost never build them, so I haven't had much opportunity to evaluate their strength.) (I tried cheat-testing by giving all the units 10-fold HP, and reached the conclusion that the bonus didn't actually exist at all; then I realized that it only applied against 1-HP units. The perils of modifying any condition at all....) Is the Civilopedia wrong on the 2-fold pikemen bonus, as it is on so many other points?

Extensive testing (not by me) indicates that 1.5 is the correct number. It's worth noting that the MISC.TXT file seems to have the latest information and lists the pikeman bonus as 50%.

[SlowThinker]

quote: Originally posted by debeest ST, I think your last post should read "5 1/8 vs. 4 7/8," right? That makes sense to me, and what it means is that the tie-to-the-defender advantage is pretty significant for low-strength units but shrinks dramatically for stronger units. So, with really flimsy units you need to pay attention to the attacker/defender distinction; with units that you'd actually choose to go into battle with, the distinction becomes minor. Right?

Right.

quote: DaveV, I can't see how you derived your formula. As a representation of the likelihood of winning the BATTLE, it seems fairly good, but I don't see the specific logic behind it. Is it calculated based on theoretical calculation, or is it estimated based on observation?

Again (sorry, Ming, I borrowed it): see link in the post dated April 21, 2001 16:57 here. DaveV converted me to the right faith there.

quote: Originally posted by Edward Your goal of making a cheat sheet for combat odds is laudable. However, when I considered making one for just full strength ancient units, I found that once you include terrain, vet ,etc. modifiers there are 250 or so possible attack and defend strength combinations! And this was after dropping duplicates.

I agree. And DaveV's (or Xin Yu's) mathematics is easy although everybody is afraid of it.
(Marquis, see my last sentence in the post from April 21, 2001 08:21 )

[Edward]

debeest,

It was I who repeated the misinformation that pikemen get a x2 bonus against mounted units. The Civilopedia is obviously AI propaganda intended to confuse humans.


Marquis de Sodaq,

Your goal of making a cheat sheet for combat odds is laudable. However, when I considered making one for just full strength ancient units, I found that once you include terrain, vet ,etc. modifiers there are 250 or so possible attack and defend strength combinations! And this was after dropping duplicates.

You may need to just give highlights where attack/defense strengths are close. (No one's too concerned about a battleship attacking a phalanx, but a catapult attacking a musketeer is interesting).

[debeest]

Jeez. Is there anything Xin Yu DOESN'T know about this game? Xin Yu, you should consider giving up Civ in favor of biotechnology or agricultural management or international relations or something; the world needs you even more than we do.

Now, can anybody explain to me HOW Xin Yu's formula is derived? My statistics are just strong enough to have a rough understanding of the combinatorials formula in the Great Library, but I don't see the connection.

[SlowThinker]

debeest,

quote: Originally posted by debeest Now, can anybody explain to me HOW Xin Yu's formula is derived? My statistics are just strong enough to have a rough understanding of the combinatorials formula in the Great Library, but I don't see the connection.

The key is "two dices (number of sides depends on the combat strength) and defender wins ties". Then you can derive formulas yourself.

But you can read "Modifiers for Attack-Defense" (see my previous posts here for the link). I think it is explained there.

[debeest]

I've read the relevant posts, and within the limits of my modest training in statistics, I think I understand them. But I don't understand how the combinatorials formula translates into Xin Yu's/DaveV's simple formula. I'd love to be educated on this, but if no one wants to be bothered I'll just shut up about it.

One more thing: what kind of testing did someone do to verify the formula?

[SlowThinker]

quote: Originally posted by debeest on 04-25-2001 04:24 PM I've read the relevant posts, and within the limits of my modest training in statistics, I think I understand them. But I don't understand how the combinatorials formula translates into Xin Yu's/DaveV's simple formula. I'd love to be educated on this, but if no one wants to be bothered I'll just shut up about it.

Which part of my post (posted January 29, 2001 19:03) in
Modifiers for Attack/Defense is not lucid?