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Combat Explained....

Discussion in 'Civ4 Strategy Articles' started by Arathorn, Nov 4, 2005.

  1. Benford's Law

    Benford's Law Warlord

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    Thanks oyzar,

    I am not familiar with this new firepower formula. Sounds like there was a radical overhaul in combat mechanics with BTS 3.17 compared to the old Vanilla days. I'm sure DanF would know all about this, he's a super-expert to be sure...but it would be nice to see a revised combat mechanics article someday :rolleyes:

    ~Benford's Law
     
  2. Roland Johansen

    Roland Johansen Deity

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    There hasn't been a major overhaul. Just this small adjustment to the way damage is calculated (for wounded units).

    Combat is still in rounds where only one unit can inflict damage until one of them dies (or retreats). Strength values are still calculated in the same way, with promotions still effecting the strength values in the same (sometimes weird) way. First strikes still work the same and collateral damage still works the same. The various formulas have also largely remained the same. The only minor change was the fact that the damage per combat round is now based of the average between a units maximum strength and its current strength. The rest of the formulas surrounding combat have remained the same.
     
  3. Benford's Law

    Benford's Law Warlord

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    Happy Holidays Roland :)

    Yes, I did read your earlier posting and mistakenly took oyzar's confirmation of your description as a sign there had been more serious changes made to combat mechanics.

    As for that quote I pasted two postings ago, let me expand it a bit:


    Now, the formula for calculating the defender's strength (after combat promos etc.) seems a bit wacky, but I think I understand it. The only problem I have is where the author of the article claimed that if the attacker's bonus outweighs the defender's bonus, it actually makes the attacker's bonuses worth more than "face value" at some point. After looking at the above example where a shock promo might have accidentally been left out (as oyzar noted), there seems to be no way an attacker's combat bonus can match face value under any circumstances (thus, weighing combat in favor of defenders more than most players realize). Can you or anyone else figure an example where the attacker would have more of an advantage over "face value" of its combat bonus? I couldn't find any and I tried a few different combat scenarios (both where the attacker's bonuses outstrip the defender's bonuses using the above formula, or the more standard formula in cases where attacker bonuses does not outstrip the defender's).

    EDIT - It seems as though an attacker's bonuses are allowed its "face value" only when they do not exceed the defender's bonuses. When the attacker's bonuses actually exceed the defender's bonuses and the usage of the formula: defender's strength = base defender str/(1+(excess attacker bonuses over defender's/100)), the performance of the attacker's bonuses actually decline compared to "face value" once the attacker has more bonuses than the defender. It almost seems as though Civ 4 slightly penalizes the attacker for bringing a "gun to a knife fight", proverbially speaking.

    DOUBLE EDIT - "Diminishing Returns" In fact, as I review this posting I just wrote, it seems as though the more an attacker's bonuses outstrip the defender's the more of a penalty is applied. Civ seems to have made it so that adding more of a disparity of an attacker's bonuses over the defender's only seems to provide diminishing returns.

    EXAMPLE: -
    a) Ignoring all other factors attacker has 50% in bonuses where defender (strength 6) has only 25%. The defender's bonuses are outstripped by 25% and it's adjusted strength is 4.8 (using the above formula)
    b) Attacker has 75% in bonuses while the defender maintains 25%. Defender's bonuses are now outstripped by 50% yet the defender's strength is still calculated at 4.0 (only a 16.7% decrease in strength even though 25% in attacker bonuses were added). Hence it seems there are diminishing returns when the attacker piles on more bonuses in excess of the defender's. This would seem to have implications in making highly promoted units slightly less valuable overall, assuming they are not of the Combat line promos.

    ~Benford's Law
     
  4. obsolete

    obsolete Deity

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    From one of my games:




    This might seem impressive and all, but what annoys me to death, is why a badly mauled leader will still defened, despite it is dead if just hit once. Basing on strength alone for battle-decision processes is just wrong.
     
  5. Benford's Law

    Benford's Law Warlord

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    @ Obsolete - Would Solver's Better AI mod help with that situation? (Somehow I have my doubts, but I've never tried it myself)

    As for the defender/attacker bonuses affecting unit strength in weird, quirky ways....I may not be correct about the diminishing returns and such.

    This is a pretty challenging math problem (at least for little 'ol me!), and I'm still not having an easy time figuring out whether the author of this "Combat Explained" article is right about certain situations helping the attacker more than the bonuses advertise in-game.

    I have seen a fair number of examples where the defender gets a hidden bonus, and it is also interesting to note that 100% bonus differences seem to work exactly as advertised, even when the strength is taken away from the defender.

    ~Benford's Law
     
  6. Milly

    Milly Warlord

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    You are correct in that the more penalties you pile on the defender... the less strength is reduced from the defender. The formula that was given, if correct, indicates that, through simple math. If you have a graphing calculator, try graphing the formula 100/(1+x/100). You'll see that a penalty of 25% (x = 25) ends up giving you 80 (80/100 = 80%).

    Really? From what I've seen, mainly from chariots attacking lone axemen on plains, the given formula still works.
     
  7. Benford's Law

    Benford's Law Warlord

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    Milly,

    I was considering a situation such as a spearman or pikeman attacking a mounted unit that doesn't receive defensive bonuses.
    If the pike/spear has no other bonuses besides the natural 100% against mounted units, then 50% of the defender's strength would be taken away which would (on its most basic level) afford the same combat odds as leaving the mounted defender's strength the same and doubling the pike/spear's strength, instead.

    As an aside, I think some of the confusion on these formulas (at least for me) is that they create some distortions compared to simply adding the appropriate % bonuses directly on the units receiving them. I do not know how serious these distortions are, and it left me very curious as to whether it would warrant any strategic considerations in a game as a result.

    ~Benford's Law
     
  8. obsolete

    obsolete Deity

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    If someone could make a little tweak... where Leaders get put into the back-ranks when health reaches 0, and not killed, then their warlords gimmick wouldn`t be so bad. The leaders should only be lost on defense when the enemy manages to occupy the tile they are on.

    It seems they tried to emulate a lot of the hex-gamer, EiA, etc. type of feel, but totally dropped the ball when it comes to leaders.
     
  9. Roland Johansen

    Roland Johansen Deity

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    For an explanation of Arathorn's remark about combat peculiarities, I quoted him without his example because some of the values of the promotions in the example seem to be wrong. Still his idea is correct.

    First of all, note that the outcome of a battle is not determined by the absolute strength values of the combatants but by their relative strength R:

    Lets take an attacker and defender with strength 10. Then R=A/D=10/10=1.
    If the attacker gets a bonus of 30%, then you get R=10/(10/1.3)=1.3. If the defender get a bonus of 30%, then you get R=10/(10*1.3)=1/1.3 (so the defender has a 1.3 relative strength advantage).

    Now we assume the attacker has a bonus of 60% and the defender has a bonus of 30%. You might mistakenly believe that this has the same combat repercusions as an attacker with a strength of 16 attacking a defender with a strength of 13 or an R-value of 16/13= 1,23.
    This is not the case. You get an R-value of 10/(10/(1+0.6-0.3))=1.3. So the battle is comparable to an attacker of strength 13 attacking a defender of strength 10.
    This is the way that the civ combat bonusses work. They first negate eachother and then the unit with the stronger bonus gets a remainder bonus. So the attacker in this case gets a bonus of 60%-30%=30%.

    Note that combat promotions work differently. They aren't negated by other bonusses, but directly give a strength bonus to the effected unit.
     
  10. BLubmuz

    BLubmuz HoF Quattromaster

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    Time to resuscitate this thread.

    Discussing with my teammates about which units to use to take a city, it cames out that, according to BUFFY, a C2 attacker has better odds than a CR2 attacker.

    Here is 2 screenies i merged showing the odds which confirm this. My game experience doesn't. And i can affirm i'm not a newbie :)



    I can think that there's something wrong, but assuming it's correct, why do we give CR promotions whenever possible?

    In the remote case that something is wrong in the BUFFY calculations, it can be an explanation why often a CRx attacker wins at bad odds. I do not think that the people who made BAT, BUG and such is not well inside the game mechanics, but maybe a mistake?

    To note that i'm testing in a WB situation and removing the city cultural and walls defences, the odds change dramatically in favour of the CR2. Both will die in the end, but that's it.
    The solution can be in the placement of the attacker bonuses in the formula: probably you need to subtract those to the defender strenght, then add to the remaining strenght the cultural and the walls bonuses. It seems to be a simple mistake of reverse factors, like to not have used a parenthesis.
     
  11. ruff_hi

    ruff_hi Live 4ever! Or die trying

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    BUG / BUFFY doesn't change the combat system from the base game. The difference you are seeing is in the base game. As to why C2 is better in this case than CR2 ...

    The C2 promotion is a +20% addition to the attackers str - the sword is showing a str of 7.2 (6 x 1.2)
    The CR2 promotion is a -55% subtraction from the defender's str - you can see the -55% in the graphic

    The probability of survival is dependent on a bunch of things but the general rule of thumb is that your chance of winning increases depending on the ratio of attack str v defender str.

    C2 the ratio is 48.00% (7.2/15)
    CR2 the ratio is 47.06% (6 / 12.75)

    Not much difference but C2 has a better ratio and hence a better win percentage.
     
  12. BLubmuz

    BLubmuz HoF Quattromaster

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    First off, thanks for your answer!

    This is why i'm thinking the formula is wrong: IMO it must subtract the CR bonus and then add the terrain, fortification and so on bonuses to the defender.

    And my experience in game tell me that it's the way it actually works.

    I know that BUG/BUFFY doesn't change the game, what i think is that mistake someone made years ago is in the "combat odds" formula. It's just a question to move a number before others, is can happen!

    Pity there's the RNG, but i can try something with better odds to see the output.
     
  13. VoiceOfUnreason

    VoiceOfUnreason Deity

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    That will sometimes be true, yes. It's a side effect of the fact that attackers combat bonus are applied to the numerator, but the city raider bonus is applied to the denominator.

    This means that, effectively, the impact of the combat bonus is multiplicative, where the impact of the city raider bonus is additive.

    Which in turn means that if the defending units own bonuses are big enough, the multiplicative effect of a combat promotion exceeds the additive effect of the city raider bonus.

    The algebra to figure out the precise cut over point is straight forward; I won't repeat it here.

    a) Because city raider promotions are stronger in most common cases.
    b) Because melee units promote to gunpowder units, which are not eligible for city raider promotions.
     
  14. LowtherCastle

    LowtherCastle Deity

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    oops wronge thread
     

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