Defense Multipliers

[Edward]

Sieve Too,

Civ II multiplies in a random number (0 to 7?, 0 to 8?). Defenders win ties. That means that with even odds, defenders win slightly more often than the attacker. Notice that the winner was always a defending warrior with (using summing) even odds of winning. He won due to defender bias.

(Edward reads #5, where the archer's extra attack point with summing should easily overcome any 8-sided die defender bias)

Hey!!! Are you using MGE or 2.42? Double production? Were those NON warriors? (sputter sputter)

Another theory dashed by cruel reality.

Thanks, Sieve Too, for straightening me out. I think I should refrain from posting until I learn a bit more about this game.

[Sieve Too]

quote: That means that with even odds, defenders win slightly more often than the attacker.

True, but when A = D, the Defender always won. Although I didn't bother collecting final hps for the winner, the defender was usually still in the yellow.

I am using the version 2.78 of CivII, FW.

I've always planned on doing more tests but I just lack the time

[Xin Yu]

Edward: Your formula can't be correct. A vet Iconclad has 4*(1.5)*3*1=18, a non-vet pikemen (on grass unfortified) has 2. By your formula the Pikemen would win 1 out of 10 battles. No, the pikemen got no chance at all.

[geofelt]

Thanks-s2, your first test shows me that the vet attribute is not rounded.
To complicate the picture, may I suggest that both addition and multiplication are involved. I think that the vet attribute becomes intrinsic to the unit. A vet warrior attacks and defends at 1.5. I think, however that the defense values are ADDED, based on the base value(vet or non-vet) of the unit. With only one defense modifier, the question is academic, because the results will be the same. With more than one, there can be a huge difference, and I think they are additive then. I base this in part, because other types of calculations are additive. For example, a factory increases production to 1.5 times the base. The same result as adding 50% of the base or multiplying by 1.5. When you add a power plant, the actual result is 2, not 2.25. A mfg plant goes to 2.5, not 3.375. The same applies to trade and science. I think the programmers would have used a consistent technique.

[Sieve Too]

One of the reasons I ran tests #2, #3 and #4 is to completely test all the combinations when 2 of the 3 modifiers are applicable (vet, terrain, fortifying). Test #4 tries the combination of a non-vet Warrior fortifying in a forest. The results are the same as a vet unit with one other modifier.

Although I didn't state it above, besides running 20 Horsemen into 20 Warriors in tests 2, 3 and 4, I also reran tests 2, 3 and 4 but attacked with Archers. In all 20 cases, the Archer won. So since a=2 Horseman always lost but a=3 Archer always won, I concluded that the Warrior's defense must be between 2 and 3.

For test #5, I also ran 20 Legions into the 20 Warriors and the Legions always won. As such, I concluded that the Test #5 Warrior's defense must be between 3 and 4.

If, as you suggest, vet status became instrinsic to the unit as a multiplier and THEN the terrain and fortifying bonuses where added in, you'd have D = (B*V) + (B*V) * T + (B*V) * F
where
D = total defense
B = base value
V = 1.5 for vets, else 1
T = terrain bonus, 0.5 for forest, 0 for grass, etc
F = fortifying bonus, 0.5 for fortifying, 0 for no fortifications, etc

Recalculating D for tests 2, 3, 4 and 5:
#2 D = (1*1.5) + (1*1.5)*0.5 + (1*1.5)*0 = 2.25
#3 D = (1*1.5) + (1*1.5)*0 + (1*1.5)*0.5 = 2.25
#4 D = (1*1) + (1*1)*0.5 + (1*1)*0.5 = 2
#5 D = (1*1.5) + (1*1.5)*0.5 + (1*1.5)*0.5 = 3

If defense was calculated this way, then in test #4, I would not expect all 20 Horsemen to lose, but they did. This suggests the Warrior's defense was between 2 and 3 and so defense could not be calculated as above.

For test #5, I would not expect 19 Archer wins and just 1 Warrior win. The results suggest that the Warrior's defense was between 3 and 4, not 3.

[Hasdrubal]

Combat calculations:
IMO, if an attacker with an attack value of 18 attacks a defender with a defence value of 12, the AI will throw thirty papers in a hat, 18 reading 'attacker' and 12 reading 'defender'. The AI will then pull out one paper, and grant a 'win' to the one who's name is one the paper. It will then deduct the FP from the winner from the HP of the loser. (the hitpoints of both have been multiplied by ten before the battle commenced). This process is repeated until either one loses all it's hitpoints.

Testing:
The most reliable way to test battle-calculations, is not by counting how often a unit will win over an other, but by checking the 'damage to hitpoints' under the cheat menu. This will give a clear indication of what damage was sustained by the victor, giving a clue as to how the battle outcome was resolved. If you set the HP of both combatants to 100, one battle outcome will have the same statistical value as 100 seperate tests with a unit which has a HP of one.

Addition or multiplication?:
I tested my question on whether combat multipliers were added up or multiplied. I used a veteran, fortified warrior on a river for this. His defensive value is one of these:
A - addition. The results are rounded down before the next multiplier is added: 1+,5+,5+,5= 1.
B - addition. The results are not rounded down before the next multiplier is added: 1+,5+,5+,5= 2,5. Or 2 if the final result is rounded down.
C - multiplication. The results are rounded down before the next multiplier is applied: 1*1,5*1,5*1,5= 1,5. Or 1 if the final result is rounded down.
D - multiplication. The results are not rounded down before the next multiplier is applied: 1*1,5*1,5*1,5= 3,375. Or 3 if the final result is rounded down.

When a non-veteran horseman attacks our well trenched-in warrior, the odds are:
A 2:1 or 66%.
B 2:2,5 or 2:2 or 44,44%/50%.
C 2:1,5 or 2:1 or 57,14%/66,66%.
D 2:3,375 or 2:3 or 37,21%/40%.
I set the HP of both to 100, and attacked ten times. The warrior won all ten battles, with an avarage sustained damage of 36,3. This means, that from the 100 attacks, the horseman won 36,3, that is 36,3%. Less than 1% off from the 37,21% that was predicted in case D. With such a slight margin, and considering that this battle calculation was made a thousand times by the AI, I think it is a safe bet to assume that defence multipliers are multiplied, that the result is not rounded down before the next multiplier is applied, and that the final result is also not rounded down. As some other people have said here before.
I'm a bit puzzled by the fact that the final result doesn't seem to get rounded down, as the manual clearly states otherwise. But then, our Civ manual doesn't have a reputation for accuracy.

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Ceterum censeo Romanem esse delendam.

[Xin Yu]

Not quite right. Actually there are 136.3 round all together and the horse won 36.3 and lost 100.

[Sieve Too]

For an (exhaustive) discussion of battle odds, check out This Apolyton page from the archives.

Mark von Wagner was nice enough to make a Visual Basic program that calculates battle odds, given unit stats that you can input. Right here is a link to his download page.

[East Street Trader]

I've been speculating lately as to whether the A1 enjoys a higher defense bonus against barbs than we do.

Anyone know the answer to that?

East Street Trader

[DaveV]

OK, here's another crack at a battle approximator:

Compare (defense+bonus)*HP*FP to (attack+bonus)*HP*FP, where bonus = defense - attack if defense >= attack. Going back to Cavebear's example (yet again), the vet musketeers have a defense of 3(base)*1.5(vet)*3(walls)=13.5; the vet pikemen have a bonus of 2(base)*1.5(pike bonus)*1.5(vet)*3(walls)=13.5. Attacking dragoons are 5*1.5(vet)=7.5. So, both the musketeers and pikemen receive a bonus of 6, for a total defense of 19.5. The musketeers have 2 HP, so their total is 39. This means it will take 2.6 dragoons to kill a musketeer, and 1.3 dragoons to kill the pikemen. I ran the attack with 10 dragoons and lost 6 (5 predicted). One of the attacking dragoons appeared to do no damage at all to the defending musketeer, so his loss may have been a quirk of the random number generator.

With respect to the bonus to the attacker when attack > defense: I don't believe it. Take the example of horsemen vs. settler: the horse has an attack of 2 vs. a defense of 1, so should get a bonus of 1 for odds of 3:1. But my experience has been that horse vs. settler is pretty much a coin flip, more like 2:1 odds (the settler has 2x as many hitpoints). I ran five attacks of horse against settlers in clear terrain; the settlers won 3 times.

EST: I think the barbs definitely don't get the attack bonus against the AIs that they do against a human player. There may also be a defensive bonus - maybe someone should run some tests?

[Sieve Too]

Hasdrubal:

quote: IMO, if an attacker with an attack value of 18 attacks a defender with a defence value of 12, the AI will throw thirty papers in a hat, 18 reading 'attacker' and 12 reading 'defender'. The AI will then pull out one paper, and grant a 'win' to the one who's name is one the paper.

Oddly enough, this is not how the winner of a single combat round is determined. Even the manual concedes that this method yields only an approximation of the actual odds. I used to think this was how it was done too but I was proven wrong.

Turns out, the computer takes the A and D values and multiplies them by some constant k (later experimentation determined k=8). The computer then gets two pseudo-random numbers, one for the attacker and one for the defender: the first number ranges from 0 to A*k-1, the second from 0 to D*k-1. The higher value wins the round and the winner's FP is subtracted from the loser's HP. Ties count as wins for the defender (This explains why you can lose an occasional round when you attack a D=0 Diplomat).

For all the gory details click here. This is the same link as I gave above.

[Hasdrubal]

Sieve Too, I regretfully overlooked your link the first time you posted it. Thanks for supplying it!
Xin Yu, you're quite right. Argghh! This brings back horrible memories of me, school and math.

[This message has been edited by Hasdrubal (edited June 15, 2000).]

[Sten Sture]

LoL! I regretfully reread that entire old post. It gave me a headache just like last time!