08-08-2002 19:55									#1
	A bombard question for the mathematically inclined Support Apolyton, buy Civilization: The Boardgame

here is the question,

what is the exact relationship of bombard strength and rate of fire to each other?

for example would a unit with 100 bombard strength and 1 RoF be equal to the following units

50 bmd str 2 RoF
25 bmd str 4 RoF
1 bmd str 100 RoF

to me it would seem like on average the total damage they inflict would be about the same, am i correct in making this observation? detailed answers are appreciated

	08-08-2002 20:12									#2
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Also, what determines the number of hp hits that a successful bombard will inflict?

	08-08-2002 20:17									#3
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I believe the expected damage from a bombard unit with strength S and against a defender with strength D is given by:

Expected HP = S / (S + D) * ROF

So in your example, versus a unit with D=10,
100 bmd str 1 RoF does 0.91 damage
50 bmd str 2 RoF does 1.66 damage
25 bmd str 4 RoF does 2.14 damage
1 bmd str 100 RoF does 9.09 damage

As you see, these numbers depend on the strength of the defender.

	08-08-2002 20:36									#4
	Support Apolyton, pre-order Civilization IV

1. How are variable results achieved?

2. Does this create a maximum damage?

Meaning, the expected HP damage for Arty bombarding a Cav is 1.6 hp... does this mean it cannot be more than 2 hp?

Another example: CM vs Spearman is 2.7... so the most it can get is 3 hp? (that's a letdown, if true)

3. Do defensive bonuses apply?

	08-08-2002 20:49									#5
	Support Apolyton, buy Galactic Civilizations

The formula above is for expected damage. It's kind of an average. It doesn't say anything about the variance of the results.

Back to the example:

The 1 ROF, 100 strength unit will attack just once. It does a 1 HP damage 91% of the time.

The 2 ROF, 50 strength unit attacks twice. It has 83% chance of taking away a HP from the defender each time. It can do 2 HP damage, 1 HP damage, or 0 HP damage. On average, it does 1.66 HP damage, although that actual number is obviously impossible.

The 100 ROF unit attacks 100 times with a 9% chance of doing damage each time. Of course this unit cannot do more damage than the HP of the defender (or one less than that if not a lethal bombard unit). On average, the defender takes about 9 HP damage, although this is based on the defender having at least 100 HP, so the number is a bit off.

Defensive bonuses do apply. I think even terrain improvements get defensive bonuses. Also, cities get extra defensive bonuses that do not apply to regular attack. Each improvement and population point adds to the defender's strength.

	09-08-2002 23:11									#6
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What does the 'Rate of Fire' mean? I've never seen any arty unit that was able to attack twice. Could you please clarify this for me?

Thanks

Last edited by steven8r on 09-08-2002 at 23:23

	09-08-2002 23:14									#7
	Avatar Enlargement: We've got the solution

quote: Originally posted by steven8r What does the 'Rate of Fire' mean?

[Edited because you edited your question ]

You don't actually see the unit attack twice. It happens automatically. Have you noticed that sometimes the defender gets more than 1 HP damage? It's because the bombard unit had ROF greater than 1 so it attacked more than once.

	10-08-2002 00:09									#8
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This is why artillery is such an improvement from cannon. Double the range, double the rate of fire, increased bombard strength.

-Arrian

	10-08-2002 01:36									#9
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Thanks for the info.

I knew artillery was better than canons, but I didn't know exactly why that was.