A bombard question for the mathematically inclined

[korn469]

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

[Theseus]

Also, what determines the number of hp hits that a successful bombard will inflict?

[alexman]

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.

[Theseus]

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?

[alexman]

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.

[steven8r]

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

[alexman]

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.

[Arrian]

This is why artillery is such an improvement from cannon. Double the range, double the rate of fire, increased bombard strength.

-Arrian

[steven8r]

Thanks for the info.

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