Combat Formula

[BomberEscort]

I did a search and couldn't find this so I will post it here for anyone who is interested...

Combat Calculation Formula

This formula will give you the probability of the attacker winning the battle with a certain number of HP remaining...

{[(A/(A+D))^dhp] * [(1 - A/(A+D))^hpl]} * [n!/(hpl! * (n-hpl)!)]

A = Attacker Strength + All Applicable Bonuses (i.e.- Radar Tower)
D = Defender Strength + All Applicable Bonuses
hpl = Hit Points the Attacker Loses [<= (Attackers Total HP -1)]
dhp = Defenders Total Hit Points (e.g. 3 for a Regular unit)
n = [(dhp - 1) + hpl]

Example: What is the probability that a veteran Tank will defeat an unfortified/unfortressed elite Spearman in Grassland, with 2HP remaining for the veteran Tank?

A = 16, D = 2.2, hpl = 2, dhp = 5, n = 6

11.5%

 

[joycem10]

there is a combat calcuator available for download. look here:

http://forums.civfanatics.com/showthread.php?s=&threadid=8068

 

[BomberEscort]

I'd don't have internet access at home though... I was looking for something like CivLackey's utility, but updated for PTW, and stand-alone.

I'll just have to write my own... :devil2:

 

[wilbill]

You might want to compare your figures with the online calculator, BomberEscort. It shows an 84% chance of the tank winning under the circumstances you set up.

 

[BomberEscort]

Originally posted by wilbill
You might want to compare your figures with the online calculator, BomberEscort. It shows an 84% chance of the tank winning under the circumstances you set up.

I wasn't testing the chances of the tank winning, I was testing the chances of the tank winning and having 2 HP left... I just wanted to post the formula for calculating the various conditions in case someone wants to design a stand-alone calculator for PTW and/or Conquests... I'm working on one for myself that includes all the PTW stuff (e.g. Radar Towers in the calculations)

 

[alexman]

Your formula is not 100% correct. You are including cases where the attacker eliminates all defender HP early, but continues fighting (against whom?) until he looses the required HP anyway.

 

[BomberEscort]

Originally posted by alexman
Your formula is not 100% correct. You are including cases where the attacker eliminates all defender HP early, but continues fighting (against whom?) until he looses the required HP anyway.

If I understand your statement, I don't think so... Could you post an example.

The above example is ONLY for a Tank that loses 2 HP in defeating a spearman with 5 HP. There are 15 ways this can happen. When the battle ends the calculation stops

There is a 98.9% chance the tank will win the battle...

Of those victories...

52.5% Tank takes no damage
31.7% Tank takes 1 HP damage
11.5% Tank takes 2 HP damage
3.2% Tank takes 3 HP damage

In all the above cases the 5 HP spearman is destoyed. The percentages above are just the likelyhood of the Tanks HP remaining after his victory... If the tank wins, one of these outcomes will happen...

 

[BomberEscort]

Originally posted by wilbill
You might want to compare your figures with the online calculator, BomberEscort. It shows an 84% chance of the tank winning under the circumstances you set up.

I got 98.9% when I used the online calculator in joycem10's post... same as what the formula at the beginning of this thread states...

 

[alexman]

Sorry, I misread your formula, which is actually correct.

(My comment would have been relevant only if you had n=dhp+hpl)

 

[wilbill]

Sorry, I didn't catch exactly what you were calculating. Makes sense now.

 

[BomberEscort]

In my continuing quest to understand the details of the Civilization combat statistics I have posted the formula to calculate Bombard statistics. It is handled differently than normal combat since it is for a limited amount of rounds (equal to the ROF) and not neccesarily to the death. The formula is below for all who are interested...

{[ A / (A + D)]^Dhpl} *
{[1 - (A / (A + D))]^(ROF - Dhpl)} *
{ ROF! / [Dhpl!*(ROF - Dhpl)!]}

Where:
A - Bombard Value of Attacker
D- Defensive value of Defender after all applicable bonuses
ROF- Rate of Fire of the Attacker
Dhpl- Hit points the defender loses (always <= ROF)

To my knowledge the online combat calculators do not calculate bombarding damage or probabilities...

 

[anarres]

BomberEscort - I recently modified TF's CombatCalc to allow your own figures in the attack/defense/terrain bonus fields (this allows it to be used for PTW and mods).

You can access it online here.

More importantly, you can download it by right-clicking the link as selecting 'Save Target As' - this will then work offline, by running it directly form your harddrive.

You can also modify it to calculate bombards (it seems you have the required maths ) - if you get around to this please let me know so I can update my online copy.

 

[alexman]

anarres, a small bug in the calculator you modified: I believe you don't get a bonus when defending against barbs.
[Edit: note to self: don't ever question anarres again!]

BomberEscort, a formula usually includes an equals sign.

 

[BomberEscort]

Originally posted by anarres
...You can also modify it to calculate bombards (it seems you have the required maths...

I'd love to, but I don't have the required programming skills... I am including these formulas for any who want to program a stand alone program (like CivLackey's). I am currently working on an Excell spreadsheet with all of this information on it. Should be finished in about a week...

 

[BomberEscort]

Originally posted by alexman
BomberEscort, a formula usually includes an equals sign.

Such a stickler, sheesh...

 

[BomberEscort]

Get your excel combat calculator here...

Combat Calculator

 

[trumpeteer]

Originally posted by alexman
anarres, a small bug in the calculator you modified: I believe you don't get a bonus when defending against barbs.

Yes you do, depending on the level. The higher the level, the less the bonus, and no bonus on Deity.

 

[alexman]

You get a bonus when attacking, but not when defending.

 

[Gengis Khan]

Gotta disagree. You get a bonus fighting barbs, hence poppin out 3 with a warrior & getting promoted to elite everytime on lower levels.

 

[alexman]

Gotta agree. I just tested it, and the barb bonus applies on defense as well. Ignore my silly comment above.