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Tuesday, May 8, 2012

Template Weapon Mathemagic

Hi Everyone,

Stolen from Krynn72 on the FoW forums
Today's Flames of War Statistics article is a relatively straightforward one and it deals with Artillery Template Weapon Systems. I had originally drawn up some work related to both Artillery and Airplane weapons in V2, but since probabilities for air planes got so much easier (read: 1 chance to range in), I added several more options for basic Artillery.

I developed a set of equations that would calculate the probability of killing a single armoured team under a template given a set of conditions (Target Skill, Top Armor, Artillery Skill, AT, FP) over all 3 attempts to range in. While it is relatively easy to hammer out an EV for a single attempt to range in, accounting for subsequent attempts/success is more complicated.



Roughly speaking, our equation starts at:

(Chance to Range In)*(Chance to Hit)*(Chance to Pen)*(Chance to FP/Kill)
+(Chance NOT to Range in On 1st Attempt)*(Chance to Range In)*(Chance to Hit)*(Chance to Pen)*(Chance to FP/Kill)
+(Chance NOT to Range in On 1st or 2nd Attempt)*(Chance to Range In)*(Chance to Hit)*(Chance to Pen)*(Chance to FP/Kill)

And that's just for a regular artillery strike......

From there we also have re-rolls to range in on the first attempt with Mortars, re-rolls to hit with 6 or more guns, re-rolls to save for Time on Target strikes (but only if the first attempt is successful), Rocket Battery strikes, etc.

The spreadsheet I developed is pretty basic, but includes several sets of equations to cover the most common scenarios and most common weapon systems. It doesn't cover all of them, but I'll see if I can't get Steve to throw the spreadsheet into the Downloads section to make it available to everyone.

For now, here are a few selected Conditions that will, again, cover the most common scenarios. Remember, this is only set up to deal with armoured targets (although, if you get your hands on the sheet, you can probably manipulate some AT vs Top armor values to create sets for Infantry & Gun saves).

And since tables are a disaster in Blogger, you'll might have to open to image to read it depending on the resolution of your monitor.

Target: Trained, Top Armour 0


Target: Trained, Top Armour 1

Target: Trained, Top Armour 2

Target: Veteran, Top Armour 0

Target: Veteran, Top Armour 1

Target: Veteran, Top Armour 2

 (The equations create some negative values for AT 2 vs TA 2.....let's just say it's not a bright idea to bombard that target.)

Looking at these weapons systems across multiple bombardment options allows us to make better choices in list selection.

For instance, we can see that Time on Target makes Trained Artillery nearly as good as Veteran Artillery, so if we have a choice between a Veteran Cannon Platoon and a Trained 105mm Platoon, the points savings will usually make the Trained 105mm Platoon a more cost effective artillery solution.

Probabilities to kill Dug-In Infantry can actually be seen on the above chart by looking at lines where the Anti-Tank - Top Armour = 3 (Add about a % or 2 to the Time on Target section since a Tie is technically a 'failed save', and reduces the chance of the re-rolled save).

Probabilities for hitting targets via ranging in on a 5 or a 6 start to get pretty dicey (Ranging in on a 6 puts pretty much everything into single digits, not matter what the top armour is). Snag the spreadsheet once it's available and you'll see what I mean. I wouldn't recommend it until you really need that thing to die or there's no other target.


And that's all there is to it. Remember that these values are for a single team under a template. If you want probabilities for multiple targets, you can run them through the Binomial Calculator at http://stattrek.com/online-calculator/binomial.aspx or add them together for a rough Expected Value calculation.


No Homework!

4 comments:

Dirty Jon said...

Excellent article! This should help folk to set expectations for artillery -- pin, not kill.

Izimu said...

This is very helpful. It's good to know look at these numbers in advance to be able to make quick decisions during the game.

Samulus said...

If I play in a tournament I'll print these off for sure.

Smithy said...

Very helpful but you have the American time on target but what about the British mike target if they all guns repeat?

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