CSA Gun-Battery Effectiveness

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grompix
Posts: 28
Joined: Sun Jun 04, 2017 10:18 am

CSA Gun-Battery Effectiveness

Post by grompix » Sun Oct 27, 2019 8:44 am

We had another very enjoyable 'Pickett's Charge' game at our club yesterday. During the proceedings, a question came up which none of us could satisfactorily answer: -
The Artillery Fire Casualty Table has 4 gun (ostensibly CSA) batteries of guns picked out in red as they have a lower performance compared to 6 gun batteries. This is fine but - the red penalty ONLY occurs twice (on the 7 and the 9 score columns) and not right across the table (or at least on more score columns).
The question is why the 4 gun battery in the rules appears not that much more ineffective than a 6 gun battery - given that it has 1/3 fewer guns?
We couldn't quite get our combined heads around the logic of it (but I know DB will have an answer for this) ;)
Are we missing something?
Any answers/reasoning/comments much appreciated.
Cheers
Chris :D

Tony TRT
Posts: 19
Joined: Sat Jul 13, 2019 10:04 am
Location: Rickmansworth, Hertfordshire, UK

Re: CSA Gun-Battery Effectiveness

Post by Tony TRT » Thu Oct 31, 2019 6:25 pm

Hi Chris,
OK, this is my two-penny worth.

If you look at the artillery firing tables I think the biggest potential disruption on there is the Elephant Test. In this respect the six-gun batteries really outgun the four-gun batteries.

At Close range the six-gun batteries have a 58.34% chance of scoring an Elephant Test versus 41.67% for the four-gun batteries.
At Effective and Long Range, the six-gun batteries are at 27.78% versus 16.67% for the four-gun batteries.

Even a Standard regiment with no casualties has a 27.78% chance of being whipped or routed and a 13.89% chance of being unformed by an Elephant Test and these percentages rise when the regiment has sustained casualties.

In casualties (therefore ignoring any Elephant Tests) the six-gun batteries have advantages where there are high percentages of rolling that number. So….

At Close range a six -gun battery has a 27.78% chance of inflicting four or five casualties versus 16.67% for a four-gun battery. In addition, a six-gun battery of 12pdr smooth-bores firing canister also gets an extra 2 casualty dice versus one for a four-gun battery.

At effective range it’s the 1.5 casualty on a die roll of seven that makes the difference. This could be either a one or two depending upon a subsequent throw for which there is a 50/50 chance of it being rounded up or down.

As a two the six-gun battery has a 58.34% chance of inflicting two or more casualties versus 41.67% for a four-gun battery.

At long range a six-gun battery has a 58.34% chance of inflicting one or more casualties versus 41.67% for a four-gun battery. And the four-gun battery has a 41.67% chance of inflicting half of a casualty versus 25% for a six-gun battery. The subsequent roll for the half casualty may of course round the half up to one or down to zero.

Does all of this make up the difference between a six-gun and four-gun battery? Well, roll the dice and we’ll find out.

Tony

grompix
Posts: 28
Joined: Sun Jun 04, 2017 10:18 am

Re: CSA Gun-Battery Effectiveness

Post by grompix » Sat Nov 02, 2019 11:20 am

Hi Tony
Yes, of course I had totally forgotten about the increased odds of getting 7s, on a double dice roll, with other numbers declining in statistical proportion - duuhh!
Thank you for taking the time to put it all down so eloquently. The locations of the 4-gun slots in the firing tables do indeed make a lot more sense.
And I had missed the important placements of the Elephant Tests too!
Much obliged to you again.
Many thanks.
Chris ;)

Tony TRT
Posts: 19
Joined: Sat Jul 13, 2019 10:04 am
Location: Rickmansworth, Hertfordshire, UK

Re: CSA Gun-Battery Effectiveness

Post by Tony TRT » Sun Nov 03, 2019 5:31 pm

You are welcome Chris, it was a good question to ask.
Its not immediately obvious whats going in the table, now I think I need more confederate guns :)
Tony

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