Wednesday, 6 November 2019

Numbers, numbers and even more numbers...

Bang on gunner! I reckon 47.5% chance of a hit after mods for stabilisation!
I have been enjoying posts by top boffin Phil Dutre on his blog Wargame Mechanics. Not being a prof, and having missed negative binomial distribution in school (I forgot my PE kit, honest), I have to take the posts very slowly. Nevertheless, there is some great stuff here.

One of the issues with many relatively simple mechanics is figuring out the parameters, what sort of results spread do I really want? This is the case for any rules where there is a roll to hit and the target is destroyed after an appropriate number of hits. Phil examines this issue in detail in his July post "1 hit for 10 damage, or 10 hits for 1 damage each?".

I strongly recommend you read his post, which has graphs and lots of squiggly equations. However, I have simplified the core of his presentation down to this:

1. What is the hit probability? You are shooting at a target and you hit on a score of 4, 5 or 6 on one d6. This gives 3 possible successes from 6 possible outcomes so 50% probability. 

Note that if this was a d8 and the same hit number is used (4 or more) the probability of success is 62.5% (5 successful possible outcomes out of 8 possible outcomes). There is great potential for using different types of dice.

2. How many hits can the target can take before destruction? Let's say 4 points of damage.

3. How much damage is caused by one hit? Keep it simple and say one point of damage per hit.

So how do we calculate the number of shots that are required to kill the target?

Shots to kill = target damage points/(hit probability x damage per hit)

In this scenario the shots to kill = 4/(3/6 x 1)

Therefore shots to kill = 4/0.5 = 8

This is easy peasie and you can set up an excel spreadsheet to work out the range of results with different parameters. 

The more tricky issues to consider are the likely number of units shooting at the same target in one turn, the number of units and the number of turns in the game. This allows you to consider what sort of attrition rates you need to have a decent and exciting game in a useful number of turns.

Lessons here are don't forget your kit when doing posh maths, don't drink beer and do hard sums and sometimes doing some proper maths rather than endless play testing will help with design decisions. I have, of course, learnt none of these but am continuing to aim to be a better person!

Edit: Many thanks to everyone for helping me with my maths homework. Hopefully this is now correct!


Kaptain Kobold said...

"You are shooting at a target and you hit on a score 3 or more on one d6. This is 3/6 or 50% probability."

3 or more is 4/6 or 66.67% probability :)

3 or less is 50%. Or 4 or more.

I remembered my PE kit :-D

david in suffolk said...

Err.. 3 or more on D6, isn't that 3,4,5 or 6 to hit? Isn't that 4/6, or 66%? Or have I got confused? The mechanics blog looks great, anyway, thanks!

Duc de Gobin said...

The analysis does remind me of some of the calcs in 'Dunn Kempf' and 'Contact' - both written by US and Canadian officers (respectively) during the Cold War, and their interpretation of the madness that was WRG. They subsumed hit probabilities into percentages rather than a daft list of unreadable modifiers - which I guess, shows the difference between Army (probability driven) and wargamers (d6+mods driven).

Great to see this developing on your blog though

Silkin_Way said...

Sorry, I think something is wrong here. If you hit with 3 or less on D6 (i.e. with 1, 2 or 3) then the probabilities are as you say. However if you hit with 3 or more on D6 (i.e. 3,4,5 or 6) then your chance of success is 4/6 or about 66.7% Your chance of succeeding with D8 is better, not worse, since you succeed with 3,4,5,6,7 or 8, so 6/8 = 3/4 = 75% . It just shows how careful you need to be if you start playing with probabilities

Andrew Freeman

Old Trousers said...

Hi all,

Many thanks for your helpful comments (and for not taking the mickey). I should take my own advice and avoid drinking and using a calculator! The post is now corrected. I should add that it is typical that the Kaptain didn't forget his kit!

Thank you Duc for mentioning Dunn Kempf, I'm pondering how far down I can crunch the die rolling into % chances without making the game less exciting.