Hi folks,

I've seen some threads looking at average dmg for rebel weapons ( @Deadwolf did some great stuff here) to compare and contrast.

Just wondering if anyone has crunched the numbers to look at average Imperial damage, per figure, incorporating abilities, surge potential, etc. and accounting for defence dice.

Would be useful info in terms of making choices by accounting for avg damage to threat ratio, damage to health ratio, damage to speed ratio...

This is an amazing calculator for generating a damage frequency graph:

http://mattyellen.github.io/imperial-assault-calculator/

but lacks a single, average damage number that can then be compared between figures.

(E.g. stormies do 1.5 dmg per figure on average, vs probe droid at 3 dmg per figure)

If it hasn't been done, I might take it on, but I'd need some math tutoring on how to come up with a proper formula for calculating weighted means using frequency data.

This is how I *think* the math would work:

If a blue die has an 83% chance of at least 1 damage, and a 33% chance of 2 damage, the weighted average would be:

((.83x1)+(.33x2))/(.83+.33) = 1.28

Can any math types weigh in (so to speak) to let me know if I'm right?

Cheers!

No that's wrong. For blue dice:

1. 1xSurge
2. 1xDamage
3. 2xDamage
4. 1xSurge + 1xDamage
5. 2xDamage
6. 1xDamage

You have average damage:

1/6 * 0 + 3/6 * 1 + 2/6 * 2 = 1.167 damage

Average surge:

4/6 * 0 + 2/6 * 1 = 0.333 surge

So in general, if you indicate with P(D = x) the probability of 'D' (damage) being equal to 'x' then:

P(D = x) = number of faces with 'x' damage on it / number of faces in a die

Hence mean value of D (aka E(D)) is:

E(D) = sum(i * P(D = i), i=0...n) = 0 * P(D = 0) + 1 * P(D = 1) + 2 * P(D = 2) + ... + n * P(D = n)

Check this out: http://jeffliu.com/iadice/

The IA calculator you mentioned calculates the Cumulative Distribution Function (CDF), you need to use the Probability Distribution Function (PDF) instead.

2 hours ago, Golan Trevize said:

Check this out: http://jeffliu.com/iadice/

Thanks for the feedback! Clearly my career in mathematics was doomed.

Would there be a way to use this calculator to find an average damage number with ability and surge potential included (e.g., +1 dmg, ~: +1 pierce, etc. )? Essentially the same functionality as the matty ellen CDF calculator, but distilled to a single number?

5 hours ago, TeethAlmighty said:

Thanks for the feedback! Clearly my career in mathematics was doomed.

Would there be a way to use this calculator to find an average damage number with ability and surge potential included (e.g., +1 dmg, ~: +1 pierce, etc. )? Essentially the same functionality as the matty ellen CDF calculator, but distilled to a single number?

I was creating a simulator for that. I didn't have time to ultimate it. Ideally you could give the attacker and defender profile and plot the chart. In example you could get Han vs Vader or Han vs Riot and see how well it performs. Problem was the handling of priorities of abilities. I had to implement a sort of AI to make the "best" choice of abilities.

24 minutes ago, Golan Trevize said:

I was creating a simulator for that. I didn't have time to ultimate it. Ideally you could give the attacker and defender profile and plot the chart. In example you could get Han vs Vader or Han vs Riot and see how well it performs. Problem was the handling of priorities of abilities. I had to implement a sort of AI to make the "best" choice of abilities.

Amazing! When you say attacker and defender profile, do you mean from the matty ellen CDF simulator or from the other tool you mentioned?

I could certainly generate some data if that would help.

1 hour ago, TeethAlmighty said:

Amazing! When you say attacker and defender profile, do you mean from the matty ellen CDF simulator or from the other tool you mentioned?

I could certainly generate some data if that would help.

I think those tools are using combinatorial calculus for calculating CDF. In my case because of the complexity of choices I had to use a Monte Carlo method. It was simulating a high number of rolls and related choices, it was like having Han attacking Vader for real and 2 players choosing what to do with abilities of attacker and defender. Rolling, let's say, 5000 attacks you could get a clear idea of the average outcome, although I understand that a more accurate and rigorous way is to look at confidence intervals.

The problem is because of the nature of the dice, as well as things like pierce, using simple averages is not particularly accurate (it is with starter weapons but less so as you go on).

I did make a chart a long time ago using averages a long time ago and I basically got chewed out by people.

Which is why I went the route of comparing the line graphs for weapons. And it does give you a more accurate look at what the weapon will do.

I did make a simplistic damage analysis of imperial troops on the spreadsheet in the link. This is not 100% accurate, only considers average, and has a lot of other assumptions. its primary purpose was to create an imperial deployment efficiency list to help quantify which units are more effective.

https://docs.google.com/spreadsheets/d/1JaO1MVllj1R83ys9uHDo9qG-RR5XdaXi3fxLpGlWC-E/edit?usp=sharing

The imperial efficiency analysis is still in a draft state and is not polished.

On 29/03/2018 at 5:43 PM, Golan Trevize said:

I think those tools are using combinatorial calculus for calculating CDF. In my case because of the complexity of choices I had to use a Monte Carlo method. It was simulating a high number of rolls and related choices, it was like having Han attacking Vader for real and 2 players choosing what to do with abilities of attacker and defender. Rolling, let's say, 5000 attacks you could get a clear idea of the average outcome, although I understand that a more accurate and rigorous way is to look at confidence intervals.

Whoah. Sounds like a lot of work. Would love to see what you have so far!

On 30/03/2018 at 6:59 PM, Deadwolf said:

The problem is because of the nature of the dice, as well as things like pierce, using simple averages is not particularly accurate (it is with starter weapons but less so as you go on).

Very true. Hard to hit on a solution to give you a single numerical value. Especially, as @Golan Trevize noted above, the vast number of possibilities that go into each dice rolling event...

On 30/03/2018 at 6:59 PM, Deadwolf said:

I did make a chart a long time ago using averages a long time ago and I basically got chewed out by people.

Well, you can't please all the people all the time ?

On 30/03/2018 at 6:59 PM, Deadwolf said:

Which is why I went the route of comparing the line graphs for weapons. And it does give you a more accurate look at what the weapon will do.

Yes, line graphs are most accurate. Just a bit cumbersome you are comparing multiple units and trying to draw conclusions based on threat value, etc ?

I thought of just comparing values based on an 80% cutoff. E.g., this unit will do at least this much damage to this type of hero 80% of the time. Would give conservative estimates, but at least somewhat comparable...

4 hours ago, kyo55082 said:

I did make a simplistic damage analysis of imperial troops on the spreadsheet in the link. This is not 100% accurate, only considers average, and has a lot of other assumptions. its primary purpose was to create an imperial deployment efficiency list to help quantify which units are more effective.

https://docs.google.com/spreadsheets/d/1JaO1MVllj1R83ys9uHDo9qG-RR5XdaXi3fxLpGlWC-E/edit?usp=sharing

The imperial efficiency analysis is still in a draft state and is not polished.

Intriguing! I saw your chart in another thread and didn't realize you did imperials! Exactly what I'm looking for. What did you base your damage averages on?

the damage average is based on a normal attack with no imperial class cards against a single defense dice.

it is based on the entire squad attacking (not just a single unit)

I am currently factoring in rolling too much surge (a common imperial problem)

Additionally, I am factoring in their own surge abilities which I am making some assumptions on. stun = 4 damage, bleed = 3.66 damage, pierce 2 = 1.5 damage.

keep in mind my math is not perfect and I am making a lot of assumptions but I think it gives a decent idea for what units are more efficient. I need to work on it some more because a few units are funny like hired guns...

3 hours ago, TeethAlmighty said:

Whoah. Sounds like a lot of work. Would love to see what you have so far!

Too rough I'll need some work to make the code usable by others and perhaps let people contribute. At some stage I'll make it available. Have faith!