Musings on damage reduction skills - Avernum 5

[Brocktree]

I've always wondered whether it was worth unlocking Resistance. I suspected that it was probably wasn't.

 

To confirm my suspicions, I calculated the damage reduction per skill point invested for each level of luck, hardiness, and resistance up to 20 points. This (should) help guide us on where to invest a PC's skill points to obtain the best return in damage resistance. Note that the following is a table, simply copy and paste it into Excel to fix up the formatting.

 

Code:

Level		Luck	Hardiness	Resistance				1		0.25	2	0.62		0.25	2	0.63		0.2	1	0.54		0.2	1	0.55		0.17	0.67	0.436		0.17	0.67	0.437		0.14	0.5	0.388		0.14	0.5	0.389		0.13	0.4	0.3310		0.13	0.4	0.3311		0.11	0.33	0.312		0.11	0.33	0.313		0.1	0.29	0.2714		0.1	0.29	0.2715		0.09	0.25	0.2516		0.09	0.25	0.2517		0.08	0.22	0.2318		0.08	0.22	0.2319		0.08	0.2	0.2120		0.08	0.2	0.21

 

 

According to the values above, you would receive the greatest damage reduction for the least amount of skill points if you begin to invest in resistance once you have 6 levels of hardiness. Likewise, you should start investing in luck once you have obtained 14 levels of hardiness and resistance. You would then proceed by increasing the level of the skill which has the highest damage reduction per skill point value at the time. Sounds simple, right?

 

No, it's not. Indeed, those values are misleading, because:

 

1. You need to sink a lot of skill points into Dexterity to open up Resistance. I'm ignoring the skills points pumped into endurance, since you'd expect that investment for any sort of meat shield, independent of damage reduction. I'll also ignore it for the sake of simplicity, as it alters acid and poison resistance.

 

2. More importantly, armour resistance is multiplicative instead of additive. This detracts from the damage bonus provided by successive layers of armour. For example, let's say you have 10 points of hardiness (20% damage reduction). You then invest in 5 points of resistance. A casual glance would have you think that you would gain a 15% damage reduction from this investment. But in practice, you only receive 80 * 15% = 12% damage reduction. That really complicates predictions!

 

In case you don't follow, here is the table for damage reduction per skill point for resistance and luck, where the values have been modified to take the 20% damage reduction from hardiness into consideration (note: copy/paste these values in Excel):

% damage reduction per skill point

Level Hardiness Resistance (modified for 80% damage remaining) Luck (modified for 80% damage remaining)

 

Code:

1	2	0.48	0.22	2	0.48	0.23	1	0.4	0.164	1	0.4	0.165	0.67	0.34	0.136	0.67	0.34	0.137	0.5	0.3	0.118	0.5	0.3	0.119	0.4	0.27	0.110	0.4	0.27	0.111	0.33	0.24	0.0912	0.33	0.24	0.0913	0.29	0.22	0.0814	0.29	0.22	0.0815	0.25	0.2	0.0716	0.25	0.2	0.0717	0.22	0.18	0.0718	0.22	0.18	0.0719	0.2	0.17	0.0620	0.2	0.17	0.06

 

As you can see, we have a paradox of sorts. As you continue investing in hardiness, you get diminishing returns on it. This should be a driving force for you to unlock resistance, so that you can gain damage resistance at a lower skill point cost. However, due to the multiplicate nature of Avernum 5's armour system, you also get diminishing returns on *resistance* and *luck* as you increase hardiness (and vice versa). This is directly related to the observation that many players have made, regarding the fact that it is better to have one thick layer of armour, rather than several layers of moderate strength armour, due to the multiplicative mathematics.

 

It's almost as if you are railroaded into blowing all your points in hardiness (or resistance) to obtain appreciable damage reduction! By dividing your points between the two, you actually aren't optomising your skill point allocation! Furthermore, you will *never break even* with luck in a normal game, where you are limited to 200 skill points. It will always be better for you to add another point in hardiness/resistance, rather than luck, no matter how high your hardiness value is.

 

Finally, let's answer the original question: When should you start investing in Resistance. Let's assume you have 200 points to invest in damage reduction (I'm being generous). By investing solely in hardiness, you obtain a 54% damage reduction.

 

If you choose to open up resistance, you are left with 149 points left to distribute between hardiness, resistance and luck. With optimal distribution between hardiness and resistance (6 in hardiness, 16 in resistance), you obtain... 54.24% damage reduction.

 

That's a difference of 0.24%. Wow. So if you decide to open up resistance, you may end up with an extra +0.24% resistance to cold/energy/fire (debatable, as you will likely have many other layers of armour). But then remember that hardiness provides a bonus to armour, whereas resistance does not.

 

So the answer to the question "When should I unlock Resistance" is NEVER!

[Aoslare]

Interesting analysis, although I think your final conclusion has been generally assumed, it is nice to see it done out.

 

What game are you talking about? I assume not A6, where Luck is substantially cheaper. I'm guessing A5, but you should specify, since these things are different in different games.

 

Also, I tried to help with the formatting. if you truncate your repeating and irrational decimals, your tables will look much nicer.

[Brocktree]

Originally Posted By: CRISIS on INFINITE SLARTIES

Interesting analysis, although I think your final conclusion has been generally assumed, it is nice to see it done out.

In what sense has my final conclusion been assumed? It arose out of a lot of number crunching in Excel, where I allocated 200 skill points to Luck/Resistance/Hardiness to reach the highest damage resistance value. The tables I generated are an attempt to explain the mechanics of why you won't come out ahead if you unlock resistance.

Granted, some of my premises are a little shaky. You could argue that you spend more than 51 skill points unlocking resistance, although this would further support my conclusion that it is not bothering with resistance. Likewise, nobody in their right mind would drop 200 skill points on damage reduction skills. But again, if anything, this supports my conclusion.

Then there is the little problem that when you open up resistance, you are highly likely to have several layers of armour, further mitigating the skill's benefit.

Ergo: I gave the Resistance skill the benefit of the doubt by:

1. Assuming you only need to waste 51 skill points to unlock it.

2. Assuming that you only had 20% in damage reduction before investing in it.

3. Assuming that you had 200 skills points to invest in damage reduction

and even with such generosity in my thought experiment, you don't even break even by unlocking the skill.

Quote:

What game are you talking about? I assume not A6,

Avernum 5, sorry. Although you can apply similiar principles to Avernum 6.

Quote:

I'm guessing A5, but you should specify, since these things are different in different games.

Yeah, that's a good idea

Quote:

Also, I tried to help with the formatting. if you truncate your repeating and irrational decimals, your tables will look much nicer.

Thanks for that. I'll fix that up tonight.

[Lilith]

Originally Posted By: Brocktree

In what sense has my final conclusion been assumed?

In the sense that the standard advice on Resistance has been "Resistance is overpriced and a pain to unlock; don't use it".

[Harehunter]

"We are Borg. Resistance is futile."

 

Sorry, I just can't help myself.

[Brocktree]

Originally Posted By: Lilith

Originally Posted By: Brocktree

In what sense has my final conclusion been assumed?

In the sense that the standard advice on Resistance has been "Resistance is overpriced and a pain to unlock; don't use it".

Oh, whew. I thought I'd made some sort of basic error which invalidated all that number crunching.

[Lilith]

Yes. To clarify, we were the ones doing the assuming, not you. You just showed that we assumed correctly.

[Brocktree]

Ahh, so I would be correct in assuming that I was wrong to assume that you were assuming that I was making assumptions? Cool.

[Aoslare]

It's true