Avadon 1: How do skill effects actually work?

[Rabenrecht]

I'm not a math genius, but I'm also not an idiot having a degree in computer science and being a programmer and all that.

But I can't figure out how skill effects are actually calculated.

 

In some RPGs there is no transparency of effects of character abilities, skills etc.

But in Avadon the skills suggest that their effects are communicated to the user. But when you raise one skill during level up the observed effects don't seem to line up with what the skill is advertising. Or maybe the skill effects are described in a very unintuitive way.

 

For instance:

 

The shadowwalkers Earth Discipline: according to the description each point should raise your magic and "elemental" resistance ("elemental" probably refering to fire and cold, maybe poioson and acid). At level 7 you should get 10% per level of poison, acid and mental resistance.

At level up I have 4 points in Earth Discipline with 2 points specialization. When I raise Earth Discipline to 5 points I excpect the following things to happen:

- fire resistance +4%

- cold resistance +4%

I wonder if the following things happen:

- acid resistance +4% OR +70% OR +74%

- poison resistance +4% OR +70% OR +74%

- mental resistance +70%

 

I wonder about those because:

- I'm not sure if acid is considered "elemental"

- I'm not sure if poison is considered "elemental"

- I'm not sure of bonus skill levels by specialization count towards the thresholds

 

What does actually happen? None of the above!

- fire resistance +3%

- cold resistance +3%

- poison resistance +7%

- acid resistance +7%

- mental resistance +10%

 

 

From that I suspect the following things:

- that the threshold effects of skills don't count all the skill ranks but should read as "from now on, for every skill point above (threshold - 1) you get +x% to y"

- even though the descriptions claim a linear relationship between skill ranks and effects, the actual function produces some kind of diminishing returns.

 

Spoiler

I don't like this. If you don't want to give precise information about skill effects then just write skill descriptions like "Increases elemental resistance for each level". If you DO want to give precise information, then actually BE precise.

 

Description that give detailed information but is ambiguous or just wrong is the worst of both worlds.

 

Any insights on the actual skill effects?

[TriRodent]

I'm going to personally duck your specific questions... (as there are a couple of people around here who 'really' get into the #s & will probably be along relatively shortly)

 

Did you look in the Strategy Centrals (stickied at the top of the forum)?  There are generally discussions on if 'this' skill is better than 'that' one which tend to dig into the #s you are looking for (you may also want to look in the Strategy Centrals for Avernum & Geneforge forums as Jeff/Spiderweb tends to do those sort of calculations across all the games.

 

The typical greeting for a new member is "Welcome to the forums (which I will certainly convey to you), please leave your sanity at the door (this part I have a problem with as anyone who wants to dig that deeply into the #s is probably lacking in the sanity department & has none to drop off... 😛 )".  Anyway, welcome.  I hope that you're able to dig out/get pointed in the right direction for the info you're seeking.

[Ess-Eschas]

Hello Rabenrecht,

 

First off, welcome to the forums! It’s always good to see people who are interested in looking into the numerical detail of the game mechanics!

 

The descriptions of the skill effects in Avadon 1 can be a little ambiguous at times. From what you’re written here, I think you’re slightly misinterpreting these descriptions, particularly when looking at how probabilities are being applied. I like to point out what I think the problem is, and let you know what I think is going on under the game’s hood.

 

First off, let’s look at the in-game description of the example you’ve given, Earth Discipline:

 

“Gives 4%/level resistance to magical and elemental attacks.

 

At level 3:

 

Adds 5%/level resistance to physical damage.

 

At level 7:

 

Adds 10%/level resistance to mental, poison and acid attacks.”

 

I think the critical issue here is in how the probabilities stack. I appreciate that the wording here is ‘Adds x%/level’, so that might imply that the probabilities are being combined by adding them together. However, I think this is just an unfortunate choice of wording. I think ‘Add’ in this case simply means ‘increases’.

 

While of course there are exceptions, generally speaking in RPGs and other games, probabilities combine in a multiplicative way, rather than in an additive way. So, probabilities are combined by multiplying them together, rather than just taking the sum. The effect of this is to produce diminishing returns for each additional probability stuck on to the combination – as you yourself noted!

 

This might seem unfair, but there’s a very good, practical reason for making this choice. If you simply add probabilities together, eventually you get to the point where you have more than 100% probability of some skill or resistance. And that doesn’t make any sense! By contrast, multiplicative probabilities only ever tend towards 100%. They never exceed it, so the maths all remains within plausible bounds.

 

To go into this in a little more detail, let’s look at the 4% increases. In an additive model, which you’ve been assuming, the probabilities combine like this:

 

Total Additive Resistance = 4% + 4% + 4% + 4% + ...

 

In a multiplicative model, it’s a little more complicated. Instead, we need to think about the chance of an attack hitting, which is (100-4)% = 0.96. In this case, the total resistance is calculated like this:

 

Total Multiplicative Resistance = 100%*(1 – (1 * 0.96 * 0.96 * 0.96 * 0.96 * ...))

 

If you’re monitoring this by looking at the resistances displayed in the game, you’re going to be looking at how much the probabilities are added to after each level, even if the effect is actually due to multiplication. The effect of the multiplication is to slightly lower the effective amount by which probability is added for each successive level. So, for example, the effective amounts you’ll see for the first few levels are:

 

Level 1: 4.00%
Level 2: 3.84%
Level 3: 3.69%
Level 4: 3.54%
Level 5: 3.40%

 

By level 5, the effective additive probability increase, rounded to the nearest percent, is 3%. And that’s what you’re seeing!

 

On your second point, I think this is just an issue of a slight disagreement with the wording. You’ll see that the phrasing says that the 10% increases are added "At level 7". While it’s not explicitly stated, I think the implication here is that the increases happen only for points at level 7 or higher. After all, points accrued up to level 6 don’t meet this criterion, so the implication is that points from the first 6 levels don’t count.

 

If you don’t like that reasoning, consider the situation from a balance perspective. If reaching level 7 suddenly gave you 10% increases for all the points you currently had, that would be a vast increase compared to all other level changes. Level 7 would give you a flat increase of about 52% (remember, the probabilities multiply), compared to level 8, which would only give you an effective increase of about 5%. Subsequent levels would give you even less than this.

 

This sort of spike is a huge imbalance in the effectiveness of the skill allocation. It invalidates most of the skill allocation in favour of a single level which, given that this single level is so much more important than all the others, effectively limits the choices a player can sensibly make. So it’s bad game design! I hope you’ll find that Spiderweb games are better written than that!

 

To summarise, the behaviour you’re seeing is what’s being indicated by the skill description, I think – it’s just been presented in a slightly ambiguous way. Firstly, the probabilities are being multiplied together, rather than being added together. As a general rule, it’s always best to assume multiplicative probabilities in a situation like this. It tends to be a more common approach. Secondly, those additional increases are only being added for the level at which the increase is unlocked, and for all subsequent levels – but not any earlier levels that have already been accrued.

 

I appreciate I’ve gone into some detail here, so do by all means ask for clarification if anything I’ve written is confusing! Also, to echo TriRodent, a good place to seek information about the numerical aspects of these games are the posts linked in the Strategy Central threads. Pay particular attention to posts by Slarty (currently posting under @"Nothing Left"), whose analyses of the numerical details of these games are second to none!

 

Otherwise, all the best for the rest of your time working for the Black Fortress! :)

[Slawbug]

Those aren't actually probabilities, those are reduction percentages.

[Ess-Eschas]

Ah, of course. Sorry for using slightly misleading terminology of my own, too!

 

Just to clarify, the example we’re looking at here looks at how much damage is reduced from different sources, rather than a particular probability. I tend to think of these in similar terms to probabilities, since all the mathematics is the same, but of course they’re not actually the same thing.

 

However, because the mathematics is the same, my analysis still holds – and it applies equally well to other examples where probabilities are being stacked, rather than resistances. After all, it makes just as little sense to have greater than 100% damage reduction as it does to have greater than 100% probability! Because of this, games like these tend to combine both resistances and probabilities in a multiplicative way. The importance of the distinction between additive and multiplicative combinations still applies.

 

So, sorry for slightly confusing the issue with my poor choice of words!

[Slawbug]

Don't want to beat this to death, but Ess, the mathematics isn't the same.  Running two percentile factors in sequence results in a single outcome.  Running two probabilities in sequence results in multiple outcomes.  Depending on what the probabilities are measuring, there may be a mean outcome that is equivalent to multiplying two percentile factors together -- or there may not be.

 

I think you're also not quite right about greater than 100% damage reduction.  PC damage reduction is capped at 90%, but Spiderweb games, like many RPGs, store this internally a percentile modifier to damage taken, and use a negative number (the equivalent of over 100%, as you're discussing it) when an entity is healed rather than damaged by a particular type of attack.

 

Additionally, reading through your longer explanation more fully, you're flatly incorrect about how the game handles these reductions.  Reductions from a single instance of an effect are added together and applied as one.  Thus if a passive skill grants +4% resistance per level, and you have 5 levels in it, you do not multiply by 0.96 five times -- you multiply by 0.8 once.

[Ess-Eschas]

2 hours ago, "Nothing Left" said:

Don't want to beat this to death ...

 

Of course. I am a little worried that we’re talking slightly at cross-purposes here, though, and that this might be slightly muddying the waters when it comes to Rabenrecht’s query. I’d like to return to the main drive of that query, if I may. Rabenrecht has, very helpfully, given us an example with figures taken from the game. I’m hoping we can use those figures to determine which of our two explanations is more plausible!

 

Here’s the example as I understand it. Do correct me if I get anything wrong, Rabenrecht! Rabenrecht is looking at a situation where they are increasing Earth Discipline from level 6 to level 7. The resistance percentages are displayed on the character statistics page, and Rabenrecht is taking the difference of the level 7 value and the level 6 value. The differences Rabenrecht records are:

 

Fire and cold: 3%
Poison and acid: 7%
Mental: 10%

 

Now, you say:

 

2 hours ago, "Nothing Left" said:

Reductions from a single instance of an effect are added together and applied as one.  Thus if a passive skill grants +4% resistance per level, and you have 5 levels in it, you do not multiply by 0.96 five times -- you multiply by 0.8 once.

 

If I am understanding you correctly, you are saying that all resistances are applied in an additive way. So, referring to my quotation of the in-game description above, this should mean that the differences are the very percentages referred to in the description. In other words, you seem to be proposing that the increases should be these:

 

Fire and cold: 4%
Poison and acid: 10%
Mental: 10%

 

I am proposing that the resistances are being combined in a multiplicative fashion. Going through the maths of this gives my predications as:

 

Fire and cold: -(1-0.04)^7+(1-0.04)^(7-1) = 3.1%
Poison and acid: -(1-0.04)^6*(1-0.10)+(1-0.04)^6 = 7.8%
Mental: 1-(1-0.1)^1 = 10%

 

Without any further information, my figures seem to match Rabenrecht’s much more closely than yours. If one assumes that Avadon always rounds resistance percentages down, then my figures match exactly. Doesn’t that imply that my model matches the game's behaviour in this case? Or I am I doing something stupid in my maths, or going wonky in my interpretation? And if I am wrong, how do you explain the figures that Rabenrecht is recording here?

 

Let me just make a brief aside about those probabilities. I think the issue here has arisen because I wasn’t very clear on my terminology. When I was referring to probabilities 'stacking', I wasn’t referring to a combination of two individual events, each with distinct probabilities. I was referring to a probability of a single event, where the probability of a given outcome was being modified by an additional factor.

 

In other words, I’m not talking about rolling two dice. I’m talking about, for want of a better metaphor, fusing two dice together to make a super die.

 

If the probability of an outcome is modified in this way, then it makes sense for it to be done in a multiplicative way. That’s what I was thinking of. Now, I’ll certainly grant that’s not often done in games, and I suspect it's not how probabilities are combined in Avadon – so I’ll scratch that part about games tending to combine probabilities in a multiplicative way!

[Slawbug]

3 hours ago, Ess-Eschas said:

If I am understanding you correctly, you are saying that all resistances are applied in an additive way.

 

No.  You are not understanding me even remotely correctly.  Please point to where I said anything remotely resembling that.  I used narrowing qualifiers, and you chose to replace them with the word "all."  Ess... seriously... I love you, but you're in wacko-land here.

 

What I said is: "Reductions from a single instance of an effect are added together and applied as one.  Thus if a passive skill grants +4% resistance per level, and you have 5 levels in it, you do not multiply by 0.96 five times -- you multiply by 0.8 once."

 

If you have 5 levels in a skill that gives 4%/level fire resistance, and are wearing a shield that gives 10% fire resistance, your final damage taken will be 80% * 90% = 72%.  Not 96% * 96% * 96% * 96% * 96% * 90% = 73.4%

 

You are attempting to extrapolate a contradictory conclusion by starting with the already-rounded game output, which includes already-stacked reduction from a particular skill, then looking at what the new rounded output is after investing an additional point in that skill.  Given the small percentages being dealt with, the rounding kind of removes the possibility of concluding anything at all from that.

 

3 hours ago, Ess-Eschas said:

Let me just make a brief aside about those probabilities. I think the issue here has arisen because I wasn’t very clear on my terminology. When I was referring to probabilities 'stacking', I wasn’t referring to a combination of two individual events, each with distinct probabilities. I was referring to a probability of a single event, where the probability of a given outcome was being modified by an additional factor.

 

OK, you used "probabilities" plural to refer to one probability plus an additional factor which has no probability attached to it at all.  The issue isn't that you were being unclear, you just literally said something different from what you meant.

 

3 hours ago, Ess-Eschas said:

If the probability of an outcome is modified in this way, then it makes sense for it to be done in a multiplicative way. That’s what I was thinking of. Now, I’ll certainly grant that’s not often done in games, and I suspect it's not how probabilities are combined in Avadon – so I’ll scratch that part about games tending to combine probabilities in a multiplicative way!

 

Um, this is done all the time in games?  You make one roll.  Then you make another roll.  Voila, the two probabilities have effectively been combined by multiplication.

[Rabenrecht]

Ess-Eschas and Nothing-Left, thank you for your discussion :-)

 

I think now I understand how resistances work and stack with each other. That really helps evaluating items for my characters :-)

 

Than, of course, I do  think the item descriptions are wrong or at least misleading: take the fire resistance shield. The effect is to provide an instance of 10% fire resistance. But he description would read "+10% fire resistance" and that is NOT the same. The + implies that the shield would increase your fire resistance by 10%. But the actual increase in fire resistance is anything from 10% to 0%.

 

I would challenge the notion that this is common way if doing things in games. From the top of my head I can't think of any RPG (other then Avernum where I guess all of the above is true as well) that treats resistance effects as isolated instances instead of adding them together. If you put on the Red Dragon Scale Armor (+50% fire resistance) and a Ring of Fire Resistance (+40% fire resistance) in Baldurs Gate, your character has 90% fire resistance. If you then cast a spell that provides 25% fire resistance, you will have 115% fire resistance and actually heal from fire damage.

[Randomizer]

In the oldest Spiderweb games, resistances were shown as additive. In original Nethergate for example it was possible to stack so you couldn't get hit.

 

Starting with Avernum 4 this was explicitly changed to multiplicative calculation for resistance. Also resistances got capped so you couldn't avoid any damage since some items gave total immunity to a damage type.

[Slawbug]

I think both ways are quite common, both for resistances and for armor.  First off, almost any game that doesn't have a dedicated resistance stat is going to handle it multiplicatively -- resistance is simply going to be implemented as an individual check for each thing that could provide it.

 

There are also games that don't handle resistance percentages directly at all.  Diablo II had sort of a hybrid system, where resistance "points" were added together, and then converted to a single percentage with diminishing returns.  In practice, this ends up working a lot like Spiderweb's.

 

And of course, there are games where resistance simply doesn't stack at all, such as D&D these days, and most games based on its systems.  This is common, too.

 

1 minute ago, Randomizer said:

In the oldest Spiderweb games, resistances were shown as additive. In original Nethergate for example it was possible to stack so you couldn't get hit.

 

Starting with Avernum 4 this was explicitly changed to multiplicative calculation for resistance. Also resistances got capped so you couldn't avoid any damage since some items gave total immunity to a damage type.

 

Actually, in the oldest games -- the Exiles -- resistance percentage effects were so rare that they weren't displayed, but if you managed to get multiple sets equipped (from rings typically), the impact was indeed multiplicative.

 

Nethergate and A1-3 did things differently.  However, the shift back to multiplicative calculation actually happened prior to A4 -- but the display wasn't updated until A4.  In particular, G1-3 showed additive numbers on the character sheet but operated via multiplication when applied.

[Randomizer]

I did state were shown and not how they worked, because of Jeff's comments when he clarified them for Avernum 4.

 

[Triumph]

Ess fell victim to one of the classic blunders, the most famous of which is "Never get involved in a land war in Asia," but only slightly less well known is this: "Never go in against a Slarty when math is on the line."

[Ess-Eschas]

16 hours ago, Rabenrecht said:

Ess-Eschas and Nothing-Left, thank you for your discussion :-)

 

I think now I understand how resistances work and stack with each other. That really helps evaluating items for my characters :-)

 

Great! I’m pleased that we’ve helped you come to a greater understanding of how these systems work in Avadon, despite some of the confusion that has arisen in this discussion!

 

I think the takeaway message from this is that systems involving combining percentages in RPGs, be it through resistance calculations or other effects, are not always implemented in a completely straightforward way. If a game says that raising a statistic will increase some property by x%, that doesn’t necessarily mean that the net result will be a flat x% increase! The actual difference in percentage might vary due to all sorts of factors.

 

This can get quite complicated, and can sometimes lead to some confusion about what is going on – as you’ve seen in this thread!

 

So, for the example you’ve given, the issue is not how the percentages from Earth Discipline are applied. These percentages are indeed being added together, rather than being multiplied. I was certainly wrong about that and, amusingly, the maths conspired to make my assumption look correct for your case!

 

The issue you’re experiencing here is that some items, or perhaps some other stat effects, are also causing your resistance percentages to change. These additional changes are interfering with the increases caused by Earth Discipline, making the effective increases seem a little less than advertised.

 

If you were to remove all of your equipment and skills providing you with resistance boosts, and then do your experiment again, you’d see that the percentages being added are indeed as described. I did that experiment myself, too, just as a sanity check.

 

So, as you progress through the rest of the game, just remember that some of the resistance increases you gain from now on might not always be as much as you might initially expect – and be prepared to start hitting the resistance caps at high percentages!

 

In any case, do enjoy the rest of your time with Avadon, and do by all means ask if you have any more questions!

 

6 hours ago, Triumph said:

Ess fell victim to one of the classic blunders, the most famous of which is "Never get involved in a land war in Asia," but only slightly less well known is this: "Never go in against a Slarty when math is on the line."

 

By no means, although I appreciate the wit. This is a simple mathematical issue with a clear correct answer. All I was doing was asking for some clarification when Slarty said that I was mistaken, and Slarty’s response cleared everything up. In a situation like this, it’s pretty clear who’s right, and I just wanted to get to the truth of the matter – I certainly don’t mind being wrong!

 

So, I wasn’t combating Slarty here – just asking for their opinion!

 

Now, if you’ll excuse me, it’s probably getting just cold enough to start that land war in Asia I’ve always been planning ...

 

*The slith fires up Civilisation 1*