How to win Deep Elves?

[damerell]

Also damerall, veryangry felid wrote

First character blocks 20% attacks and dodges 0.8*0.3=24% attacks so it blocks/dodges 44% attacks which is roughly 46% (44/30*100%-100%) improvement.

Can you not see that he has completely swopped his numbers around? For his first character, it makes no sense to claim that to be hit 24% of the time is now 44%.

No, VAF hasn't. You have made two obvious errors here; VAF is discussing the chance of not being hit, and it makes perfect sense to claim that 20% of attacks blocked plus 24% of total attacks dodged makes 44%. The first error is a fairly fundamental one - it is this that has led you to suppose VAF has swapped some numbers around, when in fact their first character had a "30% chance to dodge attacks" and indeed that makes 0.3 correct when calculating the proportion of attacks they dodge.

Of course I pointed out in my very first line that one of you is calculating the chance of being hit and one the chance of not being hit. It's a pity you didn't read that bit.

Simply put, the maths looks correct but is utter nonsense. It doesn't face basic scrutiny.

It is not. It was entirely correct, something I explained at length. It is regrettable that you are unable to comprehend that explanation, but it doesn't make it wrong; it just means you didn't comprehend it. I would say you will be unable to point out any actual error in my analysis, but if you make another howler like the one above you'll probably think you have.

In particular it passes basic scrutiny because it produces exactly the same chance of being hit as yours does, something I also pointed out. A simple challenge for you is to suggest any combination of block and dodge chance where the two methods don't produce the same answer.

[VeryAngryFelid]

If undodged attacks goes from 1% to 0.01%, that is a 10000% (hundredfold) improvement.

You have just proved that relative values are meaningless for defense. Should I get
1) 10000% improvement by having my chance to be hit go from 99.9% to 99% or
2) 50% improvement by getting AC from 30 to 45.

That's just reality.

That's just mathematics, you can create millions of terms and formulae and it all does not make anything with real world (or DCSS). You have to prove it applies to specific case.

[Berder]

You have just proved that relative values are meaningless for defense. Should I get
1) 10000% improvement by having my chance to be hit go from 99.9% to 99% or
2) 50% improvement by getting AC from 30 to 45.

If your chance to be hit goes from 99.9% to 99%, your time to live is multiplied by 99.9/99 = 100.9%. Not 10000%.

Perhaps you meant to talk about when the chance to be hit goes from 1% to 0.1%. That is a 900% improvement in time to live; you can live 1000% as long, or ten times as long. It is worth noting that this does not happen in any actual games because evasion will never give you a 1% chance to be hit. It only goes down to around 20% against mildly dangerous enemies. Therefore, your intuition about evasion can mislead you here.

But, in the theoretical situation where all damage you are receiving can be dodged or blocked, and you have the choice to to increase AC from 30 to 45 or to somehow decrease chance-to-be-hit from 1% to 0.1%, you definitely should go with the reduced chance-to-hit. It increases the length of time you can stay in combat by 10x, instead of maybe 2x with the improved armor.

[damerell]

You can't get 100% dodging chance. You also, in practice, can't get 99% dodging chance.

I'm not sure why you mention this since it is common knowledge. That does not, of course, prevent us considering these hypothetical cases to assess the validity of a metric, which is all I did.

Look at "turns you have to live": disregarding regeneration for simplicity, you can live HP/(average incoming damage per turn) turns. This has a clear in-game meaning for how long you can continue to fight.

Regeneration is not the most important thing you are disregarding. More important is that if the fight goes on long enough you will dispatch your opponent and additional turns to live against that opponent aren't relevant. The utility of additional turns to live is not linear; it is nothing like linear, so much so that even a proportionate increase isn't worth as much if you already have a lot.

Shields increase turns-to-live by a fixed percentage. If you block 30% of attacks, this increases your turns-to-live by a factor of 1/0.7, a 42% increase. This percentage increase is regardless of your current evasion chance.

And this matters a lot if I am going to die soon. It's incredibly useful if I just blocked something with my shield and as a result went from 0 turns to live to 1. If I have 100 turns to live against a given opponent, who cares if a shield makes it 142?

Of course, this is why VAF's metric is better. Blocking 30% of incoming damage is worth a lot more when there's a lot of incoming damage.

[Berder]

And this matters a lot if I am going to die soon. It's incredibly useful if I just blocked something with my shield and as a result went from 0 turns to live to 1. If I have 100 turns to live against a given opponent, who cares if a shield makes it 142?

Because then that permits you to kill more of that type of opponent. Maybe the game throws 20 monsters at you in a row. Either way, you're 42% stronger than you were before.

If you instead pour that XP into armor or EV, the result can also be described as a percentage reduction of incoming damage compared to before. It's all multiplicative: damage taken per turn = (1 - block chance) * (1 - evasion chance) * (damage per hit reduced by armor). If you decrease (1 - block chance) by 30%, this has the same effect as decreasing (1 - evasion chance) by 30%, and that has the same effect as decreasing (damage per hit reduced by armor) by 30%.

A similar thing is true for attack skill: increasing your attacking damage by 42% lets you kill 42% more monsters, same as decreasing your (1 - block chance) by 30%. Attack damage and the three defensive stats are all multiplicative to yield your final combat effectiveness.

[VeryAngryFelid]

And then we should take into account defense-ignoring attacks (smiting, torment, hellfire), SH-ignoring attacks (bolt spells), EV-ignoring attacks (fireball), AC-mitigating attacks (electro), AC-reducing attacks (corrosion), monster accuracy, monster damage, monster attack types and PC resists, density of different monsters on different floors, monster AC, monster HP, monster speed, PC spells, spells from spell library, aptitudes, available body armour items, species size etc.

TL/DR Crazy complexity

[damerell]

And this matters a lot if I am going to die soon. It's incredibly useful if I just blocked something with my shield and as a result went from 0 turns to live to 1. If I have 100 turns to live against a given opponent, who cares if a shield makes it 142?

Because then that permits you to kill more of that type of opponent. Maybe the game throws 20 monsters at you in a row. Either way, you're 42% stronger than you were before.

No, you aren't, because it only matters in the rare situations where it does throw 20 monsters at you in a row. A defence that lets you beat one monster without having to use a consumable (or piety, etc) is far more useful than an incremental improvement that lets you beat 20 in a row instead of 19.

I think the analysis you do of (for example) the relative value of AC/EV/SH is valuable, but it's not enough to deduce figures without considering what they imply. The way that a hypothetical character who dodges 99% (or 99.9%, etc) of all attacks supposedly gets exactly the same value from a shield does illustrate there is a problem with this metric.

[Plantissue]

Also damerall, veryangry felid wrote

First character blocks 20% attacks and dodges 0.8*0.3=24% attacks so it blocks/dodges 44% attacks which is roughly 46% (44/30*100%-100%) improvement.

Can you not see that he has completely swopped his numbers around? For his first character, it makes no sense to claim that to be hit 24% of the time is now 44%.

No, VAF hasn't. You have made two obvious errors here; VAF is discussing the chance of not being hit, and it makes perfect sense to claim that 20% of attacks blocked plus 24% of total attacks dodged makes 44%. The first error is a fairly fundamental one - it is this that has led you to suppose VAF has swapped some numbers around, when in fact their first character had a "30% chance to dodge attacks" and indeed that makes 0.3 correct when calculating the proportion of attacks they dodge.

Of course I pointed out in my very first line that one of you is calculating the chance of being hit and one the chance of not being hit. It's a pity you didn't read that bit.

Simply put, the maths looks correct but is utter nonsense. It doesn't face basic scrutiny.

It is not. It was entirely correct, something I explained at length. It is regrettable that you are unable to comprehend that explanation, but it doesn't make it wrong; it just means you didn't comprehend it. I would say you will be unable to point out any actual error in my analysis, but if you make another howler like the one above you'll probably think you have.

In particular it passes basic scrutiny because it produces exactly the same chance of being hit as yours does, something I also pointed out. A simple challenge for you is to suggest any combination of block and dodge chance where the two methods don't produce the same answer.

"24% attacks so it blocks/dodges 44% attacks" is just pure nonsense. It's a pity you didn't read that bit. Regrettable that you are unable to comprehend that explanation, but it doesn't make it wrong; it just means you didn't comprehend it. I would say you will be unable to point out any actual error in my analysis, but if you make another howler like the one above you'll probably think you have.

viewtopic.php?f=17&t=25605

[damerell]

"24% attacks so it blocks/dodges 44% attacks" is just pure nonsense.

Only because it is a selectively quoted sentence fragment; the complete sentence, as I've explained twice now, makes sense.

That you are reduced to a sort of "no u" approach does emphasise that you don't have any actual argument here. I've given you a very simple challenge; produce any set of block and dodge chances where VAF's calculation doesn't give the same answer as yours. You can't.

[Plantissue]

No it doesn't. It makes utterly no sense. The maths looks like it makes sense but it makes utterly no sense that to block/dodge 24% is blocking 44%

You cannot explain how it makes sense, because it makes no sense at all. You can only insult me.

You wrote: "blocks/dodges 44%" is the same statement as your "56% attacks get through" and "blocks/dodges 76%" is the same statement as your "24% attacks get through"

That is factually correct but VAF has taken the values from the second character and interposed it to the first character for no reason, but for the reason of supporting his argument. You too support that argument, even though the maths used is entirely nonsense and so you resort to insulting me. There's utterly no reason to take numbers from the second character and apply it to the first character, as they are two different characters.

I don't know why you, damerall is still continuing to arguing this. I linked the thread because you clearly missed it. In that thread VAF has ran fsim numbers (twice because he accidently made a mistake on one of the numbers!) confirming that his maths is wrong, so why argue that he is right?

What do you think are the chances that his VAF's maths make sense when his fsim contradicts himself, when it contradicts mine and berder's explanations?

[damerell]

No it doesn't. It makes utterly no sense. The maths looks like it makes sense but it makes utterly no sense that to block/dodge 24% is blocking 44%

It does, however, make sense that 24% plus 20% is 44%, which is the actual calculation involved.

When are you going to produce the block and dodge chance for which VAF's method does not produce the same answer as yours? It's still a simple challenge. It would be far less work to produce a counterexample - if one exists - than the vast screeds you are actually writing. Doing so would completely explode my argument. So, why haven't you done it?

The answer, of course, is that this counterexample doesn't exist. It doesn't exist because VAF's method produces the correct answers, something I proved above.

You wrote: "blocks/dodges 44%" is the same statement as your "56% attacks get through" and "blocks/dodges 76%" is the same statement as your "24% attacks get through"
That is factually correct but VAF has taken the values from the second character and interposed it to the first character for no reason, but for the reason of supporting his argument.

We're making some progress here. You admit my assertion that in fact VAF's method produced the same answers as yours. The next step is to recognise it produces the same answer in every case, and as such was entirely correct.

VAF did not swap any values. I am now for the third time explaining that this is simple confusion on your part. You were thinking of the chance to be hit, so you thought the use of 0.3 for the character with a 30% chance to dodge was transposed with the character with a 70% chance to dodge. It wasn't. If VAF's first character had had a 40% chance to dodge the figure would have been 0.4 and the confusion would not have arisen.

I don't know why you, damerall is still continuing to arguing this. I linked the thread because you clearly missed it. In that thread VAF has ran fsim numbers (twice because he accidently made a mistake on one of the numbers!) confirming that his maths is wrong, so why argue that he is right?

I'm arguing that VAF's mathematics in this thread are correct, which they are. The other thread is not pertinent to that question.

What do you think are the chances that his VAF's maths make sense when his fsim contradicts himself, when it contradicts mine and berder's explanations?

The chance that his maths in this thread is correct is 100%. I have proven it above, and offered you a very simple way to show that I am wrong. So, where's that counterexample? If one exists, producing it would be far simpler than all this bluster.

9897b7704c2d3b4f6408d7fb69684d74

[Siegurt]

No it doesn't. It makes utterly no sense. The maths looks like it makes sense but it makes utterly no sense that to block/dodge 24% is blocking 44%

It does, however, make sense that 24% plus 20% is 44%, which is the actual calculation involved.

The math doesn't make sense because you can't simply add evasion and block chances together and come up with a useful number, if you evade 24% of attacks, and you block 20% of attacks, then you will block 20% of the 76% that remain after you evaded 24% of them, so you will actually end up dodge/blocking 24+(76*.2) = 39.2% of all attacks, not 44%, (as you can't block an attack you've already dodged) and while the math may have been incorrect (I suspect it was originally just written in a hurry, I know VAF knows how block and dodge percentages add up, he's proven that repeatedly in other threads by doing the math correctly in them), I don't think that matters at all for anybody's point.

His FSIM does actually show that you continue to block 20% of the things that remain after you evade a percentage of them, the point in the other thread is about what that *means* not whether the math adds up correctly. The argument is that if you can only block a percentage of not-evaded things, then doesn't that mean that SH gets less valuable? Which actually comes down to what you mean by 'valuable'. Yes, shields reduce less damage in an absolute sense if you have a high evasion, but when you already have a given evasion, the percentage improvement shields give you is the same, so the only question is how does that improvement compare to the improvement you would see for doing other things (for which the fact that you've already evaded a percentage of attacks is irrelevant) since the percentage of damage that AC reduces, offense mitigates and HP reduces the risk of, are all *also* dealing with the non-dodged proportion of attacks, everything is reduced (in an absolute sense) by the exact same measure and they all stay proportionally equal in value to each-other.

[akaean]

The math doesn't make sense because you can't simply add evasion and block chances together and come up with a useful number, if you evade 24% of attacks, and you block 20% of attacks, then you will block 20% of the 76% that remain after you evaded 24% of them, so you will actually end up dodge/blocking 24+(76*.2) = 39.2% of all attacks, not 44%, (as you can't block an attack you've already dodged)

Siegurt has the right of it, and his math is spot on. Its comparable to doing the math on a six sided dice with a re-roll (as when people do math to calculate odds in table top games). The other important thing about shields as compared to EV, is that you have to calculate benefit to Experience spent. Shields is a separate skill than Dodging, and even a deep elf may gain more immediate benefit from increasing shield skill as opposed to pushing dodging levels higher for diminishing returns. Crawl at its heart is a game about stacking the odds as heavily in your favor as you can. Shields give you an extra chance to evade damage, something you want. AV gives you more predictable damage, letting you better judge how a fight is going to go.

Still this thread started as a thread about how to win Deep Elves. I think the best piece of advice I can give is to play carefully. I watch my good buddy play, and he knows what he is doing but he always plays so fast and loose it gives me anxiety. He has gotten two wins under his belt on webtiles one of which is a 15 rune game, but he struggles with casters because of his happy go lucky brute force playstyle. The easiest thing you can do to improve your performance with Casters (and any character) is to forget 'o' and 'Tab'. Explore in a way that keeps you appraised of what areas you have already cleared- so you can fall back, and avoid exploring when not fully loaded on MP. Another thing, and i am personally guilty of this- is make sure to keep a mind on how much MP you have and how much MP you need to execute an escape plan if things go south. If you are playing well you should not empty your tanks on pure offense unless you know that you can clear the enemies on screen, or are not relying on MP to quickly exit a bad situation. For example, if you have enough MP for one more cast, and you can either try to kill that Ogre with Throw Frost, or you can start retreating and save it for Swiftness to gain some distance to the Stair. Getting some stealth experience helps with this, as it lets you take frequent rests to restore your MP with a much lower chance of something interrupting you while you rest- you can always come back to that Ogre and cut him down from across the room after your MP has restored!


tl;dr Basically, don't auto explore with casters and make sure your MP is fully restored before exploring new areas.

[duvessa]

Autoexploring with casters is generally safer than autoexploring with non-casters imo.

[VeryAngryFelid]

Siegurt, I am really disappointed you missed that 24% dodged attacks is calculated as "not blocked" multiplied by "chance to dodge".
20% block chance, 30% dodge chance, that means 20% attacks are blocked and (100%-20%)*30%=24% attacks are dodged (by EV, SH failed to protect from them) and of course 20%+24%=44% attacks are either blocked or dodged because those are mutually exclusive (and were calculated as such!)

[damerell]

No it doesn't. It makes utterly no sense. The maths looks like it makes sense but it makes utterly no sense that to block/dodge 24% is blocking 44%

It does, however, make sense that 24% plus 20% is 44%, which is the actual calculation involved.

The math doesn't make sense because you can't simply add evasion and block chances together and come up with a useful number, if you evade 24% of attacks, and you block 20% of attacks, then you will block 20% of the 76% that remain after you evaded 24% of them, so you will actually end up dodge/blocking 24+(76*.2) = 39.2% of all attacks, not 44%, (as you can't block an attack you've already dodged) and while the math may have been incorrect (I suspect it was originally just written in a hurry, I know VAF knows how block and dodge percentages add up, he's proven that repeatedly in other threads by doing the math correctly in them), I don't think that matters at all for anybody's point.

The VAF-style calculation doesn't "simply add evasion and block chances together". It adds the block chance to the proportion that will be evaded if we block first. This is exactly the same as you did above, adding the supposed evasion chance to the proportion that will be blocked if we evade first. Your error here is in taking 24% as the initial dodge chance. It's not; the initial dodge chance was 30%.

(Rewritten at the realisation that Siegurt actually did a VAF-style calculation here themself).

[VeryAngryFelid]

S=0.2
E=0.3
My calculation: s + (1-s)×e.
Your calculation: 1-(1-s)×(1-e).
But funny thing is that we can simplify my calculation to s+e-s×e and your calculation to ... s+e-s×e. Good luck trying to find fsim which would show different results for those formulae

[Siegurt]

S=0.2
E=0.3
My calculation: s + (1-s)×e.
Your calculation: 1-(1-s)×(1-e).
But funny thing is that we can simplify my calculation to s+e-s×e and your calculation to ... s+e-s×e. Good luck trying to find fsim which would show different results for those formulae

Ah, I had just not read carefully enough, I didn't realize that 24% wasn't the initial evasion, but was the post-shield-block evasion, in that case, they're both the same and it doesn't matter which one you use, in that case the math was correct originally, which as I said earlier doesn't matter and has nothing to do with anyone's point.

[damerell]

Ah, I had just not read carefully enough, I didn't realize that 24% wasn't the initial evasion, but was the post-shield-block evasion, in that case, they're both the same and it doesn't matter which one you use, in that case the math was correct originally, which as I said earlier doesn't matter and has nothing to do with anyone's point.

It has quite a lot to do with my point since my point initially was that VAF got it right, with which I am glad you agree, and was the target of a completely unjustified attack by Plantissue because of Plantissue's inability to follow the arithmetic and the explanations that followed. It may be too much to hope they will now apologise.

[Plantissue]

No it doesn't make sense.

Let's compare 2 characters. One has 30% chance to dodge attacks, another has 70% chance to dodge attacks.
Now let's add a shield which blocks 20% attacks.
First character blocks 20% attacks and dodges 0.8*0.3=24% attacks so it blocks/dodges 44% attacks which is roughly 46% (44/30*100%-100%) improvement.
Second character blocks 20% attacks and dodges 0.8*0.7=56% attacks so it blocks/dodges 76% attacks which is roughly 9% (76/70*100%-100%) improvement.

Not because the numbers added/multipled taken from each other is inaccurate, but because there is utterly no reason to calculate the numbers in that manner. Neither of you can describe why you have placed the constants in such a manner. It's just simply a case of VAF and damerall mashing numbers together in a manner that makes no sense at all. If you are woking out chances of survivability it makes no sense to work out absolute percentage differences for if you imagine going from 0% to a 50% dodge rate. You have now doubled the chance to save the life. When you go from 50% dodge rate to 100% you don't double the chance to save the life, your character now cannot be hit and you now made your character invincible.



It only looks like it because there is a method where it does make sense to (1-s)×(1-e) but it makes no sense to then 1- that value from that or to s + (1-s)×e and then to divide it by e afterwards.

If you want to use (1-s)×(1-e), then it is because you are working out the new rate of being hit. You then need to divide that be the old rate of being hit which would be: (1-e), not e.

You both know you are wrong and have concentrated on the bit of maths that could be right but the next part makes no sense at all.

Damerall'ss method is [ (1-s)×(1-e) ]/ e ,but this makes no actual sense, as there is no reason to divide by e from the first part of the calculation.

It should be [ (1-s)×(1-e) ]/ (1-e) ,

VAFs apparent method is [ 1-(1-s)×(1-e) ]/ e, but this too makes no sense as there is no reason to divide by e

it should be [ 1-(1-s)×(1-e) ]/ (1-e)

You have both calculated a rate of being hit but with that in mind, the next part of the calculation bears to reasoning to the previous, as you don't seem to understand what exactly you want to calculate except a predetermined answer to confirm your intuition. Both berder and I worked it all out from first principles and came to independent conclusion on the right calculations are part of working out combat power altogether.

Spoiler: show

Actually you then have to inverse that number to obtain the actual increase in survivability but whatever. Keeping it simple.

---

VAf's fsim here:

By the way there was an error in my fsim.
It should be
82% is decreased to 55%, ... or relative 32%.
70% is decreased to 47%, ... or relative 32%.
61% is decreased to 39%, ... or relative 36%.
49% is decreased to 33%, ... or relative 32%.
38% is decreased to 25%, ... or relative 34%.
30% is decreased to 20%, ... or relative 33%.

confirms that when calculating EV and SH the relative difference should be exactly the same. (The relative increase in survivability actually about +55% not =33% because you should had taken the inverse as opposed to [100% - the chance] but whatever, since the main point is that the relative values are the same)

That the figures obtained by VAF confirms mine and berder's calculations, either means that either fsim is wrong or the random way you both have calculated the survivability rate is entrely wrong. So which is it?

Is it the fsim that is wrong, or are you both open to the idea that your calculations, which neither of you can describe why you have chucked the numbers the way you have, but I and berber can, that it must be your calculations that must be wrong?

[damerell]

No it doesn't make sense.

So when are you going to produce the counterexample, the block and dodge chance for which VAF's method gets it wrong? That would be far easier than producing this wall of text (which frankly is too incoherent to analyse if I don't have to, and I _don't_ have to because your inability to produce the counterexample says it all) - if it existed. Put up or shut up.

Note that Siegurt above acknowledges that VAF's method got it right all along.

Here are the most obvious errors in what you wrote:

Let's compare 2 characters. One has 30% chance to dodge attacks, another has 70% chance to dodge attacks.
Now let's add a shield which blocks 20% attacks.
First character blocks 20% attacks and dodges 0.8*0.3=24% attacks so it blocks/dodges 44% attacks which is roughly 46% (44/30*100%-100%) improvement.
Second character blocks 20% attacks and dodges 0.8*0.7=56% attacks so it blocks/dodges 76% attacks which is roughly 9% (76/70*100%-100%) improvement.

Not because the numbers added/multipled taken from each other is inaccurate, but because there is utterly no reason to calculate the numbers in that manner. Neither of you can describe why you have placed the constants in such a manner.

There are no constants and in my very first post I explained why this method always gives the same answers, so one reason to calculate the numbers in that manner is "it gives the right answers", something which is also demonstrated by your complete inability to show when it gives the wrong answers.

It only looks like it because there is a method where it does make sense to (1-s)×(1-e) but it makes no sense to then 1- that value from that

It does. That method calculates the odds of being hit. If you have another method (VAF's) which calculates the odds of being not hit, to compare the two you must subtract those odds from 1. I did this in the very first post, where I observed your .56 odds of being hit was the same as VAF's .44 odds of blocking or dodging. I did this by subtracting .56 from 1.

If you want to use (1-s)×(1-e), then it is because you are working out the new rate of being hit. You then need to divide that be the old rate of being hit which would be: (1-e), not e.

This is starting to be in the realm of complete incoherence, but VAF's method never did work out the rate of being hit; it worked out the rate of not being hit. It doesn't use (1-s)x(1-e).

Damerall'ss method is [ (1-s)×(1-e) ]/ e ,but this makes no actual sense, as there is no reason to divide by e from the first part of the calculation.

This is simply not true. I have never, in any calculation here, divided by the chance to evade. (Nor has this "Damerall" - it is typical of your attention to detail that you still haven't noticed how to spell my name.)

VAFs apparent method is [ 1-(1-s)×(1-e) ]/ e, but this too makes no sense as there is no reason to divide by e

This is also simply not true. At no point does VAF multiply (1-s) by (1-e). This is perhaps down to the old confusion where you thought VAF had swapped two values.

[Siegurt]

No it doesn't make sense.

So when are you going to produce the counterexample, the block and dodge chance for which VAF's method gets it wrong? That would be far easier than producing this wall of text (which frankly is too incoherent to analyse if I don't have to, and I _don't_ have to because your inability to produce the counterexample says it all) - if it existed. Put up or shut up.

Note that Siegurt above acknowledges that VAF's method got it right all along.

I acknowledge that the math is correct, in that it accurately represents the percentage of attacks that get through, which was never in debate, and still isn't. (If 30% of attacks are evaded, and 20% are blocked, no matter what order you do the math in, you end up with 44% of all attacks not reaching the player)

The actual *question* is one of terminology and what you mean when you say "an improvement in defenses" or "more or less effective". Really it comes down to whether you're paying attention to the "absolute difference" or the "relative difference" with one camp saying that what matters is the absolute difference and the other camp saying that it's the relative difference which is actually important for decision making.

One camp says "adding a 20% shield to a player who evades 30% of all attacks, only results in 14% more of all attacks being eliminated, so clearly that shield is less effective when you've got more evasion" the other camp says "No no, you're thinking about this wrong, it doesn't matter what percent of attacks you currently evade, the shield will *always* eliminate 20% of the *remaining* attacks, so the shield is always be the same 20% improvement in your defenses, no matter where they are now"

Both statements are technically and mathematically correct, but the former one gives the misleading impression that it's a smaller net reduction in risk to add a shield when you have high evasion, which isn't actually true, adding a shield that blocks 20% of all attacks always reduces your risk *from wherever it is now* by 20%

[Plantissue]

It doesn't matter what VAF's and your method is damerell, that if your calculation gives the same answer as VAF's; it makes no sense because SH is independent of EV. If yours and VAF's maths contradicts the fsim, (which was provided gracefully by VAF), and contradicts the game mechanics of crawl, then it is wrong.

If my trying to correct your calculations is wrong in my assumption in what you are trying to achieve is wrong, then I apologise, but neither have you explain the reasoning behind your calculations whereas I have, but I guess in the first place you aren't interested in where you went wrong. it's right headache trying to work out what you are trying to do. It's like debugging without documentation.

If you want to say, as siegurt has been saying, that you are trying to work out the absolute values as opposed to relative values, then as had been explained, that is a nonsensical way of working out differences in values as it relates to improving defences.

Going from always being hit to being hit half the time is an absolute difference of 50% to be hit, and a character will die in double the time. Going from being hit half the time to never being hit is also an absolute difference of 50% to be hit, but the character doesn't die in double the time again, it simply doesn't die.

[damerell]

It doesn't matter what VAF's and your method is damerell, that if your calculation gives the same answer as VAF's; it makes no sense because SH is independent of EV.

VAF's calculation gives the same chance of being hit as yours in every case. If that's not so, when are you going to produce a counterexample?

If my trying to correct your calculations is wrong in my assumption in what you are trying to achieve is wrong, then I apologise, but neither have you explain the reasoning behind your calculations

I have in agonising detail. You've just failed to comprehend it. If that's not so, when are you going to produce a counterexample?

I guess in the first place you aren't interested in where you went wrong.

I haven't gone wrong. You haven't been able to name a single error of mine. If I'd made an error, you'd be able to produce that counterexample.
I have named multiple errors of yours on multiple occasions - including in my very previous post.

Going from always being hit to being hit half the time is an absolute difference of 50% to be hit, and a character will die in double the time. Going from being hit half the time to never being hit is also an absolute difference of 50% to be hit, but the character doesn't die in double the time again, it simply doesn't die.

This has nothing to do with the question of whether VAF correctly calculated the chance of being hit. They did, as can be seen both from the proof above and your complete inability to produce an example of a block/evade chance for which their method doesn't produce the correct chance.

What it is is failing to understand how VAF calculated the improvement, but we'll get to that next. First you need to either produce a block+evade chance for which VAF's method produces the wrong chance of being hit, or admit the very simple fact that you got it wrong and you've been wrong all along.

[Plantissue]

I have provided a counter example. There's a whole thread that you was directed to and participated in viewtopic.php?f=17&t=25605 whre the only objection you appear to have is to derail it with irrelevancy. Whilst your maths individually might be factually correct, the whole method is wrong.

I only need to be correct. If I am wrong then VAF fsim is wrong, as in the end, VAF calculated that for different values of EV, with SH added the relative difference are exactly the same. Your assertations and calculations do not follow VAF's fsim results and VAF's own eventual realisation that working out that the relative difference is exactly the same. Why do I need to try to comprehend your method when it doesn't follow the basic premise of the game mechanics of crawl that SH is independent of EV? It is contrary to basic logic, and it is contrary to Vaf's fsim.

You are entirely unwilling to lay out why you are calculating the numbers the way you do. In good faith, I tried to work out what you were trying to do to correct them, but each time you simply claim that I haven't pointed out your error, in which case I can only come to the conclusion that you are simply acting in bad faith. Your entire working method is wrong because the basis you are undertaking is wrong. You genuinely don't want to see where you went wrong, you are only interested to say that I am wrong. So I'll stop being nice and stop giving you a chance to correct yourself, the same way I let VAF realise that one of his calculations on fsim was wrong.

Your error is actually quite simple: your method makes no sense to work out the improvement of shield has on the character in that way. With that same maths, you might as well say that higher SH results in EV becoming less useful. Heck, it doesn't even make sense to work out the improvement of changing solely dodge value in that way.

Imagine improving EV so the original dodge rate was improved from a 30% dodge rate such that a further 20% of attacks that wouldn't had been dodged was dodged instead. Your's and Vaf's method would work out that it would be a 46% improvement, which you would think is complete nonsense, therefore the method must be nonsense but somehow you think it is correct, if that secondary dodge chance was called SH.


---

As far as I can tell, both VAF and you both have worked out the chance of not receiving the attack with combined shield and evasion, and then divided that with the chance of not receiving the attack with evasion alone.
Though that is on face value appears to be a reasonable way of working out improvement, it isn't. It is an entirely nonsensical way of working out the improvement of shield, or of the effect and improvement of any defensive attribute has on the character.

All you have worked out is the chance of not receiving the attack with a shield, divided by the chance of not receiving the attack without a shield.

As an end result this has no relation to anything.

This makes no sense in the broader context of working out the improvement that shield or evasion has on the survivability of the character.
Since that makes no sense, your entire working method makes no sense.

[damerell]

I have provided a counter example.

No, you haven't. A counterexample would look like this: "for block rate 25%, and evade rate 60%, VAF's method calculates chance of being hit X%, where actually it is .75*.4=30%". What you've produced is a vast volume of bluster.

There's a whole thread that you was directed to and participated in viewtopic.php?f=17&t=25605 whre the only objection you appear to have is to derail it with irrelevancy.

Pointing out your many errors is not "irrelevancy".

So, where's the counterexample? Stop blustering, stop bluffing: just answer the question. For what block and evade chance does VAF's method not produce the right odds of being hit?

The rest of your post is arguing the relative merits of VAF's metric vs yours (although it does contain a number of silly mistakes). I don't know why you're doing that with me; I am still on the first point, that when you said VAF had miscalculated the odds of being hit - not the improvement, just the odds - you were completely wrong.

I suppose I may as well point out some of your errors:

With that same maths, you might as well say that higher SH results in EV becoming less useful.

You might indeed, and it would be a perfectly sensible thing to say. A character who could block every attack would receive no benefit (against blockable attacks) from increased EV. A character who can block almost every attack would receive little benefit. A character with no shield receives maximum value from increased EV.

Imagine improving EV so the original dodge rate was improved from a 30% dodge rate such that a further 20% of attacks that wouldn't had been dodged was dodged instead. Your's and Vaf's method would work out that it would be a 46% improvement, which you would think is complete nonsense,

Would I? Chance of dodging beforehand: 0.3. Chance of dodging afterwards: .3+(.7*.2) = .44. .44 is 46% more than .3, so it is clearly in some sense a 46% improvement. The question now is not whether this 46% was correctly calculated - it was - but whether it is a useful basis for comparison. I almost feel what you are struggling with is the idea that one can calculate the improvement in more than one way (percentage increase in chance not to be hit, percentage decrease in chance to be hit) and it is unremarkable these can produce different answers; the interesting question is which is more meaningful, not which is "wrong".

However, this is all besides the first point, which is that you still can't produce an example of where VAF's method for calculating the chance of being hit gets the wrong answer. Don't spew up another wall of text, just produce that example.

[VeryAngryFelid]

I wonder how that conversation would look like IRL.

- The higher your salary is the less useful playing poker online is.
- Poker online always can double your income.
- I already have more money than I can spend, I don't need extra money, I would rather spend my free time with family or on my hobby.
- It does not matter, you can still double it.
- So you mean if I earn just 1$ per hour or huge $5.000 per hour, in both cases you still recommend to play online poker when I get home after work because there is no difference between the salaries and poker usefulness is the same, right?
- Right, exactly.

[Plantissue]

It would help if either of you could actually tell me why or what you are doing, but you both steadfastedly refused to do so, prefering to insist I am wrong. I might as well turn it around and ask you where I am wrong. There's a whole thread to it where I laid out my methods, but then you ran away to this thread.


---

Your method makes no sense, even though your individual maths itself may make sense. At this point you both are akin to claiming that the sky has a red polka dot pattern.

Here is another example:

Lets assume block chance is 100%. Dodge chance can be anything you like, but lets stick with 30%.

Yours/VAF's maths will, as far as I can tell, by simply plugging in the numbers, would give 233% improvement.

This cannot possibly be correct. As every attack will be blocked, the character cannot be hit at all and so the character cannot die. The relative improvement must be infinite.

[VeryAngryFelid]

Lets assume block chance is 100%. Dodge chance can be anything you like, but lets stick with 30%, so as to be consistent.

Yours/VAF's maths will as far as I can tell, by simply plugging in the numbers, would give 233% improvement.

This cannot possibly be correct with a 100% block chance, as every attack will be blocked, the character cannot be hit at all and so the character cannot die, the relative improvement must be infinite.

if you disagree you can plug in the numbers to the black box that is your formula and tell me what you get. I know you hate infinity but the correct result should be infinity.

Low EV character evaded 30% attacks, high EV character evaded 70% attacks. Now thanks to that wonderful shield both characters dodge 100% attacks. Don't you see how you have just proved my point? The higher EV you have the less useful SH becomes.
Also you have proved another my point: relative measures don't make much sense, you have to interpret them very carefully (basically prove they apply at all) while it is always safe to say "Now I dodge 15 attacks less/more when 100 monsters try to hit me" and it makes sense even when my initial or modified dodged attacks were 0 or 100.

[Plantissue]

You PM me to tell me not to reply back to you, that you have placed me on your foes list and cannot see my posts, and now you are quoting me and carrying on your nonsense?
I can only but laugh.

[bel]

Why is this still going on? There's no referee here. All sides: declare victory and go home.

[VeryAngryFelid]

Oh, I think I know where the confusion happened.

First character blocks 20% attacks and dodges 0.8*0.3=24% attacks so it blocks/dodges 44% attacks which is roughly 46% (44/30*100%-100%) improvement.
Second character blocks 20% attacks and dodges 0.8*0.7=56% attacks so it blocks/dodges 76% attacks which is roughly 9% (76/70*100%-100%) improvement

I should have written it something like that:

First character blocks 20% attacks and dodges 0.8*0.3=24% attacks so it blocks/dodges 44% attacks which is 14% improvement (44-30).
Second character blocks 20% attacks and dodges 0.8*0.7=56% attacks so it blocks/dodges 76% attacks which is 6% improvement (76 - 70).

Edit. But then relative measure is a bit useful because there is some difference between going from 10% to 30% and from 70% to 90%, that's why I did use relative measures.

[VeryAngryFelid]

You PM me to tell me not to reply back to you, that you have placed me on your foes list and cannot see my posts, and now you are quoting me and carrying on your nonsense?
I can only but laugh.

I wanted to write "my last attempt to explain obvious things despite my decision to ignore you talking to me" but decided that would look arrogant. Now I feel sorry that I haven't added that remark. You don't see the forest for the trees IMHO.

[Plantissue]

Bel, people argue about crawl all the time. You don't have to read this thread if you don't want to. Is it hurting you? It's actually pretty rare where maths is involved that one side would refuse to be persuaded even when proven demostrably wrong. I tried to divert the off-topic to CYC, but they insist to argue here instead.

[VeryAngryFelid]

Specifically I replied because of your "It would help if either of you could actually tell me why or what you are doing, but you both steadfastedly refused to do so" while you believed that I don't read your posts.
It's like one person closing his ears and another starting saying dirty things about his mom...
If you cannot understand obvious, there is nothing to do, we can just accept it.

[bel]

No, it's not hurting me, and I don't care if you argue Til Kingdom Come. I was giving a suggestion. Up to you to follow it, or not.

[Plantissue]

You PM me to tell me not to reply back to you, that you have placed me on your foes list and cannot see my posts, and now you are quoting me and carrying on your nonsense?
I can only but laugh.

I wanted to write "my last attempt to explain obvious things despite my decision to ignore you talking to me" but decided that would look arrogant. Now I feel sorry that I haven't added that remark. You don't see the forest for the trees IMHO.

You also wrote "Sorry, I leave the thread. It is no longer fun" "Oh, it's fun again so I am back for one post " and then carried on posting, and then PM me telling me to stop relying to you, so if you didn't want to look arrogant that's the wrong way about it.

Anyways, now that you have finally posted a reasoning behind your maths, even though you still haven't explained it properly, looking at it, as I have already written, as far as I can tell, both you and damerell have worked out:

the chance of not receiving the attack with combined shield and evasion, and then divided that with the chance of not receiving the attack with evasion alone.

Though that is on face value appears to be a reasonable way of working out improvement, it isn't. It is an entirely nonsensical way of working out the improvement of shield, on the effect and improvement of any defensive attribute has on the character.

All you have worked out is the chance of not receiving the attack with a shield, divided by the chance of not receiving the attack without a shield.

As an end result this has no relation to anything.

You can tell this as when given a 100% shield block chance at 30% dodge it is a 233% improvement, and at 70% block chance it is a 43% block chance. This aboslutely makes no sense at all. You can argue that strange things happen at infinity so you can run it through at 99%. The result is the same. It makes no sense at all to use your method as method to ork out improvement, even though at face value it appears to do so. Surely you must finally admit that this is an entirely nonsensical way of working out the improvement, or of the effect and improvement of any defensive attribute has on the character.

[VeryAngryFelid]

As I wrote above you don't see forest for the trees.
The chance to dodge an attack got from 30% to 100% for one character and from 70% to 100 for another character, obviously the former got much greater benefit from the shield than the latter did.
The measure we are discussing (which is not perfect or maybe even good, as I told above absolute values are more meaningful) gives 233% for the former and 43% for the latter but you don't see how the measure is related. You know that 233% is greater than 43%, right?

[Siegurt]

Oh, I think I know where the confusion happened.

First character blocks 20% attacks and dodges 0.8*0.3=24% attacks so it blocks/dodges 44% attacks which is roughly 46% (44/30*100%-100%) improvement.
Second character blocks 20% attacks and dodges 0.8*0.7=56% attacks so it blocks/dodges 76% attacks which is roughly 9% (76/70*100%-100%) improvement

I should have written it something like that:

First character blocks 20% attacks and dodges 0.8*0.3=24% attacks so it blocks/dodges 44% attacks which is 14% improvement (44-30).
Second character blocks 20% attacks and dodges 0.8*0.7=56% attacks so it blocks/dodges 76% attacks which is 6% improvement (76 - 70).

Edit. But then relative measure is a bit useful because there is some difference between going from 10% to 30% and from 70% to 90%, that's why I did use relative measures.

So this actually is super weird, again while you're doing the math, you're coming at this backwards, while technically there's nothing wrong with the math here, the problem is that you and planttissue are using a completely different scale and are proving completely different things, but calling them by the same name.

What this chunk of math actually proves is that if you already have really good defense, you might have enough defense that you don't need more which is fine for what it's worth, but doesn't really address the notion of improvement, also if you have a pre-defined notion of how much defense is good enough that you don't need more, this would let you concretely express how good your overall defense is.

Planttissue is saying "You can be in two states to start with, either you have enough defense or you do not, if you do, then obviously you should not get more defense, if you do, then *it doesn't matter how much defense you have*, from a desirability standpoint, the bonus provided from a shield is always the same improvement over your current condition*

To put this into a more step-by-step solution:
1. Consider Two characters fighting two monsters Character A (CA), fighting Monster A (MA) and Character B (CB) fighting Monster B (MB)
2. CA evades 70% of all attacks, CB evades 0%
3. CA and CB have the same number of hit points, AC, GMDR, and identical offense
4. MA does 333.33% of MB's damage, such that the amount of damage incoming after everything to CA and CB are the same, (333.33% damage * 70% evaded is roughly 100%)
5. CA and CB both decide that this is more damage than is acceptable.
6. Consider the impact of adding a shield that blocks 20% of incoming attacks to either or both CA and CB, the increase in the absolute reduction in the number of points of damage taken is identical, and since the other values are the same their ability to survive combat is identically impacted.

That CA's potential points of damage if they didn't have the 70% evasion would be much much higher, and that the 20% block provided doesn't do anything about the already-evaded attacks doesn't make any difference at all to CA's ability to survive, they have the 70% evasion, and their incoming damage is what it is, and 20% block helps them exactly the same amount as it does for CB.

So the point is that *even though CA already blocks 70% of the incoming damage* they don't care, they have already decided that's too much, the fact that the absolute improvement is less than the absolute improvement in defense for CB is wholly irrelevant, all that matters is "what improvement would I see by adding a shield to my existing condition" which is *not* effected by how much EV/HP/AC/offense they have.

The question that *is* influenced by how much EV/HP/AC/Offense you already have is "Do I already have enough combat power" That is to say, if CA (and by implication CB) have enough defense for the monsters they face now. However since crawl is a progression, and you can never be too safe, and you can never reach 100% protection (you can only get closer and closer incrementally) and there's always more things to attack you, you can never actually say in practice "I have enough combat power that I cannot be made safer." This method is only useful if you want to compare one measure of "making you safer" vs another measure, so this *is* a useful measure if you want to compare something like "I would like to get this 20% shield block, but it will reduce my offense by 30% to switch to a one-handed weapon" for example, which isn't an unreasonable thing to want to measure, but it's not actually a measure of the *effectiveness* of the SH itself, it's a way to compare the relative effectiveness's of two parts of your combat effectiveness's (Which is only meaningful if you have to sacrifice one to get the other)

So ultimately this comes down to which question you ask, if the question is "Is this shield worth sacrificing some other part of my combat effectiveness, like offense, or additional XP that would go elsewhere in my build" then the measure being used by VAF has some value (You also need to calculate the cost half of the cost/benefit, which isn't mentioned here, but it's at least a start), if the question is "How much more effective will I be in combat (compared to how I am now) if I add this shield, irrespective of any costs" then it's not a useful measure at all, and you want to go with Planttissue/Berder's measure.

This disagreement is entirely predicated on two different answers to two entirely different questions.

[Siegurt]

As I wrote above you don't see forest for the trees.
The chance to dodge an attack got from 30% to 100% for one character and from 70% to 100 for another character, obviously the former got much greater benefit from the shield than the latter did.
The measure we are discussing (which is not perfect or maybe even good, as I told above absolute values are more meaningful) gives 233% for the former and 43% for the latter but you don't see how the measure is related. You know that 233% is greater than 43%, right?

It's helpful when mentioning ratios between percentages to not also use percentages to express the ratios, the most common convention I've seen is to express them as multipliers, so rather than saying 233%, you would say that going from 30% to 100% is improving them by x3.33 rather than 233%, they mean the same thing, but it helps not conflate the two different types of percentages.

[svendre]

How to win with a deep elf. I'll simplify this answer for you based on experience:

1) Yes, use shields... they are good. Probably not higher than a medium shield. An enhancer staff is 1-handed.
2) Use an enhancer staff, usually conjuration or fire/earth, and/or energy
3) Don't let your strength slip terribly. Try to wear at least ice dragon armour (balanced with ring of flames.), try using steam or acid dragon until then.
4) Don't forget to train a weapon as a backup. Staff of fire/earth is a decent substitute.
5) Fire is probably the easiest school to build around. Use flame tongue, throw flame, conjure flame, inner flames, sticky flames, fireball, bolt of fire, ignition, firestorm.
6) Earth is a decent backup secondary magic school. Use stone arrow, bolt of magma, statue form (if needed), iron shot, LCS, shatter
7) Best gods: TSO, Makhleb (use necromutation), Kiku, Vehumet (has problems killing greater mummies if doing extended)

Primary training: fighting, armour, evasion, shields, spellcasting, conjuration, fire, earth, necromancy (if going evil)
Secondary training: charms, air, weapon, invocations, evocations, translocations (for blink), summoning (for aura of abjuration)

[VeryAngryFelid]

What this chunk of math actually proves is that if you already have really good defense, you might have enough defense that you don't need more

Not really. The math shows that dodging 14 extra attacks out of 100 is different from dodging 6 extra attacks out of 100 and this is what 20% block shield does for characters with 30% evade and 70% evade correspondingly, the math proves my initial claim: the higher EV you have the less useful shield becomes.

[Siegurt]

What this chunk of math actually proves is that if you already have really good defense, you might have enough defense that you don't need more

Not really. The math shows that dodging 14 extra attacks out of 100 is better than dodging 6 extra attacks out of 100 and this is what 20% block shield does for characters with 30% evade and 70% evade correspondingly, the math proves my initial claim: the higher EV you have the less useful shield becomes.

That's not the correct way to define "less useful"

The math proves that if you have good defense, more defense has a smaller effect on your total damage mitigation. However, how much a shield improves your total damage mitigation is totally unimportant, all that matters for "usefulness" is how much a shield mitigates the damage *you would suffer without the shield*

If you would suffer X damage without the shield (whatever your evasion is, it doesn't matter) and a shield blocks 20% of X, it blocks 20% of X, that's it, the shield doesn't care how much damage it doesn't block because it evaded.

You might care how much *total* damage you're going to take, and figuring that out might entail the use of the math you put up, but the fact is no matter how much damage you already evade, the shield still blocks 20% of remaining damage.

Look at my step-by-step example above and see if you can reconcile "shields are less useful with more evasion" and the proposed example.

[VeryAngryFelid]

That's not the correct way to define "less useful"

It is. You can basically consider that low EV character had 2 shields, one saved from 6% attacks and another from 8% attacks. When people train Shields, shield becomes more useful to them in identical way i.e. by increasing number of blocked attacks.

[VeryAngryFelid]

Consider the picture.


You basically pick a random point in the rectangles, first is for character with really low EV, second is for character with really high EV.
Green means the attack was evaded by EV but not by shield, red means the attack was blocked by SH but not evaded by EV, orange means the attack was blocked by both EV and SH, white means you are hit.
Now please tell me you don't see difference in usefulness of red area. For first character many attacks fall into red, for second character very few do.
Also take a look at orange area, that's duplication of defense, you can literally remove either EV or SH and still be protected from those attacks.
Now compare orange to red, those are "shield is useless" and "shield is useful" correspondingly when making a decision whether the character without shield should equip one.

[Siegurt]

Consider the picture.


You basically pick a random point in the rectangles, first is for character with really low EV, second is for character with really high EV.
Green means the attack was evaded by EV but not by shield, red means the attack was blocked by SH but not evaded by EV, orange means the attack was blocked by both EV and SH, white means you are hit.
Now please tell me you don't see difference in usefulness of red area. For first character many attacks fall into red, for second character very few do.
Also take a look at orange area, that's duplication of defense, you can literally remove either EV or SH and still be protected from those attacks.
Now compare orange to red, those are "shield is useless" and "shield is useful" correspondingly when making a decision whether the character without shield should equip one.

The problem is that you're looking at the whole picture.

When considering whether a shield is useful, you can only compare the white area to the red area, the rest of the picture has no bearing on your decision. (We can say the same thing about a dozen different ways, you just aren't getting it, I understand your point, and your wrong, that's all there is to it.)

If you want to use your picture analogy, the picture on left is six inches from you, the picture on the right is sixteen kilometers from you.

The question is: Is the red+white area significant enough to cause you to worry, if it is, then the amount of space taken up by the red area in both pictures is equally important, if the total red+white area is insignificant, then of course the red area is equally insignificant.

Comparing the orange area (the area that could've been blocked by a shield, but wasn't because it was evaded) to the red one is wholly unrelated to the utility of a shield.

[VeryAngryFelid]

I see, I wonder if it's called "math blindness" or something. It's when you are a full HP Sp with Ancient Lich in view, you are likely to die or not in 1 turn depending on shield presence, or you are at 1 HP with 5 adjacent monsters and your chance to die is decreased either from 75% to 20% or from 1% to 0.5% but you still insist that it's still the same usefulness. I wonder why you picked "red" to "red + white" ratio as measure. Why not "red" to "orange" ratio? Why not log10? Why not sinus? Because it is number of dead stone giants and thousands of turns you live in that math fantasy?
I guess it won't make sense for me to tell you that you might imagine the same happens with AC and send a picture with 3rd axe i.e. with a cube where there is some area with AC 80+ where both SH and EV are dozen times less useful than in area with AC 1?

[VeryAngryFelid]

More fsims.

First character.
Without shield and with shield:

  Code:

           AvHitDam | MaxDam | Accuracy | AvDam | AvTime | AvSpeed | AvEffDam
Defending:     26,9 |     55 |      18% |   4,9 |   100  |  1,00 |      4,9
Defending:     26,4 |     55 |       5% |   1,4 |   100  |  1,00 |      1,4

Second character.
Without shield and with shield:

  Code:

           AvHitDam | MaxDam | Accuracy | AvDam | AvTime | AvSpeed | AvEffDam
Defending:     27,4 |     55 |      97% |  26,8 |   100  |  1,00 |     26,8
Defending:     27,4 |     55 |      29% |   8,0 |   100  |  1,00 |      8,0

Question. Would you train shields to 27 and use +8 large shield for the former? Really???

[VeryAngryFelid]

For more clarity look at accuracy, not damage. Blocking 68 attacks out of 100 cannot equals to blocking just 13 attacks.

[duvessa]

Question. Would you train shields to 27 and use +8 large shield for the former? Really???

I wouldn't train shields to 27 for either one, personally.