Triple defense hypothesis


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Snake Sneak

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Post Sunday, 26th January 2020, 13:40

Triple defense hypothesis

Correct me if I'm wrong.

It took me a bunch of years to realize this because Crawl used not to display skill costs so well. But it appears that if you want to use your xp efficiently, it's best not to focus on a single defensive skill (Dodging/Armour/Shields). For the purpose of this thread we'll assume the goal is to maximize AC+EV+SH (the sum).

If you focus on, say, AC and Armour skill, your AC increases slower and slower because the skill gets more and more expensive to train. If all you care about is the sum, it's better to use at least 1 more defensive skill. Then you get to benefit from a fast skill growth once more. Your defensive skills get more expensive two times slower. If you add a third skill, they start getting more expensive 50% slower (relative to 2 skills) or 3x slower (relative to a single defensive skill).

I used to focus on a single defensive skill and to dismiss hybrids as jack of all trades and not particularly good at anything. Now I started to believe that the main benefit of multi-skill defense is not the access to multiple types of defense, really, but that you can get more points before it slows down to a crawl.

A bigger issue with shields is that they limit what you can wield and can't be swapped quickly.

A problem with armour/dodging hybrid is determining the exact point and Strength requirement where you can still dodge reasonably. This gets doubly more important with Cheibriados or when you play a Demigod, because they come with significant sacrifices.

The only way to opt out of multi-skill defense is to use some magic.

The only good reason to focus on a skill if it's the only way to punch through monster AC or deal a bunch of damage in a single turn. So missile skills. Conjurations and pals. With melee you want to train until weapon min delay and then switch to Fighting.

Ziggurat Zagger

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Post Sunday, 26th January 2020, 18:49

Re: Triple defense hypothesis

b0rsuk wrote:For the purpose of this thread we'll assume the goal is to maximize AC+EV+SH (the sum).
this is a hell of an assumption

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Slime Squisher

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Post Sunday, 26th January 2020, 19:47

Re: Triple defense hypothesis

Question: wouldn't playing a follower of Chei actually make the difference less important because of the divine extra stats? The dodging boost from high Dex tapers off at some point, and having up to +15 Str would also make armour penalties in many cases a moot point.
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Snake Sneak

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Post Monday, 27th January 2020, 16:07

Re: Triple defense hypothesis

duvessa wrote:
b0rsuk wrote:For the purpose of this thread we'll assume the goal is to maximize AC+EV+SH (the sum).
this is a hell of an assumption

Hey, just wanted to point out my threads are happier without you. Most of what you do are drive-by attacks, snide remarks and passive aggressive behaviour. Real Duvessa would be ashamed of you, you're nothing like her. I could tolerate that toxic behavior if your posts had some merit to them or you provided some alternative. Now does this forum have the "ignore user" functionality...
Sorcerous wrote:Question: wouldn't playing a follower of Chei actually make the difference less important because of the divine extra stats? The dodging boost from high Dex tapers off at some point, and having up to +15 Str would also make armour penalties in many cases a moot point.

If the wiki is up-to-date, the diminishing returns kick in at 35 EV. But a Chei follower could get away with wearing heavier armor, to the point where you brute-force your way through armour EV penalties with high EV.
In theory, every character that gets bonuses to everything woud benefit the most from dabbling a bit in everything. Defensive skills combine pretty well, it's not like you're just using a single Throwing skill. If you're playing a gnoll or Chei follower and not casting spells / dodging / fighting, shame on you ;-).

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Slime Squisher

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Post Monday, 27th January 2020, 18:11

Re: Triple defense hypothesis

b0rsuk wrote:Hey, just wanted to point out my threads are happier without you. Most of what you do are drive-by attacks, snide remarks and passive aggressive behaviour. Real Duvessa would be ashamed of you, you're nothing like her. I could tolerate that toxic behavior if your posts had some merit to them or you provided some alternative. Now does this forum have the "ignore user" functionality...


Strangely enough, I made a thread relatively recently about this feature because it's really negative imo. When you are viewing a user profile you can "Add foe" which hides posts from that user unless you manually unhide them. Now, "If the wiki is up-to-date" would have a lot more joke value with the "this is a hell of an assumption" response because using information directly from the wiki is a meme on the forum.

In theory, every character that gets bonuses to everything would benefit the most from dabbling a bit in everything. Defensive skills combine pretty well, it's not like you're just using a single Throwing skill. If you're playing a gnoll or Chei follower and not casting spells / dodging / fighting, shame on you ;-).


I tend to play a lot of casters (shocking, yes) and being able to dabble can actually hurt my plays more than streamlining does. In a lot of RPGs actually I like the idea of creatively using a specialty for as many situations as possible, just to see what happens. As for gnolls, they're among my favourites exactly because I'm in no way restricted by XP allocation. It's all done in the background and I just choose how to season the broth, so to speak. :)
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Cocytus Succeeder

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Post Monday, 27th January 2020, 21:17

Re: Triple defense hypothesis

b0rsuk wrote:I used to focus on a single defensive skill and to dismiss hybrids as jack of all trades and not particularly good at anything.

I don't know where you got this notion. It is clearly absurd.

b0rsuk wrote:A problem with armour/dodging hybrid is determining the exact point and Strength requirement where you can still dodge reasonably.

What about this simpler method: train armour and dodging and shields to some reasonable level without worrying about maximizing something. As for Strength, put a lot of points into it if you want a heavy armour and don't otherwise.
By the way, if you use weird phrases like "armour/dodging hybrid" that really risks than no one will understand what you are saying. This happens again and again, see below:

b0rsuk wrote:The only way to opt out of multi-skill defense is to use some magic.

I have no idea what this means.

b0rsuk wrote:The only good reason to focus on a skill if it's the only way to punch through monster AC or deal a bunch of damage in a single turn. So missile skills. Conjurations and pals.
I don't know what you mean by "focus on a skill" here. I guess not focusing a skill on the skills screen, but what else?

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Blades Runner

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Post Monday, 27th January 2020, 21:21

Re: Triple defense hypothesis

XP does have diminishing marginal utility per skill spent, yes. With defenses it's more complicated because you often don't want to invest in dexterity (non-chei), and heavier armors somewhat reduce the benefit of training EV. But hybrid defenses are still very effective, you can wade through a ton of stuff with a stat line like 30-20-20. At least until the game laughs at you and starts using torment/damnation to ignore all 3 and trivialize your skill investment choices.

Hidden break points are kind of annoying. Not so hidden break points...like getting certain spells castable...make the diminishing marginal utility interesting. It takes a LOT of investment to get cBlink or firestorm going, more than is usually practical in 3 rune. But these are strong spells and worth considering for extended, to the necessary exclusion of other options if you're not a gnoll. But there is an opportunity cost. Having PoG, irradiate, OOD, iron shot, swiftness, passwall, shadow creatures, and mana vipers all castable at once is also a lot of value, even in extended. And you can have all of these up before you could *just* get firestorm up, on many species, so you better really want that firestorm if pursuing it before like ~zig or late extended.

For similar reasons, taking fighting to 16 or 20 is a lot more practical than going to 27 with it in 3 rune, because you can put the points giving ~20-30 hp into some pretty strong evocations, invocations, or magic as an alternative. Things that can outright trivialize stuff that would threaten that hp pool.

Players can take it too far and train things they don't use often/need before things they do are sufficiently high, however.

Ziggurat Zagger

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Post Thursday, 27th February 2020, 19:29

Re: Triple defense hypothesis

I'm not entirely sure I want to get into some of the back and forth here, but here's the rough general skill training guidelines I generally use:

1) Start with your main offensive skill. I tend to prefer melee, so this is usually unarmed/weapon skill. It can also be your main magic school or ranged weapon, but those cases are a bit more complex.

2) add in a primary defensive option, or two. This is typically fighting + either armor or dodging.

3) Choose to either reinforce your offense again, or branch into a secondary ability (melee character picking up ranged, caster picking up additional spell schools, etc.

4) Raise the levels of everything to reach more mid/end game threats. Speciality skills can be picked up as needed late game.

The problem with rule sets like this is it's tough to be specific enough without occasionally being wrong, as there's many choices and different characters have different demands.

Example character: troll fighter
Step one is raise unarmed to a decent value, probably around 6-8. Step 2 adds fighting and possibly armor (this will likely start when you find an armor heavier than robes). When fighting gets up to around 6-8 and unarmed is at 10-12, you're at step 3, and can either go into throwing, shields, dodging, or pick up magic (unlikely, but there are some builds that would do this, ex, chei statue trolls). You may have picked a "final" set of skills for a simple okawaru troll as: Fighting, unarmed, shields, armor, throwing, dodging. Then step 4 is just to raise those skills. Invocations based on your god, Okawaru only takes about 8, which is fairly trivial to reach.

This is sometimes shortened to the tavern meme of "first get your killdudes skills, then defenses" or something along those lines (it's been a while).

Snake Sneak

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Post Friday, 28th February 2020, 16:49

Re: Triple defense hypothesis

Okay, but I think we can agree that multiple defensive skills work much better than multiple offenses because they stack. It's a lot trickier with offenses, because ultimately you need to kill big tough brutes either in melee or from a distance. So-so attack ranged attacks only works against glass cannon monsters. For spells, some depend on spell power while other do not. Merely getting a powerful spellpower spell castable is not great - it will be weak and cost a lot of hunger. It's a different matter with ones like blink or when a spell checks HD.

I rarely play strong casters. What are the best uses for Brilliance potions?

Tomb Titivator

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Post Friday, 28th February 2020, 17:17

Re: Triple defense hypothesis

Throwing is your secondary defensive skill as troll though. UC/Fighting into UC/Fighting/Throw or UC/Fighting/God feels way better than developing into UC/Fighting/Dodge on troll.

Okay, but I think we can agree that multiple defensive skills work much better than multiple offenses because they stack. It's a lot trickier with offenses, because ultimately you need to kill big tough brutes either in melee or from a distance.


Not at all. You need to be able to (1) kill or (2) avoid big tough brutes (or other threats), it is fine to have a character that will engage them at multiple distances. Perfectly good characters can run longbow/2hmelee on swap.

Swamp Slogger

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Post Monday, 2nd March 2020, 12:14

Re: Triple defense hypothesis

Not only is it more skill efficient to round out your defenses, its actually better defensively too. If you've ever played a character with like 50 AC and single digit EV, you will notice extreme vulnerability to bolt spells and such. Shield is effective in reducing variability too, but doesn't help against bolts.

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Post Monday, 2nd March 2020, 12:32

Re: Triple defense hypothesis

gameguard wrote:Not only is it more skill efficient to round out your defenses, its actually better defensively too. If you've ever played a character with like 50 AC and single digit EV, you will notice extreme vulnerability to bolt spells and such.

Not that extreme since, while you'll get hit a lot, your 50 AC will reduce the damage.
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Post Monday, 2nd March 2020, 15:57

Re: Triple defense hypothesis

damerell wrote:
gameguard wrote:Not only is it more skill efficient to round out your defenses, its actually better defensively too. If you've ever played a character with like 50 AC and single digit EV, you will notice extreme vulnerability to bolt spells and such.

Not that extreme since, while you'll get hit a lot, your 50 AC will reduce the damage.


Elec will still hurt (lots w/o rElec) and the iron shot/crystal spear line is extremely dangerous like that. Acid too, though there are only a handful of enemies that do a lot of it late game (acid blobs, deep elf sorcerors, and caustic shrikes come to mind).

I've had the most luck with a well rounded spread of defenses. Even stuff in extended struggles to do a great deal of damage through 35/20/20 type defenses, except torment/smite/damnation which doesn't care about any of them regardless. You're not invincible like that but can still wade through enemies easily enough.

AC is the best defense but I've found any practical combination that adds up to > 60 tends to be sufficient to a) win and b) do so w/o extremely careful play. You can win with much lower defenses than that but you start having to really mind each movement with enemies around.

Temple Termagant

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Post Saturday, 25th April 2020, 20:27

Re: Triple defense hypothesis

crawler is a game of thresholds. theres a point where EV is high enough to avoid significant damage in shorter fights. having 20 EV makes a big difference over 16 or even 17/18 EV, although on paper it doesn't look so. Due to the way the game doles out experience it also feels like the impact of armour/dodging accelerate through the mid-teens of skill levels, making it more effective to focus one defense up to about 15 before generalizing strongly. I think skills get harder to train the more XP you have, so you want to "burn in" a good level of defense in one category before generalizing too much, usually. The thresholds are more important than layered defenses--even when experience-wise layers look better.

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Post Sunday, 26th April 2020, 00:35

Re: Triple defense hypothesis

what are the thresholds?

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Post Thursday, 30th April 2020, 01:55

Re: Triple defense hypothesis

duvessa wrote:what are the thresholds?

it depends. besides min-delays and penalty-removals, other thresholds exist based upon repeated "tests". I suspect playing with a binomial distribution (or repeated Bernoulli trials) could reveal thresholds in success rates for AC, EV, and SH tests that would minimize damage in the limit--for the least amount of training. It depends because each character will be affected differently by these tests.

I simple example might be average damage for 20 AC vs 20 damage is 0, clearly not zero because some damage gets through and over-prevented damage doesn't heal. now try 21 vs 20, 22 vs 20. at some point getting a defense threshold beyond damage/to-hit thresholds renders defense much more effective. it might take training armor from 12 to 15 to get a few extra points of AC, and it seems so underwhelming when you could have 12 dodge AND 12 armor. however due to the repeated nature of these tests reaching a threshold will be more important early on than adding layers.

I'd have to run a simulation to give a hard answer. anecdotally, I have greater success on melee/range runs with focusing a primary defense skill up to close to 15 before adding another skill.

----

after a bit of thought I see that it is the "damage-variance" that must be minimized and suggests to me why thresholds are important. Focusing on AC (EV and SH should generalize but I think they are only success trials) Let's assume a reasonable distribution exists for crawl's damage rolls parameterized by AC and damage, named CD(AC, dam). It's a one-tailed distribution because it's lower bound is clamped at zero--it might be a Poisson or similar. Indeed Poisson variance equals the average, so to minimize variance the average must be minimized. Discrete distributions can't have average 0, but can get really close. it'd be a matter of summing the area under the distribution curve above average, and you want that curved centered around average as much as possible. AC>dam pushes average closer to zero. One could build an empirical distribution for CD(AC, dam) by simulating a damage roll of those parameters 10000 times and observe the average. It would be a count and Poisson would be reasonable to model the variance of the count. Variance here refers to variance in total damage--possible damage outcomes won't change (you can always roll a 0 on AC) but the distribution of those outcomes will shift towards lower results.

that's my intuition at least.

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Post Thursday, 30th April 2020, 09:04

Re: Triple defense hypothesis

I cannot follow the argument in the above post. It does not give any "thresholds", nor does it show why any threshold would exist at all. Looks very handwavy to me.

Temple Termagant

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Post Thursday, 30th April 2020, 13:48

Re: Triple defense hypothesis

a simple simulation for function damage(AC, dam) -> "damage recieved"

damage(19, 20) <mean 3.52>

damage(20, 20) <mean 3.32> (plot included to show Poisson shape)
  Code:
    +--+------------+-------------+------------+------------+--+
    |  *                                                       |
0.5 +  *                                                       +
    |  *                                                       |
0.4 +   *                                                      +
    |   *                                                      |
0.3 +   *                                                      +
    |   *                                                      |
    |   *                                                      |
0.2 +   *                                                      +
    |    *                                                     |
0.1 +    *                                                     +
    |    *************                                         |
  0 +                ****************************************  +
    +--+------------+-------------+------------+------------+--+
       0            5            10           15           20 


dam(21, 20) <mean 3.16)


A plot of mean damage for AC 2 to 22 vs damage 20:
  Code:
  +-------------+-------------+------------+-------------+-----+
9 +  *                                                         +
  |     *                                                      |
8 +       *  *                                                 +
  |             *                                              |
7 +                *                                           +
  |                  *                                         |
6 +                     *  *                                   +
  |                           *                                |
5 +                             *  *                           +
  |                                   *  *                     |
4 +                                        *  *                +
  |                                              *  *          |
3 +                                                    * *  *  +
  +-------------+-------------+------------+-------------+-----+
  0             5            10           15            20


and the likelihood of receiving 5 damage vs 20 damage attack at mean damage values of 2 to 4 in 0.1 increments (modeled using Poisson) NOTE sorry the x-axis wrong label, it should be the increments: 2.0, 2.1, 2.2, and so on...
  Code:
0.16 +------------+------------+------------+-------------+----+
     |                                                    * *  |
0.14 +                                              *  *       +
     |                                         *  *            |
     |                                    * *                  |
0.12 +                                 *                       +
     |                               *                         |
 0.1 +                         *  *                            +
     |                       *                                 |
0.08 +                 *  *                                    +
     |               *                                         |
0.06 +          * *                                            +
     |       *                                                 |
0.04 +  * *                                                    +
     +------------+------------+------------+-------------+----+
     0            5           10           15            20


It all looks fairly linear, doesn't it? seems to be no thresholds here, but I'll code up a simulation to interact EV and SH and see how they affect the outcome. I believe the statistics will show us something.
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Vaults Vanquisher

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Post Thursday, 30th April 2020, 15:05

Re: Triple defense hypothesis

So you figure the average damage is going to go negative in that second plot or what? Like knives in my brain reading this shit.

Look, obviously there are thresholds. When you roll multiple dice, you get S-shaped cumulative probability distributions and the more dice, the steeper. You'll see this with hit probabilities for different accuracies and EV/SH values (also you have natural 40 rules that swamp small differences in hit probability at high EV/SH values -- this is actually the dominant factor in diminishing returns there). You also have thresholds from differences bottoming out at zero. You see this with AC, but with AC you never hit these thresholds for all attacks, so you always want more.

If you hold the type of attack you're defending against constant, you'll usually see "thresholds" for various defensive stats where the benefit of the marginal point of the stat either quickly increases then declines or simply begins to decline. Some of these values are realistic to surpass, others aren't. The only ones people often talk about are for hydra melee, where the phenomenon is especially pronounced and useful to know about.
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Temple Termagant

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Post Thursday, 30th April 2020, 15:48

Re: Triple defense hypothesis

hmmm you may be onto something, the cumulative distribution would be s-shaped and where it flattens after inflection might be a threshold. it can't be negative because it's discrete (you can't count negative apples!) you can see the second plot just starts to flatten at 20 where AC=damage, if it stayed linear it'd go negative but it can't hence why discrete distributions are non-linear. if I plotted out to 30 AC vs 20 damage the flattening out after 20 AC would be more pronounced; AC greater than damage is a little less effectual from over-prevented damage. The thresholds might be an AC value equal to damage rolls of monsters at that point in the game. A stone giant does 45 damage! wardens 36. tentacled monstrosities 22.

Blades Runner

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Post Friday, 1st May 2020, 11:28

Re: Triple defense hypothesis

Defensive training still has legit thresholds, in that AFAIK the game doesn't track fractional AC/EV/SH. Maybe I'm mistaken though? Dex can throw a wrench on EV scaling, too, as can size. We do see something of a pseudo step function in the graphs above.

The values of these from training thresholds isn't large enough that I'd agree with the notion of emphasizing defenses as "about thresholds". Weapon training before/after mindelay is a much more apparent threshold for example. There are apparent thresholds in defenses, but they don't really define the system.

Another potential threshold is the value of really high AC values against really low damage attacks, where adding another point of AC has close to no practical value. Of course, worrying about such a situation also has close to no practical value.

Lair Larrikin

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Post Saturday, 2nd May 2020, 15:56

Re: Triple defense hypothesis

Sum of AC+EV+SH is a good rule of thumb. But note that EV and SH are binary: either you dodge or block or you don't. AC always shaves off melee damage. Even with heavy armor a melee char can get 30+ EV so I think it is worth investing in dodging after your stats are good enough in other skills.

Blades Runner

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Post Sunday, 3rd May 2020, 07:48

Re: Triple defense hypothesis

I'll save you the trouble of all the complicated math and guesswork: You get the best protection from pumping fighting for a higher maximum health, combined with armour. Things can look good adding up AC+EV+SH and you balance your stats and it all seems great then SPLAT.

If you just want reliability, you need to forget about dex and EV and only put points into them if they are stupidly cheap. Train fighting, then AC after you find a good amount of armour, and I mean heavy armour.. not middle of the road. GDA, Ice dragon, pearl, maybe lightning if you are missing the resist are my top picks. You do want to train shields but it's not a consideration much until you've found a shield (unless you start out as a fighter).

The trouble with the theorycraft is that it just doesn't take into account all the many details. Heavier armour comes with higher GDR (and worse EV), and I'll argue that getting paralyzed on a failed MR check is one of the deadliest things in the game for an experienced player, and you can kiss your 100 EV goodbye, it won't do a thing.

I think it's stupid how important health+AC is above and beyond practically everything else in the game, to the point of frustration with the game, but I don't expect changes. People might argue what I'm saying, I don't care - I have so many games under my belt, I know what I'm talking about. If you want to know what's up, here you have it.
Last edited by svendre on Monday, 4th May 2020, 03:16, edited 1 time in total.

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Post Sunday, 3rd May 2020, 18:59

Re: Triple defense hypothesis

bjourne wrote:Sum of AC+EV+SH is a good rule of thumb. But note that EV and SH are binary: either you dodge or block or you don't. AC always shaves off melee damage. Even with heavy armor a melee char can get 30+ EV so I think it is worth investing in dodging after your stats are good enough in other skills.


That's true, until it isn't.

Torment, damnation, smite, crystal spear, and iron shot are all examples of things that don't care about AC much (or at all). Some of these also ignore EV/SH of course.

However there are a reasonable quantity of spells/ranged attacks that are better served dodging rather than tanking. If you look at end-game stats for even reasonably heavy armors with ~11 EV training, dodging and shield often avoid or absorb far more total damage than AC across the run.

High variance is unfavorable to the player. However, reasonably high HP + AC smooth the variance of damage enough that SH and EV legit approach the value of AC from a reasonable spread of damage sources. In some cases they're equal or better. Pulling up a 15 MuIE rune run, dodge + block amounted to roughly triple the count of taking hits to fire dragon scales.

Even with gold scales, very respectable 55 AC, and more training in armor this run still saw EV/SH contribute very strongly to survival throughout https://crawl.kelbi.org/crawl/morgue/Th ... 215438.txt

AC is the best defensive stat on average (after HP), but advice against investing in EV/SH is still bad advice.

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Post Thursday, 21st May 2020, 16:46

Re: Triple defense hypothesis

TheMeInTeam wrote:Defensive training still has legit thresholds, in that AFAIK the game doesn't track fractional AC/EV/SH.

Yep, on this level there are definitely thresholds. You don't gain TOO much by optimizing for them, but I definitely run the math for armour training breakpoints on any light or medium armour character.
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