Eliminating Dodging Penalty (was STR Target)

[MainiacJoe]

In the "Stat rises for HOFi" thread, Sprucery gave his rules of thumb for stat gains:

Int if you want to raise the spellpower of your spells, otherwise Str if you have strength less than about 1.2 times the encumbrance rating of your body armour, otherwise Dex.

This 1.2x EVP suggests that when choosing a stat gain for a melee build, one ought to have not the current armor in mind, but rather the sort of armor you want to end the game with. Once you have enough STR for that, you can start gaining DEX. Here then is a table of STR, the EVP associated with it by the 1.2x rule, and the heaviest armour that STR is adequate for.

  Code:

STR      STR/1.2   Heaviest Armor
 3       -2.5      Robe
 4       -3.3      Robe
 5       -4.2      Leather / TLA
 6       -5.0      Mottled
 7       -5.8      Mottled
 8       -6.7      Mottled
 9       -7.5      Ring / Swamp / Qsilver
10       -8.3      Ring / Swamp / Qsilver
11       -9.2      Ring / Swamp / Qsilver
12      -10.0      Scale
13      -10.8      Scale
14      -11.7      FDA / IDA / PDA
15      -12.5      FDA / IDA / PDA
16      -13.3      FDA / IDA / PDA
17      -14.2      FDA / IDA / PDA
18      -15.0      Chain / Shadow
19      -15.8      Chain / Shadow
20      -16.7      Chain / Shadow
21      -17.5      Storm
22      -18.3      Plate
23      -19.2      Plate
24      -20.0      Plate
25      -20.8      Plate
26      -21.7      Plate
27      -22.5      Plate
28      -23.3      CPA
29      -24.2      CPA
30      -25.0      GDA


So for instance if you intend to end up in FDA, you ought at some point to get to STR 14. Am I understanding Sprucery's rule of thumb correctly?

[tasonir]

Sounds like you're interpreting it correctly, yes. Personally the 20% over encumbrance sounds a bit high to me, but maybe I need to look over the formulas a bit more. I wouldn't mind an extra 1-2 points for the mediumish armors (FDA, etc) which works out to roughly 20%, but seems a bit harsh saying you need 30 strength for GDA. Aren't GDA and CPA both 23 encumbrance?

[Sprucery]

I believe GDA has been 23 since 0.16.

[greedo]

If I understand things correctly, encumbrance is almost a meaningless number since it is only used in a function where it is squared. You should really think of, say, FDA as "121" encumbrance, not 11, and GDA as "529" encumbrance. So you probably want even more than 30 before you raise dex, and probably need even less for ring/swamp/etc.

Edit: hrm okay it's used linearly elsewhere as well, but AEVP it is squared, which is the brunt of where strength matters.

[MainiacJoe]

According to the wiki FWIW, AEVP has EVP squared in the numerator and STR linear in the denominator. But the Dodge Penalty has AEVP (adjusted) in the numerator and STR linearly in the denominator, so overall Dodge Penalty is dividing the square of EVP by the square of STR. Thus EVP is being compared to STR, not EVP^2.

[greedo]

Ah interesting, you're right, and the graph at the bottom of the page here really spells it out http://crawl.chaosforge.org/Encumbrance_Rating. Although it does seem like ~e^2/~S is the only thing used for the penalty in spell success? Which would mean strength is more important for casters in heavy armor, than non-casters.

So in crawl, casters benefit from strength and shields, while melee fighters generally don't

Edit: hrm, a logarithmic second derivative graph. Gotta be berder.

[daggaz]

Some fine day he will learn to actually label his axes.

[duvessa]

I like how it claims the graph leads to the "rule of thumb that you should at least raise it to the same number as your encumbrance", when the graph directly shows that rule doesn't make sense.

[daggaz]

I cant make sense of it at all, to tell the truth. I would much rather see the base graph, I cant imagine why you would take the second order derivative instead unless you want to exactly identify inflection points.

[tasonir]

Agreed that the graph is confusing, but it seems like it's saying the biggest jump up per point is actually a point or two under the encumbrance rating. At first a character with 5 strength in GDA has huge 80ish point penalties (Not sure how this is stepped down later, I don't think you actually get -70 EV), and each point of strength gives a bit less of a decrease until 20, then 21 gives you a larger jump, and then it's back to diminishing returns. IMHO it sounds like its saying GDA should have at least 21 strength, just because that point is worth roughly twice the points on either side of it.

Any of this might be wrong, I don't really know if I'm reading the graph right, but that's what it seems to say...

[MainiacJoe]

I also found the graph to be a bit confusing. I went back to the actual calculation and discovered that, unlike AEVP itself, it is possible to completely eliminate the Dodging Penalty with enough STR and/or Armour skill. This Penalty is the only contribution that STR, Armour, or body armor make to the EV calculation. Caveat: I'm using the wiki supplemented by LearnDB.

Here is the calculation for the STR needed to eliminate the Dodging Penalty:

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StrengthMath.gif (5.68 KiB) Viewed 5032 times

Here is the table of necessary STR to eliminate the Dodging Penalty for Size +4 (Sp). All these tables are images because I had too much trouble formatting Excel to code tags (Mod: kill the post as needed and if so please advise of a different way to post this information)

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Strength+4.gif (5.15 KiB) Viewed 5032 times

Size +2 (Ha, Ko)

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Strength+2.gif (6.59 KiB) Viewed 5032 times

Size 0 (most species)

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Strength0.gif (6.64 KiB) Viewed 5032 times

Size -2 (Og, Tr)

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Strength-2.gif (5.29 KiB) Viewed 5032 times

[MainiacJoe]

Here is the math for the Armour Skill necessary to completely eliminate the Dodging Penalty:

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ArmourMath.GIF (5.75 KiB) Viewed 5025 times

Table of necessary Armour skill for Size +4 (Sp)

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Armour+4.gif (7.47 KiB) Viewed 5025 times

Size +2 (Ha, Ko)

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Armour+2.gif (12.53 KiB) Viewed 5025 times

Size 0 (most species)

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Armour0.gif (13.85 KiB) Viewed 5025 times

Size -2 (Og, Tr)

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Armour-2.gif (12.31 KiB) Viewed 5025 times

[ThreeInvisibleDucks]

Are the sizes in the wrong order? Spriggans can't have an easier time in GDA than ogres.

[MainiacJoe]

Are the sizes in the wrong order? Spriggans can't have an easier time in GDA than ogres.

This is what I thought, too, and so I have checked and re-checked my math, and please you do so, too.

The size factor appears in the Dodging Penalty as (AEVP - AEVP*size/8) in the numerator (and recall that these charts concern Dodge Penalty only). Positive size factor means that the AEVP is reduced! And size factor is certainly positive for Sp, for base EV is 10 + size.

So yes, if STR and Armour Skill are equal, the spriggan will have a lower Dodge Penalty than the ogre: the Sp has 0.5*AEVP, the ogre 1.25*AEVP. The trick must therefore be getting the spriggan's STR to match an ogre's.

http://crawl.chaosforge.org/Evasion#Dodging

[MainiacJoe]

After net dodging bonus and penalty are added to EV (ranging from 0 to Dodging Bonus) then un-adjusted AEVP is subtracted again. Size factor does not appear in this calculation at all, only STR and Armour. So again, unless the wiki is obsolete or my math is wrong, smaller species get a smaller EV penalty from armor than larger ones, in addition to their higher base EV.

[greedo]

Heh, "how many forum posters does it take to calculate your EV"? There appears to be something wrong with your chart. The wiki page here http://crawl.chaosforge.org/Encumbrance_Rating

says dodge penalty has 20-F in the denominator which would mean higher size (little) has higher dodging penalty.

Edit: ah no, I see B there is the dodge bonus, a bit confusing with the header right above saying dodge penalty xD

Hrm, going to check the source code, because if this is right, wow is it dumb. Would not be surprised, though.

[MainiacJoe]

Please do check both my math posted above and the source. Whether it's me or the wiki that's wrong, let's find out!

[greedo]

Long story short, this entire player_evasion() is retarded and should be redone. But, here's what I'm finding:

3 assumptions:

no shield, since penalties are negligible anyways,
dex < 24 since gains above are negligible
str > e - 3 since , e.g., str >= 8 for FDA and str >= 20 for GDA are no brainers

EV =
10 + size <--- base dodging
((7 + dodging*dex)/(20 - size)) * (1 - (encumbrance-3)/(strength*2) ) - <----Essentially dodging bonus - dodging penalty
encumbrance /3 - <---- guaranteed EV penalty from armour
2 * encumbrance^2 * (45 - armour)) / (5 * (strength() + 3)) / 45; <---- AEVP


I mean.. so simple you can do it in your head!

this from the evasion page on wiki:

ABAEVP= body_armour_encumbrance_rating - body_armour_encumbrance_rating*size_factor/8
dodge_penalty = max(0, (10*ABAEVP - 30)/str)

is bogus. I don't see it anywhere.

Wiki and learndb both get AEVP right, they're just in different forms.
Wiki gets dodging penalty wrong. It's not B(2 - (e-3)/s). It's B * (e-3)/(s*2). It's a subtle but very large difference. It also gets B slightly wrong, in fact just ignore it.

Edit: getting rid of some 0s that were only for integer division reasons.

[MainiacJoe]

this from the evasion page on wiki:

ABAEVP= body_armour_encumbrance_rating - body_armour_encumbrance_rating*size_factor/8
dodge_penalty = max(0, (10*ABAEVP - 30)/str)

is bogus. I don't see it anywhere.

Wiki and learndb both get AEVP right, they're just in different forms.
Wiki gets dodging penalty wrong. It's not B(2 - (e-3)/s). It's B * (e-3)/(s*2). It's a subtle but very large difference. I also gets B wrong, in fact just ignore it.

Well that explains why my charts are wrong, since my charts display the wiki's dodge penalty. At least I can say I wasn't embarrassed by an arithmetic error!

[greedo]

Incidentally. this is one of the few equations that you really don't need to source dive and go crazy since it's all in one file , I will past every bit of code here. This is ignoring stepdowns.

  Code:


//GREEDO- This is basically 10 + size, using I think the 4,2,0,-2 scale not 2,1,0,-1
const int scale = 100;
const int size_base_ev = (10 + size_factor) * scale;

//GREEDO- EV
    const int prestepdown_evasion =
        size_base_ev
        + _player_armour_adjusted_dodge_bonus(scale)
        - _player_adjusted_evasion_penalty(scale)
        - you.adjusted_shield_penalty(scale);

//GREEDO- Dodge - dodge penalty.
static int _player_armour_adjusted_dodge_bonus(int scale)
{
    // stepdowns at 10 and 24 dex; the last two parameters are not important.
    const int ev_dex = stepdown_value(you.dex(), 10, 24, 72, 72);

    const int dodge_bonus =
        (70 + you.skill(SK_DODGING, 10) * ev_dex) * scale
        / (20 - _player_evasion_size_factor()) / 10;

//GREEDO-Basically encumbrance, see below a bit
    const int armour_dodge_penalty = you.unadjusted_body_armour_penalty() - 3;
    if (armour_dodge_penalty <= 0)
        return dodge_bonus;

//GREEDO- Ignore the first return
    const int str = max(1, you.strength());
    if (armour_dodge_penalty >= str)
        return dodge_bonus * str / (armour_dodge_penalty * 2);
    return dodge_bonus - dodge_bonus * armour_dodge_penalty / (str * 2);
}

//GREEDO- basically encubrance
int player::unadjusted_body_armour_penalty() const
{
    const item_def *body_armour = slot_item(EQ_BODY_ARMOUR, false);
    if (!body_armour)
        return 0;

    return -property(*body_armour, PARM_EVASION) / 10;
}

//GREEDO-AEVP, no need to look here, wiki gets it right
int player::adjusted_body_armour_penalty(int scale) const
{
    const int base_ev_penalty = unadjusted_body_armour_penalty();

    // New formula for effect of str on aevp: (2/5) * evp^2 / (str+3)
    return 2 * base_ev_penalty * base_ev_penalty
           * (450 - skill(SK_ARMOUR, 10))
           * scale
           / (5 * (strength() + 3))
           / 450;
}

//GREEDO - just AEVP + encumbrance/3
static int _player_adjusted_evasion_penalty(const int scale)
{
    int piece_armour_evasion_penalty = 0;

    // Some lesser armours have small penalties now (barding).
    for (int i = EQ_MIN_ARMOUR; i < EQ_MAX_ARMOUR; i++)
    {
        if (i == EQ_SHIELD || !you.slot_item(static_cast<equipment_type>(i)))
            continue;

        // [ds] Evasion modifiers for armour are negatives, change
        // those to positive for penalty calc.
        const int penalty = (-property(you.inv[you.equip[i]], PARM_EVASION))/3;
        if (penalty > 0)
            piece_armour_evasion_penalty += penalty;
    }

    return piece_armour_evasion_penalty * scale / 10 +
           you.adjusted_body_armour_penalty(scale) ;
}



There's a lot of * and / by 10s you should ignore btw.

Edit: Added GREEDO comments.

[MainiacJoe]

I'll print out your code and look at it this evening, then hopefully make new (correct!) charts. Thank you so much.

[greedo]

Yeah, I probably made mistakes in my own formulas, but it appears in my own rough calculations that everything but AEVP is making sense to me, which is coming up essentially 0 in hand calculations. So I'm going to throw in some logs in game and have it spit out aevp for me.

Edit: While the simplified AEVP I have about is a bit wrong, it is very low, and for "normal" values is always going to be ~ 1 or 2 for dodging purposes. E.g. deep elf getting ring mail has 280 with 4 str and no armour, which cuts off only about 2 dodging since it's in the 100s scale. I would ignore it really. Which is funny since I thought it was a big deal since it was squared, but looks like it's only a big deal for spellcasting.

Edit: yeah my aevp is off by a factor of 10, fixed. It's still very small, though, and only seems to matter, in dodging anyways, in the beginning of the game when you have no dodging skill.

As for dodging penalty, the thing that matters really, looks like size has no part in the dodging penalty and the bigger your dodge the more penalty, which means spriggans etc probably have a worse time. Not because size matters, just because they've got more dodging to lose.

And as a heuristic, seems like if you have strength = encumbrance - 3 you lose about half of your dodging, double strength would mean losing a quarter, and 33% with an extra 50% of e-3.

So: In FDA you lose 50% at 8 str, 33% at 12, 25% at 16.
In CPA you lose 50% at 20, 33% at 30, and 25% at 40, etc
Quicksilver you lose 50% at 4, 33% at 6, 25% at 8

'Kinda surprised it boils down to a pretty simple formula. I would say then that what matters less is armour and more str in relation to dex. So basically, my recomendation would be, interpolated between these:

Quick/ring: str = dex/3
FDA: str = dex
CPA: str = 2*dex

[MainiacJoe]

As for dodging penalty, the thing that matters really, looks like size has no part in the dodging penalty and the bigger your dodge the more penalty, which means spriggans etc probably have a worse time. Not because size matters, just because they've got more dodging to lose.

Yes I found this, too. And with the new formula, there is no way to eliminate the dodging penalty altogether (though perhaps it goes away with enough strength and a low enough EVP under integer division).

[greedo]

Well you could get low enough that it's dwarfed by the gauarnteed e/3 reduction. I think the weird thing about all this is that if you have like 27 dodging and 24 dex, you really benefit a lot from getting like 30 strength even in fire dragon armour. So chei worshippers with high dodging actually could get sick amounts of ev and armour in medium armour instead of taking heavy, same with zin worshippers and demigods.

[MainiacJoe]

Found it.

In the dodge term, bring the 1 / (20 - size) into the dodge penalty term: (7 + dodge*dex)[1 / (20-size) - (enc - 3)/(20- size)]. In this last term then denominator is smaller for small races, and so the penalty from encumbrance is greater. The smaller 1/(20-size) term for them is negligible in comparison.

So for small races, it's not just that they have more EV to lose, but this encumberance penalty takes a larger percentage of what was gained from dodging away as well.