Shadow Fade nerfed?

[Snarglefrump]

Now that the Ghostly item effect provides incorporeality rather than concealment, I wanted to see if it stacked with the Ninja Spy Shadow Fade effect. My measurements (156 attacks from a kobold) seem to suggest:

• They do not stack.
• Incorporeality is checked before Dodge.
• Shadow Fade provides a 15% incorporeality bonus.

I had always read that Shadow Fade provided a 25% incorporeality bonus, although I had never personally measured it before.

Can anyone confirm?

Links to older measurements for comparison would also be useful.

[Kielbasa]

If shadow fade is not currently providing 25% incorporeal then bug report it.

[OliviaCrowley]

You have to look at shadow fade as a 25% increase to your total effective avoidance.

If I have 0% avoidance from AC, and Shadow Fade, then I will avoid one quarter of all attacks.

If I have 50% avoidance from AC, and Shadow Fade, then I will effectively avoid 62.5% of all attacks.

Total avoidance is a matter of multiplying together all sources you have. If I have 50% Defense from AC, 25% from Shadow Fade, 10% from Dodge, and a Blurry item (replace blurry with CK for true-seeing boss calculations), then I will have: 0.5 * 0.75 * 0.9 * 0.8 = 0.27, or effectively a 73% chance to avoid an attack.

Mathematically you will still take 25% fewer attacks at 50% defense as you would at 0%. If you can absolutely prove that this isn't the case, then it is indeed an issue.

[Potta]

Incorporeality bonuses do not stack, so it's a nerf in the perspective that something that used to be unique to us has been given in a weaker form to others at the expense of us being able to provide our own concealment bonus. But really, it's not a big deal. It will stack with bonuses to concealment miss chance. And blur will be available in almost any 6 man group. It's also a low level scroll (now 5 minutes base duration afaik now) that can be fairly easily handled by any moderate investment into UMD - something that is now very advisable with the +5 skill you'll get in epic levels. It'll also be available from items that offer Blurry.

As regards the 15% thing, it's hard to say for sure without seeing the numbers, but I think that you're making a mistake with your sums. Say you got 150 attacks, it'd be tempting to say that 25% of that would result in ~37 occurences of Incorporial miss. That temptation is wrong however, because the Incorporial roll is done after the AC roll. Say you had a 50% miss chance against that Kobold, now only 75 attacks make it through to even check against your incorporial percentage. 25% of that 75 would be ~19 attacks, which compared to the 150 attack number is ~13%.

[Snarglefrump]

Mathematically you will still take 25% fewer attacks at 50% defense as you would at 0%. If you can absolutely prove that this isn't the case, then it is indeed an issue.

Below is data. My toon was using Shadow Fade, has 14% Dodge, and no concealment. The monster was the first kobold I encountered going north in the Waterworks explorer area (his buddies met an untimely demise).

Incorporeal: 24
Dodge: 18
Miss (AC): 91
Hit: 23
Total: 156

Incorporeal: 15.38% of all attacks.
Dodge: 13.64% of all attacks not missed due to Incorporeal (almost exactly the expected 14%)
Miss (AC): 79.82% of all attacks not missed due to Doge or Incorporeal.
Hit: 100% of all attacks that were not missed.

The 95% confidence interval on the incorporeality with 156 measurements is about 6.8 percentage points. 15.38 is not within 25 +/- 6.8, ergo the data is not consistent with Shadow Fade providing a 25% incorporeality miss chance.

[Snarglefrump]

That temptation is wrong however, because the Incorporial roll is done after the AC roll.

I've read several times that incorporeality comes before the AC roll. Moreover, your hypothesis is not consistent with my data. If incorporeality were after AC and Dodge, both my dodge and incorporeality would have to be greater than 35%.

[Snarglefrump]

For completeness:

If we assume Dodge is checked first:
Dodge: 11.54% of all attacks
Incorporeal: 17.39% of all attacks not dodged
Miss (AC): 79.82% of all attacks not dodged or incorporeal
Hit: 100.00% of all attacks not missed.

17.39% is still not within the 95% confidence interval (25 +/- 7.2), although it's close. Dodge is somewhat far from the expected value of 14% (but 11.54 is within the 95% confidence interval of 14 +/- 5.6). I'll try to gather more data later.


If we assume AC is checked first:
Miss (AC): 58.33% all attacks.
Incorporeal: 36.92% of all attacks not missed due to AC.
Dodge: 43.90% of all attacks not missed due to AC or incorporeal
Hit: 100.00% of all attacks not missed.

I think we can safely reject the AC-first hypothesis.

[OliviaCrowley]

Hard Numbers.

Thank you for your testing. I would help on my end, but I'm not dark and I'm not going to risk losing stuff with an LR. Given your testing, yes, this looks like you may be spot on.

[Potta]

I still think you're wrong about it being less than 25%. Those permutations are hardly thorough. The sample size, while okay, is still a little small. And we're not considering possible confounding factors like shortcuts taken for code efficiency.

What if there's a shortcut in the code to improve efficiency. What if the attack roll is made in a separate function which is passed to the overall function which decides if there's a hit. And what if some clever coder has thought, "Hey, I could avoid all these CPU cycles in 5% of cases if I check for a 1 at the start. I won't have to check for Dodge, Concealment, Incorporeal or make the AC comparison." 95% of the time it takes an extra 1 CPU cycle. Totally insignificant. That 5% of the time, it's a decent improvement. It's the sort of optimization I'd expect to see. That effects your numbers.

With 156 attacks, if 5% of them are missed at the start, that makes this:

5% - Auto Miss
16.2% - Incorporeal
14.5% - Dodge
85.8% - Miss
100% - Hit


Slightly more likely, but still not satisfactory.

OR

5% - Auto Miss
12.1% - Dodge
70% - Miss
61.5% - Incorporeal

Definitely not this.

OR

5% - Auto Miss
12.1% - Dodge
18.4% - Incorporeal
85.8% - AC

I think this is the closest yet. It's close enough to 25% for this small sample size to be possible. We could compare it with the 10% Incorporeal from a ring and see what kind of figures we get for that.