Continuing the quest to find out how damage to knights actually works, I've done some further testing. Hopefully this time I've gone into enough depth with it to be useful. The results are a little more precise and a little different from previously.

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I've tested several combinations of Piercing defense on D19 spikes. Now, I don't know how spikes compare to enemies. But spikes deal pure Piercing damage and armor with Piercing defense defends against it, and arenas make spikes easy to use, so it's a start. I'd like to know how spikes work before I move on to the enemies. I have tested 18 configurations of Piercing resistance.

For non-gunners, the Justifier I'm using is defensively identical to Skolver.

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Damage is nonrandom and it is not rounded to half-bars or quarter-bars. Rounding at that level is a popular misconception.

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I am pretty certain that the health display rounds up to the nearest half-bar. Why? Well, it explains how we can have a full display of health without actually having full health. It also is nice because it means we'll never have an empty bar of health without actually being dead. But most importantly, every damage test I've done has these properties:

- Each hit of a certain type can have two possible visible values for health bar damage; these values differ by half a bar
- The first hit taken from when my knight is at full health is always the lesser of these two values

I can think of no other display rounding algorithm that would produce this effect. Let me know if there is one.

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Next, assuming that the above effect is true, we can see that any amount of damage will produce a specific chain of visible bar damage over the course of many attacks. For example, hits of 3.65 bars would produce the chain 3.5, 3.5, 3.5, 4, 3.5, 3.5, 4, 3.5, 3.5, 4, 3.5, 3.5, 3.5, 4, 3.5, 3.5, 4, 3.5, 3.5, 4...

In all 18 of the configurations I tested, I observed and recorded the visible damage chains and then compared these to the damage chains for various real damage values. I recorded about 20 damage values for each to get a good look at the chains. I found that every one of these chains fits exactly into one of the results for a real damage value that is a multiple of 1/40 of a bar.

From this, I conclude that every health bar is worth 40 points of HP. Other possibilities exist, such as multiples of 40, or HP that varies by depth. However, for the purposes of this data, 40 HP per bar will suffice.

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DATA

Pierce Defense = Damage

No Pierce Defense = 194
1x Justifier = 146
2x Justifier = 98

So each piece of Justifier seems to reduce the damage by 48 points. So far so good.

1x Justifier = 146
1x Justifier + 1x Pierce Max UV = 128
2x Justifier = 98
2x Justifier + 1x Pierce Max UV = 78
2x Justifier + 2x Pierce Max UV = 69

18 points for Pierce Max on top of one piece of Justifier. 20 points when it's on top of two pieces. The second Pierce Max UV is significantly weaker than the first. This is inconsistent with the idea that any given piece of gear reduces defense by a given amount.

No Pierce Defense = 194
1x Royal Jelly Band = 183
2x Royal Jelly Band = 172

Each Royal Jelly Band seems to reduce the damage by 11 points. Let's see if that's consistent with other armor configurations.

1x Justifier = 146
1x Justifier + 1x Royal Jelly Band = 135
1x Justifier + 2x Royal Jelly Band = 124

Check.

1x Justifier + 1x Pierce Max UV = 128
1x Justifier + 1x Pierce Max UV + 1x Royal Jelly Band = 117
1x Justifier + 1x Pierce Max UV + 2x Royal Jelly Band = 106

Check.

2x Justifier = 98
2x Justifier + 1x Royal Jelly Band = 83
2x Justifier + 2x Royal Jelly Band = 76

Not so much. Yes, two bands reduce the damage by 22 points, but for some reason the first one does 15 and the second does 7. And I triple checked these values, so it's not an error on my part. Very odd.

2x Justifier + 1x Pierce Max UV = 78
2x Justifier + 1x Pierce Max UV + 1x Royal Jelly Band = 72
2x Justifier + 1x Pierce Max UV + 2x Royal Jelly Band = 68

6 points, then 4 points. It seems there's a threshold at which the importance of more defense decreases (diminishing returns).

2x Justifier + 2x Pierce Max UV = 69
2x Justifier + 2x Pierce Max UV + 1x Royal Jelly Band = 66
2x Justifier + 2x Pierce Max UV + 2x Royal Jelly Band = 63

3 points each. Even less.

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The data's a little weird, but here's what I came up with. The only thing I can think of is a split damage formula:

1) If defense <= two pieces of Justifier, use flat values. That is, each piece of gear reduces damage by a certain amount.
2) If defense > two pieces of Justifier, use a diminishing returns formula. I don't know what formula.

What I don't have, and would be very useful in determining if this is accurate is a Pierce UV on a piece of non-Pierce armor. If anyone's got one and wants to help out with this test let me know. Probably doesn't have to be a Max.

Given that this is true (and that's a big if due to the lack of data), then the concept of diminishing returns is false before a certain point and true afterward. There appear to be three important points. The first is the point at which the formula splits. At two pieces of Justifier (220 pixels)? Perhaps at 200 or 225? Somewhere else?

The second important point is in the middle of the diminishing returns formula, which appears to start out by actually providing a higher rate of return per defense than the flat formula (which is why a Pierce Max UV provides more defense on two Justifiers than on one Justifier, and why a Royal Jelly Band on two Justifiers is 15 points instead of 11). The point in question is the one where the rate of return drops below the flat formula's rate such that further defense truly begins to be less and less effective. A true min-maxer might want their defense to be at this point because it provides the greatest possible defense per pixel, but that's a little nitpicky.

After the above point, the rate decreases, and eventually the defense per pixel returns to be in line with the flat formula's rate before dropping off further. This point appears to be around 2x Justifier + 2x Royal Jelly Band (276 pixels). This is in line with the 2x Royal Jelly Band providing 22 pixels whilst the first provides 15 and the second only 7. Is it at 275? Somewhere else?

The conclusion here is that 1 Max UV (and any lesser UVs as well) on top of two pieces that provide the same type of defense is quite good, and anything more than that not so much. Again, that's if the split formula is true, if spikes are the same as enemies, if D19 is similar to all other floors, etc. There are a lot of variables to eliminate, but it's an idea. Probably wrong given my track record on this, but hey.

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If you've got any other ideas about how to interpret the data, let me know. I intend to do some more testing on other floors (for real this time) and possibly with wolvers. Hopefully that will provide further insight.