I recently conducted a test aimed at determining what effects armor has on damage received, including defensive UVs and trinkets. There have been a few such tests done before, but I was not satisfied with the results. So I conducted my own; my findings are here.
Method
I had come into possession of a Gunslinger hat with Max Pierce defense which I decided to make into a Justifier. Justifier is the defensive equivalent of Skolver. I also have a full set of Nameless, the defensive equivalent of Vog Cub, a Justifier hat with a non-Pierce UV, and a 5* Pierce reduction trinket. This provides me enough flexibility to mix and match armor to hit several different levels of Pierce defense.
Unlike previous tests, testing on Pierce provides me a very controlled source of damage which, combined with an elevator pass, allows me to conduct as many tests as I want for free. That is, spikes. I chose to do the tests in an arena (depth 19), where I have access to both spikes and a healing pad, using an alt account to allow me to leave and join as many times as I want.
Before testing for damage, I had to make sure that spikes deal pure Pierce damage. I did so by equipping two separate pieces of armor with no Pierce defense and vastly differing levels of Normal defense. I took the same amount of damage; as such, I concluded that spikes deal pure Pierce damage.
Findings (Part I)
As I was doing the test, I noticed one thing: the damage which I received when wearing any given armor configuration followed the same pattern every time. Specifically, if I took 4.5 bars of damage on the first hit and 5 bars of damage on all other hits, then after healing to full and taking damage a second time, I would again receive 4.5 on the first hit and 5 on all other hits. From this, I can conclude that damage is nonrandom, much like the damage we deal to enemies is similarly nonrandom.
Secondly, I also noticed that the amount of damage received by any given attack does not follow any logical pattern regarding any rounding of damage to the nearest fourth-bar. Since damage is nonrandom, I can conclude that knights actually have numeric HP, much as monsters do, and that the pips on our health bars are merely a rounded display for easy viewing rather than anything that meaningfully affects damage received. Specifically, they are rounded up to the nearest half-pip.
One further conclusion to be made from this is that when recording damage received from an attack, it's important not to simply include the low and high points (i.e. I received 4.5-5 damage), but rather their relative frequency to each other (i.e. I received 4.5 damage once and 5 damage five times), to more accurately determine how much damage is actually being received.
Results
Nameless 4.5-5, 4.5 once, 5 all other times
Trinket 4.5
1x Justifier 3.5-4, 4 rarely
1x Justifier & Max UV 3-3.5
2x Justifier 2-2.5, 2 once, 2.5 all other times
2x Justifier & Max UV 1.5-2, 1.5 once, 2 all other times
2x Justifier & Max UV & Trinket 1.5-2, slightly closer to 2
Findings (Part II)
These results are consistent with the displayed Pierce defense bar in my knight's equipment loadout. I therefore conclude that the defense bar is accurate. One thing to note is that my Max Pierce Justifier actually exceeds the length of its own Pierce bar by a few pixels. These pixels are seen in the combined loadout, so it can be assumed that there is no defense cap on any one piece of equipment. Whether there is a combined defense cap in the entire loadout remains to be seen. Method for measuring bars here: http://wiki.spiralknights.com/User:Antistone
Spiral Knights is a video game, and therefore need not be subject to rigorous statistical analysis, as video games produce very deterministic results. All values should fit exactly into the damage formula as it is with no deviation at all beyond that produced by rounding. The rounding to half-bars which is done by the game provides a layer of uncertainty to us as to how much damage we are really receiving, so we cannot precisely say what the damage formula is, but we can get pretty close.
[Removed this portion of analysis as it turned out to be incorrect, read later posts for details]
Monster Defense Guide (At a Glance)
Data types taken from wiki:
Wolver - Normal/Pierce
Chromalisk - Pierce
Jelly/Ice Jelly - Pierce
Minis/Blast Cubes/Rock Cube/Imposto - Normal
Lichen - Normal (tackle), Pierce (spikes)
Polyp - Pierce
Oiler - Pierce
Quicksilver - Pierce (tackle), Elemental (zap)
Gun Puppy - Normal/Elemental
Lumber - Normal/Elemental
Mecha Knight - Normal/Elemental
Retrode - Normal (swipe), Elemental (beam)
Scuttlebot - Normal
Gremlin Melee - Normal
Gremlin Bomber - Normal
Gremlin Scorcher - Elemental
Devilite - Normal/Shadow
Greaver - Shadow
Trojan - Normal
Howlitzer - Shadow
Spookat - Normal/Shadow (bite), Shadow (bullet)
Zombie - Normal/Shadow
Phantom - Shadow
Grimalkin - Normal/Shadow
Slags - Normal
Spikes - Pierce
Elemental Grates - Elemental
Explosion Boxes - Elemental
Further Questions
- What percentage of dual-type monster attacks is Normal damage? Does it vary by monster?
- What percentage of dual-type monster attacks is Normal damage in tier 2? What about pure-type monster attacks?
- Hypothesis: All typed damage is converted into 50% normal, 50% type.
- How is armor defense scaling done across tiers?
- Base damage from attacks increases with each successive depth. How is this done?
- Shield defense: how is it done?
- Hypothesis: Shield defense works the same way armor defense does, including UVs.
- How much HP do knights have per bar?
- Analysis for Lockdown.
This is a remarkably detailed analysis, thank you.
Hopefully this adds more information to the collaborative efforts of various forumers to unlock the mysteries of SK's game mechanics!
Could you elaborate a bit more on how you came to your conclusions regarding your Damage Formula, though? I'm a little confused about that part(I'm not much of a mathematician, I'm afraid).
Also, that hypothesis about Gremlins and health capsules to determine a more accurate player HP....if that actually worked, that would be something very significant.