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Comparison of Mounts

November 16, 2014 4 comments

Nowadays there’s a shitload of various kinds of mounts available in Age of Conan, and I was getting a bit confused about their speed and various other properties, so I decided to conduct a few measurements.

To measure the speed, I chose a section of road in the northern half of the Wild Lands of Zelata, starting at (526, 1028) and moving east from there. I used several different end points depending on how long a course I wanted: ending at (671, 1053) gives you approx. 150 meters; ending at (721, 1058) gives you 200 m; ending at (982, 1174) gives you 500 m; and ending at (992, 1314) near the Wild Plains rez pad gives you 650 m. I used the longer courses for testing the faster mounts, and the shorter ones for slower mounts. In particular, the 150 m course is useful for testing sprinting with those mounts that would run out of energy before completing the 200 m course.


(Click to enlarge.)

Of course the time measurements (using F9) are only accurate up to 1 sec, so the resulting calculations of speed are only approximate. Each speed is based on the average time of 2 or 4 runs. All the speed tests were done with a level 80 guardian with 800 skill points in the Running skill and without any other speed buffs (e.g. from armor).

Note that each mount has 3 possible speeds: walk, run, and sprint. Sprint is when you hold the shift key; otherwise, you’re walking or running, and you can use backspace to switch between walking and running mode. (If you press shift, the sprint speed is the same regardless of whether you started in walk mode or run mode.) Walking while mounted is very much not recommended, as it is even slower than walking on foot!

Another measurement that I found interesting was the turning speed of the mount. In my opinion, one of the big advantages of e.g. a tiger compared to a swift horse are that a tiger can turn more quickly; with a horse you either have to slow down or make a much bigger circle before you manage to turn around. I measured turning speed by standing in one place and holding the A key until I made 10 full turns, then dividing the time it took to do this by 10.

Before proceeding, it’s worth taking a look at the update notes for update 3.3.8, which included the sprinting revamp (introduction of the Energy resource) and a minor revamp of mounts. As the update notes say, the mounts are now divided into 5 categories and all mounts from a particular category are supposed to have largely the same stats and abilities. This categorization is still useful, although there were some exceptions to it even at the time of 3.3.8 and there are a few more exceptions to it now; more on that later.

Category

Buff

Total
sprint
time

Time
to
regen.

Speed [km/h]

Turn
time
[s]
Sprint

Run

Walk
Exotic Mounts

−35 stagger

32

9

62

39

6.5

4.2
Level 80 Mounts

−20/35/40 stagger

32

9

54

42

6.5

6.3
54

39

6.5
Level 40 Mounts

−20 stagger

17

9

42

31

6.5

6.3
Basic Mounts

nothing

12

24

37

29

6.5

6.3
34

25

6.5
Siege Mounts

+1900 HP, −40 stagger chance

22

9

29

22

5.4

12.6
no mount

nothing

16

16

25

20

8.0

1.8

In the lists below, an asterisk * marks mounts that I haven’t tested myself.

(By the way, for another great overview of AoC mounts, see this post on Henryx’s blog: link.)

Exotic mounts

This category consists of tigers, wolves, Yothian war-mares, and Hyrkanian horses. They require the Exotic Animal Handling skill. As far as I know, all the mounts in this category have the same speeds and the same buff (−35 chance of being staggered).

But in addition to that, some of these mounts have special abilities: the faction tiger can hide; wolves have the Terrifying Howl ability (which puts a 50% hinder movement debuff for 10 sec on nearby enemies; 60 sec cooldown).

Tigers

  • Vaaghasan Slaughter Steed: this is the tiger from the Tamarin’s Tigers faction. To get it, you need to be rank 4 with them, complete a quest chain and buy a saddle, which costs 800 marks of acclaim and 10 gold. As far as I know, this is the only mount that can hide. It’s available in three colors (light, dark and black) but they all have the same name.
  • White Vaaghasan Slaughter Steed*: this tiger was available with some subscription offers.
  • Purebred White Vaaghasan Slaughter Steed*: from the item shop (900 Funcom points).
  • Imperial Bronzesteel Slaughter Steed*: sold by gilding vendors (13 gilding tokens); formerly also available in the item shop [1, 2].
  • Imperial Shadowsteel Slaughter Steed*: sold by vendors in PvP armories (120 campaign badges + 5 gold).
  • Imperial Greensteel Slaughter Steed: sold by the Hand of Glory faction vendor in Ardashir (requires no faction rank; costs 500 marks of acclaim + 200 rare trophies + 5 gold).
  • Imperial Bluesteel Slaughter Steed*: drops from the Zodiac in the Jade Cidatel (T4 raid).
  • Imperial Redsteel Slaughter Steed*: was available in the past in the item shop [1, 2].

AFAIK the only difference between these various tigers (apart from the hide ability on the original faction tiger) is in the color and shape of their armor and other paraphernalia.

Wolves

  • Ridden Death: this is the wolf from the Wolves of the Steppes faction. To get it, you need to be rank 4 with them, complete a quest chain and buy a saddle, which costs 800 marks of acclaim and 10 gold.
  • Xanthic Ridden Death*: from the item shop (1260 Funcom points).
  • Bluefury War Wolf: drops from the Imp in the Jade Citadel (T4 raid).
  • Greenfury War Wolf: sold by the Hand of Glory faction vendor in Ardashir (requires no faction rank; costs 500 marks of acclaim + 200 rare trophies + 5 gold).
  • Shadowfury War Wolf*: sold by vendors in PvP armories (120 campaign badges + 5 gold).
  • Bronzefury War Wolf*, Redfury War Wolf*: these two were available in the past in the item shop [1, 2].

AFAIK the only difference between these various wolves is in the color and shape of their armor and other paraphernalia. All the wolves I’ve tested (Ridden Death, Bluefury, Greenfury) have the Terrifying Howl ability.

Yothian War-Mares

These mounts are only available in the item shop, where they cost 972 Funcom points each. Three variants are available (Green Yothian War-Mare*, Purple Yothian War-Mare, Red Yothian War-Mare*).

Perhaps you remember the Curses of Travius Blacktongue quests in the Armsman’s Tavern in Tarantia Noble District. One of the insults you use during the conversation with Travius includes the following line: “Your riding skills resemble the most debased acts of love between beast and man.” Well, this is what I’m always reminded of when I see someone riding a Yothian War-Mare: it looks as if the player was molesting an enormous snail. Additionally, having now tried riding one myself, it makes your entire screen wobble left and right so badly that I almost got seasick after just a few minutes of riding. So I very much don’t recommend these mounts.

On the positive side, you might not expect an oversized snail (with hands) to be as quick as a tiger, but it is — I measured.

Hyrkanian horses

To buy these horses, you need to be rank 4 with the Hyrkanian faction; each horse costs 800 marks of acclaim and 10 gold. The Hyrkanian horses are the only horses that have the same speed or maneuverability as a tiger or wolf, so they are a great choice if you find the looks of the tiger or wolf to be too exotic. Other swift horse mounts (which we’ll see in the next category) are slower.

The following 8 horses are available; each is painted with a different pattern:

  • Hyrkanian Bitter Wind-Biter*
  • Hyrkanian Dread Ash-Tramper*
  • Hyrkanian Fleet Scream-Catcher*
  • Hyrkanian Grim Skull-Treader*
  • Hyrkanian Pale Ghost-Chaser*
  • Hyrkanian Resplendent Sun-Strider
  • Hyrkanian Sable Shadow-Dasher*
  • Hyrkanian Wicked Chaos-Clapper*

Other mounts

The Great Khan’s War Bringer (a legendary mount which can drop from the Hoard of the War Bringer, a lottery box that was introduced in the item shop in February 2015; the horse is also tradable between players) also belongs to this category. It looks like an armored horse, but has the same speed (including turning speed) as tigers, wolves etc. Unlike all the other mounts in this category, this one requires just 7 seconds to fully regenerate its energy (others require 9 seconds). Its mounted buff is −50 chance of being staggered.

The Hoard of the War Keeper can also drop another mount, Swift Ymirish Colossal Cold One, which we’ll see in the next category. (In the early days the hoard was bugged and this mount couldn’t drop, but it was fixed in a subsequent hotfix.)

Level 80 mounts

This category includes various non-exotic armored and swift mounts. In our table above, there are 2 rows for this category, because some of the mounts in it have a slightly higher run speed than the others. These will be noted below, but most of the mounts in this group belong to the slower subgroup (39 km/h run speed instead of 42 km/h). (In fact, by now a pattern is starting to emerge: it seems that all the horses are in the slower subgroup and all the non-horses are in the faster subgroup.)

Armored horses

There are 32 armored horses, all named systematically X-barded Y Horse, where X is the color of the armor (Azure, Dark, Pale, Umber) and Y gives the color of the horse itself (Buckskin, Dapple Gray, Fading Black, Mahogany Bay, Rabicano, Skewbald Pinto, Tobiano, White). The horse vendors in hub cities (Conarch Village, Old Tarantia, Khemi) sell only the Azure variants; the horse vendor in your guild city sells all variants. Each horse costs 50 gold. The buff while mounted is −20 chance of being staggered.

Swift horses

There are 8 swift horses, named Swift Y Horse, where Y is one of the horse colors, same as above. They are sold by horse vendors in hub cities (Conarch Village, Old Tarantia, Khemi), where they cost 150 gold each; in the item shop (1125 Funcom points each); and by veteran vendors (85 veteran tokens each). The buff while mounted is −20 chance of being staggered.

Miscellaneous

We’ll start with a few mounts that have recently been added to the reliquary vendors. The first two of these have the peculiar feature that their run speed is about 10% faster than that of the other mounts in this category. Perhaps this applies to the Swift Killer Rhino as well, but I haven’t tested it yet (so TBH I can’t even be completely sure that it belongs to this category at all).

  • Fleet Black Riding Camel: sold in the reliquaries (1 rare relic + 120 simple relics III + 15 gold). Buff: −20 chance of being staggered.
  • Swift Hyperborean Siege Mammoth: sold in the reliquaries (50 simple relics I + 40 gold). Buff: −40 chance of being staggered (unlike the normal siege mounts, you get no HP buff from this one).
  • Swift Killer Rhino*: sold in the reliquaries (50 simple relics II + 40 gold).

Anyway, if you ever wanted a mammoth or rhino that handles exactly like a traditional swift horse, now’s your chance to get it! 🙂

The Wolf Pict Envoys in the PvP armories also sell two swift siege mounts: Swift Vendhyan Thundering Colossus* (a kind of mammoth) and Swift Wolf Pict Rampaging Behemoth* (a kind of rhino); each costs 300 victory tokens (from open-world PvP objectives). Judging by the tooltips, their mount buff gives you −80 chance of being staggered. I don’t know how fast they are, but I imagine they most likely belong to this category, same as the other swift siege mounts mentioned above.

Another siege mount in this category is the legendary Swift Ymirish Colossal Cold One, which drops from the Hoard of the War Bringer (see above). It looks like a white mammoth with some red markings; mounting it morphs you (the player character) into an Ymirish frost giant; and it has the usual siege mount buff (1900 HP, −40 chance of being staggered). In terms of speed, this mount belongs to the faster subgroup of this category.

Next, we have a few more horse mounts. The ones that I haven’t tested yet (marked with an asterisk) are included in this list tentatively; I can’t be completely sure that they belong to this category, though I think it’s unlikely that they belong anywhere else.

  • Swift Stygian Festival Stallion: has a chance of dropping from the Crate of Random Oddities, which you could get by handing in the Sacrificial Marks from the Khemi Halloween quest (Halloween 2014). Buff: −35 chance of being staggered. Unlike all the other mounts in this category, this one requires just 7 seconds to fully regenerate its energy (others require 9 seconds).
  • Tarpani Stallion: quest reward from a quest that becomes available in your guild city at renown level 20. In the process of doing the quest, you’ll have to pay 200 gold. Buff: −35 chance of being staggered, +590 protection.
  • Purebred Tarpani Stallion*: from the item shop (1890 Funcom points).
  • Stygian Halfbreed*: quest reward from a quest that becomes available in your guild city at renown level 15. In the process of doing the quest, you’ll have to pay 200 gold.
  • Swift Shemite Horse*: sold by the horse vendor in your guild city (from renown level 10); costs 150 gold.
  • Purebred Shemite Horse*: from the item shop (1575 Funcom points).

We also have two mounts that were introduced with the achievement system:

  • Hyrkanian Riding Camel: you get this mount by reaching 1000 achievement points. Mounted buff: −20 chance of being staggered. Unlike the other mounts in this category, its total sprint time is just 17 sec (same as for level 40 mounts). Apart from that, it has the same speeds (and turning time) as the swifter subgroup of this category (i.e. like the Fleet Black Riding Camel and the Swift Hyperborean Siege Mammoth).

  • Swift Cimmerian War Mammoth: you get this mount by reaching 7500 achievement points. Mounted buff: +1900 HP, −40 chance of being staggered. In terms of speed, turning time, and stamina, it behaves exactly like the Swift Hyperborean War Mammoth mentioned above.

One thing that I haven’t investigated in my tests is which mounts can do decent siege damage; I imagine that mammoths, rhinos and armored horses can do siege damage, but I’m not sure about e.g. the Tarpani Stallion and the like.

Level 40 mounts

This category seems to consist of nothing but plain ordinary horses. They are named simply Y Horse, where Y is one of the eight horse colors (see above). You can buy them from the horse vendors in hub cities (75 silver each); from the item shop (495 Funcom points each, except the White Horse, which costs 1125 Funcom points!); and from the veteran vendors (3 veteran tokens each). The mounted buff is: −20 chance of being staggered.

Siege mounts

These are noticeably slower than other mounts, and are particularly slow at turning. Their mounted buff is: +1900 health, −40 chance of being staggered.

  • Blue Snow Mammoth, Purple Snow Mammoth*, Red Snow Mammoth*: sold by horse vendors in the hub cities (Conarch Village, Old Tarantia, Khemi). The blue one has also been included in some subscription offers.
  • War Mammoth: was included with some pre-order and subscription offers.
  • Killer Rhino: was included with some pre-order and subscription offers.
  • Purebred Killer Rhino: available from the Hand of Glory faction vendor in Ardashir (requires rank 4; costs 10 gold); also from the item shop (990 Funcom points).
  • Purebred War Mammoth*: from the item shop (990 Funcom points).
  • Tuskripper War Mammoth*: from the item shop (990 Funcom points).

Basic mounts

This category includes the (non-swift) camels and the recently introduced Reaver’s Steed. Their main feature is supposed to be that they are available from very low levels (Reaver’s Steed at level 1, camels at level 20). Reaver’s Steed is a little faster than the camels, which is why there are 2 rows for this category in the table above. The buff you get while riding them doesn’t give you any stat bonuses.

  • Reaver’s Steed: from the item shop, where it appears as Reavers [sic] Stallion (costs 1080 Funcom points).
  • Brown Riding Camel, Dark Riding Camel*, Pale Riding Camel*: from the item shop (1575 Funcom points each, except the Pale one, which costs 1890 Funcom points). The Brown one is also included in some subscription offers.

High ground bonus

October 25, 2014 1 comment

While playing with unarmed mobs in various playfields, I noticed an interesting mechanic that I have hitherto been unaware of: mobs have a hidden damage bonus of up to 5% if they stand on higher ground than you.

I did these tests with unarmed mobs, because that way all the hits are for the same amount, so it’s much easier to notice the difference due to the high ground bonus. Pull a mob and place yourself on some sloping ground, then slowly move around the mob and observe how the amount you’re getting hit for changes.

For example, here’s a level 85 Kang Zai in Paikang; the following table shows just the normal hits (the crits exhibit the same behavior). There are 3 columns of numbers because this type of mob has 3 different white hits.

Position

Hit amount
me above mob

284

342

510
me slightly below mob

289

349

520
293

353

526
me well below mob

294

354

528
me completely below mob

298

359

535

In the last row, I was standing so far below the mob that the mob’s feet were higher than my head. The “me above mob” row covers all situations where I was standing on higher ground (or approximately on the same altitude) as the mob, regardless of how much higher I was. So basically, the mob gets a bonus if you are below it, but it doesn’t get a detriment if you are above it.

You could probably find yet more intermediate damage values than the ones shown here by changing your position around the mob more carefully. (We’ll see an example of that below.)

If you compare the bottom and the top row, you see that the maximum damage (in the bottom row) is about 4.9% higher than in the top row. Probably the intended maximum bonus is 5% and the difference here is just due to the rounding errors — because we see damage rounded off to the nearest integer but the true damage is a non-integer number, the ratio for e.g. the third column could be anywhere between 534.5/510.5 = 1.047 and 535.5/509.5 = 1.051, i.e. the bonus could be anywhere from 4.7% to 5.1%.

Repeating the same experiment with other mobs gives the same results. Here’s a level 85 Hound of the Underworld in Paikang (it has 4 different white hits):

Position

Hit amount
me above mob

181

192

232

245
me slightly below mob

182

193

233

246
184

195

236

249
186

197

238

251
me further below mob

187

198

239

252
188

199

241

254
190

201

243

256
190

201

243

257
me almost completely below mob

191

202

244

257

A similar analysis as above now shows us, in the first column, that the maximum damage bonus could be anywhere between 190.5/181.5 = 1.049 and 191.5/180.5 = 1.061; in the last column, we see that the maximum damage bonus could be anywhere between 256.5/245.5 = 1.045 and 257.5/244.5 = 1.053. Assuming that the bonus is the same for all types of hits, we can conclude that the maximum bonus is somewhere between 4.9% and 5.3%, which confirms the idea that 5% is probably the correct amount.

This phenomenon is not limited to expansion mobs; here’s a level 79 Dagger-Tooth Leopard in Kheshatta:

Position

Hit amount
me above mob

104

105
me slightly below mob

105

106
me well below mob

109

111
me completely mob

110

111

Here the last row is about 5.7% greater than the first row. Of course, the less the mob hits for, the bigger the effect of the rounding errors will be.

Armed attacks

The high ground damage bonus seems to also apply to armed mobs. There it’s more difficult to investigate it because of the variance in armed hits. For the next experiment, I let a mob (level 63 Black Ring Theurgist in epic Ymir’s Pass) hit me about 200 times in each position:

Position

# of
hits

Hit amount
min

max

average

midpoint

me above mob

234

190

290

237.27

240
me below mob

228

199

303

250.58

251

No matter which of these statistics you look at, the ‘below’ hits are about 4.5%-5.5% harder than the ‘above’ hits, so the high ground bonus seems to apply here as well.

Incidentally, there’s something I don’t quite understand about this experiment. For any given position (above or below), you can see that the max/min ratio is approx. 1.52 (i.e. the maximum hit is about 52% stronger than the minimum hit). This is not what I would expect for a polearm-wielding mob: the max/min ratio for polearms should be 1.75 (which you can easily check by comparing the numbers in parentheses after the DPS amount on the tooltip of any polearm). In fact I’m not aware of any weapon type with a max/min ratio of 1.5; for 1he/2he the ratio is 1.6, for 1hb/2hb it’s 1.3, for daggers it’s 1.7 and for staffs it’s 2.35. Perhaps the max/min ratio from the tooltip only applies to a part of the hit (e.g. the part that comes from weapon damage, but not the part that comes from the character’s strength and combat rating etc.)? Anyway, hopefully some day I’ll investigate this stuff a bit further.

Magical attacks

This 5% high ground damage bonus doesn’t seem to apply to magical attacks; I made a small experiment with an Archpriest mob from the Yellow Priests of Yun faction in Paikang. He was nuking me with his ranged elecrical attacks while I moved up and down around him, and all the hits were the for same amount regardless of my location. The same applies to magical attacks by otherwise-melee mobs (I tried with a Wild Quilin, who is mostly melee but has a frost magical attack called Curse of the Quilin).

From protection to mitigation

September 16, 2013 2 comments

Protection is the attribute that enables you to mitigate incoming magical damage. Just as there are five different kinds of magic damage (holy, unholy, cold, electrical, and fire), there are also five corresponding kinds of protection: “protection (holy)”, “protection (unholy)” and so on. When you see generic protection without anything in parentheses after it, as is the case on many pieces of armor, feats, etc., this means that your piece of armor (or feat, etc.) will contribute that amount to each of the five kinds of protection.

Besides protection that you find directly on gear, feats, buffs, etc., you also get some protection from wisdom and intelligence. Each point of wisdom contributes 0.5 points of holy and unholy protection; each point of intelligence contributes 0.5 points of cold, fire, and electrical protection. Wisdom and intelligence come mostly from gear, though some of it is also innate (the exact amount depends on your class and level).


(Click to enlarge.)

In the above example, we have 1213 holy protection, of which (as it turns out) 450 came from having 5/5 points in Holy Wards (passive AA perk) and the rest came from our having 1527 wisdom (of which 190 was innate and 1337 came from gear). Similarly, we have 510 cold protection, of which 450 comes from 5/5 points in Frost Wards and the rest comes from our having 120 intelligence (all of which is innate — this was taken on a ToS, so my gear didn’t have any intelligence on it). I didn’t have any gear or buffs that would be specific to just one type of protection, so the amount of holy and unholy protection is the same, and the amount of fire, cold and electrical protection is likewise the same.

But what I’m really interested in today is the little floating tooltip next to the mitigation column. We see that our holy mitigation is 17.3%, so a hit that would otherwise (if we didn’t have any mitigation) hit us for 1000 points will now hit us for only 827 points of damage. But how exactly do we get from 1213 to 16.5%, and from there to 17.3%?

As you are no doubt familiar with if you’ve been doing any tinkering with combat-related numbers, the most important magic number in Age of Conan is 36.6. It occurs in all sorts of stat-related conversions and calculations. But when it comes to protection, the magic number turns out to be 73.7. You get the initial percentage of mitigation by dividing your protection by 73.7. Sure enough, 1213 / 73.7 = 16.4586…, which the GUI rounds to one digit after the decimal point and thus shows us 16.5%, as we saw in the above image.

After that, invulnerabilities get applied. Invulnerabilities are yet another set of stats, again one for each type of damage; they were more prominent in the pre-1.05 days than now. In my case above, I just have 1% invulnerability, which, as it turns out, comes from guild city buffs: Temple III and Architect Workshop III give you +0.5% invulnerability each, to all types of magic damage. (Tier I and II versions of these buildings give +0.2% and +0.3%, respectively, but it appears that these buffs do not stack.)

So a hypothetical incoming hit of holy damage that would hit us for 1000 points if we had no mitigation or invulnerability would, in our above example, first get mitigated by our protection, which would reduce it by 16.5%, leaving about 835 points of damage. This would then be further reduced by 1% by our holy invulnerability; now, 1% of 835 is 8.35, so that leaves us with 835 – 8.35 = approx. 827 points of damage. Thus you might say that these two things together, protection and invulnerability, have mitigated 1000 − 827 = 173 points of damage, which is 17.3% of the original 1000 points.

So you might say that our overall holy mitigation is 17.3%, and this is the figure that gets shown in the main part of the GUI (which is reasonable, since when you’re getting hit by an enemy, you probably don’t care very much whether incoming damage gets mitigated by your protection or by your invulnerability, as long as it actually gets mitigated).

Let’s summarize these things with formulas:

• Mitigation from protection, in %, is mp = protection / 73.7.

• Mitigation after applying invulnerabilities, in %, is ma = 100 − (100 – mp) · (1 – invul/100), where invul is the bonus invulnerability in %.

The magic number

But how did we get the magic number 73.7? And how reliable is it? To test this, I was swapping my gear around a bit and observing the numbers in the GUI.

At one particular combination of gear, I had 667 holy protection (most of which came 5/5 points in Holy Wards, and the rest from my 434 wisdom), and the GUI showed my mitigation to be 9.1% before invuls and 10.0% afterwards. Now, we know that these numbers are rounded to one decimal point for the sake of display, so the true mitigation after invuls can be anywhere in the range [9.95, 10.05]. If you plug ma = 9.95 into the above formula for ma (with invul = 1) and solve for mp, you get mp = approx. 9.0404%; if you similarly plug ma = 10.05, you get mp = approx. 9.1414. So from the fact that ma is in the range [9.95, 10.05], we can conclude that mp is in the range [9.0404, 9.1414]. But since the GUI showed mp as 9.1%, this means that mp must be in the range [9.05, 9.15]. Combining these two things tells us that mp must be in the range [9.05, 9.1414]. If we denote the ratio protection / mp by R, we now see that R must be at least protection / 9.1414 and can be at most protection / 9.05. Since in our case, protection was 667, this tells us that R must be in the range [72.9646, 73.7016].

I repeated this experiment with a different combination of gear, where I had 1006 holy protection (some from Holy Wards, some directly on gear, and the rest coming from my 812 wisdom), and the GUI showed my holy mitigation to be 13.6% before invuls and 14.5% afterwards. If we analyze this case in the same way as we did in the previous paragraph, we now see that R must be in the range [73.6996, 74.0476].

Combining both ranges tells us that R must be in the range [73.6996, 73.7016]. So as far as I’m concerned, it’s quite hard to imagine that the correct value of R is anything else than 73.7.

(I also observed the mitigation at numerous other values of protection and any R in the above-mentioned range would be able to explain all my observations.)

Extreme invulnerabilities

Incidentally, the way invulnerabilities work has some curious consequences. For example, the ToS bubble, Serpent Transmutation, is implemented as an invulnerability buff: it gives you +133% invulnerabilty to all normal types of damage (i.e. excluding things like fall damage, drowning damage and untyped damage). If we add 1% invulnerability from guild city buffs, we now have 134% invulnerability. This means that incoming damage is reduced by 134%, so it becomes negative and therefore heals you. You get healed by 34% of the amount that you would have taken as damage if you had no invulnerabilities.

The curious thing comes as a consequence of the fact that invulnerabilities are applied after the initial mitigation from protection. You get healed by 34% of the amount of damage that is left after it has been mitigated by your protection — so the better your protection is, the less healing you will get from your bubble. You can easily verify this by plugging invul = 134 into the above formulas, or by looking at the following screenshots. We had more unholy than electrical protection, but during Serpent Transmutation our electrical mitigation was higher than our unholy mitigation:


(Click to enlarge.)

Odd wisdom and non-integral protection

We said earlier that 1 point of wisdom contributes 0.5 points of protection. You might ask what happens if your overall amount of wisdom is an odd number. For example, 227 wisdom should theoretically contribute 113.5 protection. But can your protection be a non-integer? Will it get rounded to 114? Or maybe to 113?

That’s easy enough to test. Wearing nothing but Archpriest’s Gloves of the Underworld, my ToS had 227 wisdom (190 innate + 37 from the gloves), plus another 450 protection from Holy Wards. So theoretically my protection should be 227 · 0.5 + 450 = 563.5. The GUI showed my holy protection as 563, but the tooltip next to it says that my mitigation (before invulnerabilities) is mp = 7.6%.


(Click to enlarge.)

If we trust the 73.7 ratio that we established earlier, we can see that:

  • 563 / 73.7 = approx. 7.6391
  • 563.5 / 73.7 = approx. 7.6459
  • 564 / 73.7 = approx. 7.6526

If the game had rounded our protection up to 564 before further calculations, then the resulting mp would be above 7.65% and would therefore be rounded up to 7.7% when being displayed with one digit after the decimal point.

Walking around wearing nothing but gloves is a bit uncomfortable and makes horny people stare, so let’s put some shoes on as well! Boots of the Unutterable will increase our wisdom by 104, therefore our holy protection will increase by 52 and will now be 615.5. The GUI shows it as 615 and shows the resulting mp to be 8.4%.


(Click to enlarge.)

Just like before, we can see that:

  • 615 / 73.7 = approx. 8.3446
  • 615.5 / 73.7 = approx. 8.3514
  • 616 / 73.7 = approx. 8.3582

So if the game had rounded our protection down to 615 before further calculations, the resulting mp would be below 8.35% and would therefore be displayed in the GUI as 8.3%, not 8.4%.

So we can see that neither rounding down nor up can explain our observations — the game internally works with the correct protection value even if it isn’t an integer, and this value gets rounded (down, as it happens) only for display purposes (in the “Protection” column on the left).

Some related mechanics

While making a few tests on my guardian (on which more below) I noticed the following:

Bonus Protection: this stat (you see it e.g. on a guardian’s Mental Barrier maneuver or the Juggernaut ability) affects only generic protection, not the damage-specific kinds of it. Thus it also doesn’t affect the protection you get from wisdom, intelligence, or from the Wards AA perks.

Damage Mitigation: this appears as a stat on the tooltips of Defensive Stance and a guardian’s Defense tactic. In terms of how it affects magical mitigation, it seems to be nothing else than a synonym for invulnerability. If you switch to defensive stance, just add 10 to invuls in our above formulas and everything works the same as before.

Tests with the guardian also confirmed that protection is always rounded down for the purposes of display in the first column of the Magical attributes tab. At one point I had 3310 holy protection, of which 35 came from my 70 wisdom, 450 came from Holy Wards, and the rest was in the form of generic protection on gear, Stone Skin, and Chromatic Warding. Thus you would expect that 3310 − 35 − 450 = 2825 of this protection would be affected by Mental Barrier, and switching to it should therefore give us an extra 15% · 2825 = 423.75 protection, so our holy protection should now be 3310 + 423.75 = 3733.75. So you might expect the GUI to show the protection as 3734 if it wanted to round it to an integer, but in fact it displayed 3733.

High protection

I’ve made the measurements described so far on my ToS, but fortunately I then decided to do a few tests on my guardian to see if the formulas also work there. It turns out that the formula mp = protection / 73.7 that we’ve seen so far only works as long as the resulting mitigation is no higher than 50% (which happens at 3685 protection). After that point, the mitigation is no longer a linear function of protection; it’s something sublinear, but I didn’t manage to figure out the exact formula.


(Click to enlarge.)

Each dot on the chart represents one particular combination of gear (and buffs such as Mental Barrier maneuver and the Juggernaut ability, each of which gives you +15% bonus protection). The dots are of two different colors, but this difference isn’t really important. Blue dots represent spiritual protection (i.e. holy and unholy) and purple ones represent elemental protection (i.e. fire, cold, electrical) — they were different partly because my guardian has more wisdom than intelligence (70 wis, 60 int), and partly because I equipped a Quill of Ibis with an elemental protection gem (Sanguine Radiant Sapphire: +156 elemental protection). This was convenient as it allowed me to get two different data points from each combination of armor and accessories; and as we can see, both series of dots lie on the same curve anyway.

We can see how all the dots up to 3685 protection = 50% mitigation lie on a straight line; in fact this line is shown in orange below the dots, but it’s mostly hidden by the dots themselves. From that point onwards, the measurements no longer form a straight line, but a curve which grows more and more slowly. I showed two straight lines of different slopes for comparison, to make it easier to notice how the data is not on a straight line. In between those two is a curved orange line which fits the data a lot better, though not perfectly; it is based on the formula at the end of this section.

I suspect the origins of this nonlinear relationship go back to update 1.07; see the following post by a developer named Ilaliya, replying to people who noticed that their mitigation had been decreased [source]:

I apologize this was not in the patch notes.

In order to support a level-less expansion, we had to recalculate the section of the armor formula where armor values give above 50% mitigation (not including things like defensive stance). Note this change should only really impact soldiers who are in gear greater than T1. And even then, players will only be affected in most cases by less than 1%.

This change was to make armor much more future proof, in order to accommodate the substantial power increases obtainable through the expansion. Due to how %-based mitigation works mathematically, each additional % of mitigation is more valuable than the previous %. To illustrate this, consider that someone with 50% mitigation is taking half damage. 75% mitigation is taking half-damage of that, and 87.5% is taking half damage of that. The closer you get to 100%, the fewer and fewer % mitigation it takes to continually half incoming damage. At the extreme case, someone with 99% mitigation is taking half the incoming damage as someone with 98% mitigation.

When we raised the existing stat caps for the expansion, we found the existing armor formula scaled too quickly for the new values we wanted to give out. The armor formula above the 50% mitigation mark was changed as an outcome of this. Again, we apologize for any confusion or inconvenience this may have caused you guys.

He talks here about armor (and hence physical mitigation), but I suspect that the same thing happened to protection (and magical mitigation).

So perhaps the idea is that (once your mitigation is above 50%), adding a constant amount of extra protection should decrease your incoming damage in the same proportion regardless of what your initial protection was. Or in yet other words, it should cost the same amount of protection to move your mitigation from 50% to 75% as it would cost to move it from 75% to 87.5% or from 98% to 99%.

The proportion of damage that reaches us after mitigation is 1 — mp/100 (where mp is the mitigation in percent). Let’s call this quantity d. So if we had 50% mitigation, we’d have d = 1/2; at 75% mitigation we’d have d = 1/4; at 87.5% we’d have d = 1/8 and so on. If we take the base-2 logarithm of d and multiply it by −1, the result tells us how many times damage had been halved from the initial (unmitigated) amount. This quantity, − log2 d, is what we would expect (based on Ilaliya’s post above) to be a linear function of protection. Let’s explore this idea with a chart:


(Click to enlarge.)

Here we have protection on the x-axis and − log2 d on the y-axis. Thus y = 1 corresponds to 50% mitigation; y = 1.1 corresponds to approx. 53.3% mitigation; y = 1.2 corresponds to approx. 56.5% mitigation; and y = 1.3 corresponds to approx. 59.4% mitigation. The dots are based on the same measurements as the previous chart, except that they are all the same color and that those with less than 50% mitigation have been discarded. Unfortunately, as we can see, the relationship isn’t quite linear — our dots clearly don’t all lie on a single straight line. (The red trendline is a straight line, given for comparison.)

I tried a few other ways to transform the data in the hopes of finding some sort of elegant linear function somewhere, but without success. One of the best attempts was to use a logarithmic scale on both axes. On the following chart, the x-axis shows log(protection − 50 · 73.7) and the y-axis shows log(mp). The scattering of the dots on the lower left part of the chart might seem a bit odd at first but it’s just due to the fact that our mitigation values (as we see them in the GUI) are rounded to just one digit after the decimal point. The more annoying thing happens at the right end of the chart, where we can again see that the relationship between y and x is sublinear — the dots clearly don’t all lie on a straight line.


(Click to enlarge.)

So, anyway, I don’t have a nice exact formula for computing mitigation from protection above 50%. The closest one I managed to find is:

mp ≅ 50 + (protection − 50 · 73.7 − 15)0.892 / 78.55.

If you round the result of this formula to one digit after the decimal point, it doesn’t differ by more than 0.1 from the value shown in the GUI for any of my measurements (i.e. the dots in the previous charts). (The extra −15 subtracted from the protection helps with the accuracy, but it does mean that you can’t use this formula for protections below 3701. Between 3685 (= 50 · 73.7) and 3701 you can still use the old formula, mp = protection / 73.7; again the results, rounded to one digit after the decimal point, won’t differ from those in the GUI by more than 0.1.)

This approximate formula might be potentially useful for some rough calculations, but it isn’t really satisfactory if you want to be exact. The whole reason why I started this investigation of protection was because the mitigation rounded to 0.1% as shown in the GUI was too imprecise for some of my subsequent calculations. Now we have a more precise formula for mitigation below 50%, but above 50% our formula doesn’t really have any advantages over just taking the mitigation as it is shown in the GUI.

Hit amount as a function of DPS

January 26, 2013 22 comments

(This post is a kind of continuation of my post about combat mechanics from a few weeks ago.)

Well, here’s at least one thing that makes sense. I measured the amount of damage done by an unarmed white hit (i.e. while having nothing in my main hand) — an ‘up’ attack to be precise, though it seems that other directions hit for the same amount anyway. The theory here is supposed to be that the amount of damage done is computed as

damage = DPS · animation_length,      (*)

where DPS is the DPS number from your Attributes/General tab, and consists of your weapon damage plus the DPS coming from strength (or dexterity, depending on your weapon) and combat rating. I varied my DPS by swapping some gear around, and I also did the tests with several classes. To my considerable surprise, all the measurements match up perfectly:

We see that all the measurements lie on the same straight line; the slope of this line is the animation length of our unarmed ‘up’ attack. It must be equally long regardless of your class, since the measurements of different classes all lie on the same line.

As often with this sort of testing, we are slightly hampered by the fact that damage is rounded to the nearest integer in our combat log, even though the game internally works with non-integer amounts. (The DPS as shown in the Attributes/General tab is similarly rounded to one digit after the decimal point, but this isn’t a problem as we can compute the exact value by ourselves from combat rating and strength.) For example, at 132.2 DPS (actually more like 132.2295; coming from 1.0 weapon damage + 4803 combat rating) our hits were shown as being 164 points, so the real amount must have been somewhere between 163.5 and 164.5. And the animation length must therefore have been somewhere between 163.5/132.2 = 1.236 sec and 164.5/132.2 = 1.244 sec.

So we don’t know exactly what the animation length is, but we at least found a lower and an upper bound on it. Other measurements from the chart above give us slightly different bounds. The highest lower bound I could find was 1.24107, and the lowest upper bound I could find was 1.24154; between these two, we have estimated the length of this particular animation with an accuracy of less than half a millisecond!

So as we can see, the formula (*) above isn’t some sort of approximation; it’s the real thing. For any of the measurements shown on my chart, you can take any animation length from the range [1.24107, 1.24154] that we’ve just established, multiply it by DPS and round the result to the nearest integer, and you get exactly the amount of damage that really appeared in my combat log. (Of course, if we made more measurements at still different values of DPS, we could perhaps narrow down the range of possible animation lengths still further. But the current range is already very narrow.)

These measurements also demonstrate that when the tooltip says you got 1.0 weapon DPS from your unarmed main hand, it isn’t joking. If you subtract 1.0 from the DPS in all my measurements, you can no longer explain the amount of damage done in each hit with a linear function of the form DPS · animation_length — you’d have to add a constant term to it.

Defensive stance

Among other classes, my tests in the previous section included two soldiers (guardian and DT) in neutral stance. But what happens if we switch to defensive stance instead? The tooltip on defensive stance says, among other things, “−10% damage multiplier”. This multiplier seems to affect nothing more or less than the DPS value shown in the Attributes/General tab; in other words, the formula for DPS is actually

DPS = (weapon_damage + combat_rating / 36.6) · damage_multiplier.

By default, the damage multiplier is 1 (or 100%), but there might be various buffs or debuffs that modify it. Switching from neutral to defensive stance brings your damage multiplier to 0.9 (or 90%), due to the −10% damage multiplier on defensive stance. If there are several things affecting your damage multiplier, they stack additively rather than multiplicatively. For example, the death penalty debuff includes −1% damage multiplier; together with defensive stance this brings your damage multiplier down to 100% − 10% − 1% = 89% = 0.89, and not to (100% − 10%) · (100% − 1%) = 0.90 · 0.99 = 0.891.

So, here are some measurements of hits made in defensive stance. For the x-coordinate, we used the DPS as shown in the GUI during defensive stance, so it’s already been multiplied by the 0.9 damage multiplier.

Now, here’s an odd thing: the measurements in defensive stance still all fall on a straight line — but it isn’t the same line as in neutral stance (or on non-soldier classes for whom stances don’t apply at all). For example, in the previous section we saw that when our DPS was 132.2 (in neutral stance), our hits were for 164 points. Switching to defensive stance brings our DPS down to 119.0, which is good, as this really is 90% of 132.2 (rounded to one digit after the decimal point). But if you now plug this DPS into our formula (*), and use the same animation length that we established in the previous section (around 1.241 sec), you’d expect the resulting hit to be around 147.7 points. So the combat log, where things are rounded to the nearest integer, should show us hitting for 148 points; but it actually turned out that we were hitting for 150 points.

This anomaly, where our hits in defensive stance are slightly stronger than we expected, was present in all my measurements in defensive stance, both on my guardian and my DT. I’m not sure how to explain it. One way is to imagine that although the GUI (in the Attributes / General) tab shows our DPS exactly as we would expect it given a −10% damage multiplier, it’s actually lying to us and the game actually uses a slightly higher DPS when calculating how much we’re hitting for. It’s as if, instead of having 90% as much DPS as in neutral stance, we actually had around 91.6% or 91.7% as much; i.e. as if the damage multiplier stat on defensive stance was not −10%, but around −8.3% or −8.4%. But this idea, that the GUI shows one thing but internally the game uses a completely different amount when calculating damage, seems a bit too bizarre and improbable to me.

Another explanation that comes to mind is that animation length is different in defensive stance than in neutral. We can calculate bounds on animation length from our measurements in defensive stance, just like we did in the previous section for neutral stance. The result is that the animation length in defensive stance should be between 1.26395 and 1.26463 seconds — about 0.02 sec longer than in neutral stance. Now, this doesn’t strike me as completely implausible; after all, the character’s hands etc. are in a slightly different position in defensive stance than they are in neutral, so it might require a slightly longer animation to perform the hit.

I tried to test this explanation in the following way. If each hit is 0.02 seconds longer in defensive stance than in neutral, then a sequence of 100 hits should be about 2 seconds longer. The combat log shows the timestamp of each hit to within 1 second, so we can perform 101 hits and compute the difference between the timestamp of the first and the 101st hit to estimate the total duration of 100 hits. We’d expect this duration to be around 124 or 126 seconds, since we’ve seen above that the animation length should be around 1.24 or 1.26 seconds. What actually turned out is that the duration of 100 hits was slightly longer — around 134 seconds — which suggests that there’s a small gap of about 0.1 seconds between each hit and the next. I doubt there’s any way to avoid this gap, since it was there even though I always pressed the button for the next attack before the current attack was finished.

If we repeat this several times, the duration of 100 hits will not be exactly the same each time; this is probably partly because it depends on where within that one whole second our first hit fell, and partly because the tiny gaps between hits are perhaps not all equally long. If we want to compare the results for neutral and for defensive stance, we’ll have to assume that the gaps are on average equally long in both stances. Under this assumption, a sequence of 100 hits should still take about 2 sec longer in defensive stance than in neutral (if it’s true that the animation length in defensive stance is 0.02 sec longer than in neutral). But is that really the case? I repeated this test 100 times in each stance and the following chart shows how often I got which duration:

As we can see, the durations in defensive stance aren’t really 2 seconds longer than in neutral stance. On average they are about 0.58 sec longer; I’m not sure if this difference is just a random statistical artefact (I did a t-test and it clearly showed that the difference is statistically significant) or if it really suggests some underlying difference in animation length, but in any case, the difference isn’t big enough to explain the anomaly in the amount we hit for.

So, to sum it up, I don’t have any good explanation for why the hits in defensive stance are stronger than you’d expect. Either the game is lying and using one damage multiplier in the GUI but a different damage multiplier when computing the actual damage of your hits; or the animation is longer in defensive stance but the uncontrollable gaps between hits are shorter and so cover up this increase in length; or there might be some other explanation altogether.

A few notes on combat mechanics

December 25, 2012 4 comments

The best laid schemes

This post is an exceedingly modest and entirely useless attempt at the sort of thing that is, I suppose, called theorycrafting in some circles. It started with my innocent curiosity to understand the mechanics behind critical hits a little better. We know that you have the critical hit chance and the critical bonus damage percentage; so presumably the critical hit chance tells you how likely you are to crit, and then the critical bonus damage percentage tells you how much stronger your critical hit is than a normal hit would be. And I vaguely remembered that critical hits are actually 50% stronger than normal ones by default,* and the critical bonus damage applies on top of that. When you express the critical bonus damage in percent, what exactly counts for 100%? The normal hit, or the just the 50% extra that the critical hit gets by default? Or something else entirely?

[* In fact, one part of the 1.05 update notes says: “Critical hits will now give you 50% extra damage. / Critical Damage Rating — increasing the damage of your critical hits”.]

So I figured I’d do some testing, whack at a straw dummy for a bit, maybe to a little bit of statistics and then write up my findings. Alas, it all turned out to be much more complicated and messier than I expected, with unexpected randomness and inaccuracy plaguing me every step of the way, half the numbers you see in the tooltips and the like can’t be trusted, etc. So although I’m far short of my original goal, I decided to make a post out of the material I got so far, and hopefully I’ll post something more on this subject if or when I have done some more experimentation.


A Funcom developer
fine-tuning the mechanics of the combat system.

Critical damage rating and critical bonus damage

Many items (and perks such as Pressing Strikes) include an attribute called ‘critical damage rating’, which increases the bonus damage done by your critical hits. The Combat Stats tab shows both your overall critical damage rating and your critical bonus damage as a percentage (of the normal hit, presumably). Their relationship is very straightforward: critical bonus damage (expressed as a percentage) = critical damage rating / 36.6.

This is a well-known fact, but I couldn’t help feeling curious and trying to verify it independently. You can swap some parts of your gear to change your critical rating, and observe how this affects the critical chance. The ratio between them is not always exactly 36.6; for example, at 836 critical damage rating I got a 22.8% critical bonus damage, giving us the ratio 836 / 22.8 = 36.666…. At 533 critical damage rating, I got a 14.6% critical bonus damage, giving us the ratio 533 / 14.6 = approx. 36.51.

Clearly, the problem here is that we don’t really see the exact critical bonus damage in the GUI — it’s rounded to just one digit after the decimal point. So if we see 14.6% in the GUI, the real critical bonus damage might be anywhere in the range [14.55, 14.65) — any number from that range would be rounded to 14.6 if we want just one digit after the decimal point. And so the ratio in this case could be anything from 533 / 14.65 = approx. 36.38 to 533 / 14.55 = approx. 36.63.

So from each measurement of critical damage rating and critical bonus damage, we get a range of possible values of our ratio. Assuming that the ratio really is just a constant (i.e. that it’s the same for any critical damage rating*), let’s take the intersection of all these ranges to narrow down the possible values of our ratio even more.

[* As the 1.05 update notes say, this ratio certainly varies with your level; this is meant to encourage you to upgrade your gear, because if you leave your combat rating unchanged as your level grows, you’ll be getting less and less DPS from it. In any case, I’m only interested in what’s going on at level 80.]

The narrowest bounds I got were the following. At 452 critical damage rating, the GUI showed our critical bonus damage as 12.3%, meaning that the ratio is at least 452 / 12.35 = approx. 36.59919. And at 463 critical damage rating, the critical bonus damage was shown as 12.7%, meaning that the ratio is at most 463 / 12.65 = approx. 36.60079. So we see that the true value of the ratio must be somewhere in the range [36.59919, 36.60079]; and so it seems quite safe to conclude that 36.6 is indeed the exact true value of the ratio.

Critical rating and critical chance

The situation here is very similar to the one above. One difference is that, according to the tooltips in your Combat Stats tab, the game distinguishes between the critical chance when using weapons and the critical chance when using spells. The weapons one seems to be present in all classes, but the spells one isn’t present on guards, sins, barbs and conqs.

Another difference is that you get some innate critical chance. For spells, this always seems to be 2.5%, whereas for weapons it depends on what you have in your main hand: 0% if it’s talisman or no weapon; 5% if it’s a dagger; and 2.5% for any other weapon type. Apart from that, increasing your critical rating by 36.6 increases your critical chance by 1% (well, by 1 percentage point, to be more exact), just like with critical damage rating.


(Click to enlarge.)

The above screenshot shows an example from when a dagger was equipped in the main hand. From 631 crit rating, we got 631/36.6 + 5.0 = 22.2% crit chance with weapons and 631/36.6 + 2.5 = 19.7% crit chance with spells.

By swapping gear around a bit, I was able to get very similar datapoints as in the case of critical damage rating in the previous section. At 452 critical rating, the critical chance with spells was shown as 14.8%; and at 463 critical rating, the critical chance was shown as 15.2%. Note that if you just subtract the 2.5% innate critical chance, you get 12.3% and 12.7%, respectively, i.e. exactly the same numbers as in the previous section, so we also get the same result as before: the ratio that converts critical rating into critical chance must be somewhere in the range [36.59919, 36.60079].

Combat rating and DPS

The Attributes/General tab of your GUI shows your DPS and moving your mouse over it tells you further that part of it comes from combat rating (at the unsurprising ratio 36.6 combat rating = 1 DPS) and part of it comes from your weapon damage. [The idea is that this DPS will be multiplied by the duration of your combat animations to get the actual damage.] Combat rating can appear either directly as an attribute on your gear, or it can come from strength and dexterity (1 str or dex gives you 3 combat rating); you have some innate strength and dexterity (depending on your class), and some of it might appear on your gear as an attribute.

Whether strength or dexterity is used here will depend on your weapon type; dexterity is used if your main hand holds a dagger, bow, or crossbow; strength is used for all other weapon types, except talismans. Being unarmed (i.e. having no weapon in your main hand) or having a talisman in your main hand are somewhat anomalous. If you are unarmed, the GUI will show as if all of your strength counted towards combat rating; if you have a talisman, the GUI will show as if none of your strength (nor dexterity) contributed anything to your combat rating. But the truth, if you try actually hitting something, turns out to be somewhere in between: in both of these cases (unarmed and talisman), your innate strength really doesn’t contribute anything to the amount you hit for, but the strength from your gear works normally (1 str = 3 combat rating). (Update: this turned out to be a mistake. The innate strength does in fact contribute to your unarmed hits, just like strength from gear does.)

Some combat rating comes from somewhat unexpected places. It seems that at level 80, every character has 146 innate combat rating, regardless of anything else — you can be guildless, naked, without feat points or AA, but you’ll still have that 146 combat rating. That’s enough for about 4 DPS.

Furthermore, some combat rating comes from guild city buildings. The Tier III Thieves’ Guild and Weaponsmith workshop give you 69 combat rating each. The Tier II equivalents should give 41 combat rating each, and the Tier I ones should give 28 combat rating each; but in my experience, these bonuses do not stack, so if you’re in a guild with T3 buildings, you’ll only get 69 from each building, not 28 + 41 + 69. (By contrast, when I was experimenting with character HP, I found that the HP bonuses from the Keep do stack across all three tiers.)

The above screenshot shows an example. We have 784 generic combat rating (146 innate, 69 + 69 from guild city, and 500 from accessories), 212 combat rating (cold) from one of the Vile Nativity cloaks, 320 combat rating (polearm) from the T3 polearm, and 4197 combat rating from strength (1399 str × 3; of this, we have 210 innate strength and 1199 from gear).

The weapon damage is the number that you can see on your weapon’s tooltip just below the level etc.:

The numbers in parentheses after the weapon damage tell us something about the variance of the hits you’ll do with that weapon; more on that later.

Of course, you could leave the weapon slots empty. In this case, the tooltip shows your weapon damage as being 1.0. Having a talisman in your main hand is even better — then the weapon damage is 0.0. One nice consequence of being unarmed like this is that all your normal hits turn out to be equally strong — there isn’t any variance in them. The same is true for your critical hits. So for example, if we’re unarmed, and we hit a target dummy multiple times, and if there aren’t any physical damage debuffs on it, all the hits will be for the exact same amount of hit points. (Well, on very rare occasions I did notice that some hit here or there was different by 1 point. I have no idea what to make of this.) This makes it a lot easier to collect statistics.

[Note: You might also get some more or less temporary bonuses to your combat rating or to your weapon damage from various combos, spells, group buffs and the like. To avoid this sort of stuff, which would just add noise to my measurements, I mostly used my ToS for experiments with this.]

Straw dummies from Fate

Having learned these things, my plan was simple: I’d start by doing some unarmed white hits on a straw dummy, and swap around some gear to change my combat rating and/or my critical damage rating. This should allow us to see how the actual amount of damage done by hits depends on the combat rating, and how the difference between critical and normal hits depends on the critical bonus damage. Then I would repeat some experiments along the same lines with a weapon, still doing just white hits, but the experiments here would be more arduous due to the variance in your hits when using a weapon.

Well, I did actually do a fair amount of the unarmed experiments, and my preliminary impression is that the amount of damage done by your hits is indeed a linear function of your DPS (from combat rating), though to my surprise if you extrapolate from there down to what it would be at 0 DPS, you still get a positive amount of damage, rather than 0. The difference between critical and normal hits seemed to be roughly 4/5 of the amount I’d expect from my critical bonus damage, and there was no trace of that supposed default 50% bonus.

But what really disturbed me was when I tried to repeat some of my experiments and found that the results are changing somewhat haphasardly. I’d wear the exact same gear, have the exact same amount of combat rating etc. as in some earlier experiment, but my hits on the straw dummy would be slightly weaker or stronger than before. From this, I can only conclude that the target dummies — at least the ones handed out by Fate on the testlive server, as this is what I’ve been testing with — have a somewhat varying amount of mitigation, and the exact value of their mitigation is chosen at random when you spawn the dummy. At that point all your hits on the dummy will be for the same amount (if you are unarmed and if your combat rating etc. doesn’t change, of course); but when the dummy despawns after a few minutes and you spawn a new one, your hits on the new one might be different than they were on the old one.

For illustration, here are some white hits from a guardian in T3.5 heavy armor from testlive. I spawned the test dummy 20 times and got the following results:

Normal hit

Critical hit

Number of dummies
165 188 4
165 189 4
167 190 1
167 191 2
168 192 1
169 193 1
169 194 2
170 194 3
170 195 2

What can we learn from this? Clearly, we see that we’re being inconvenienced by the fact that our combat log shows damage amounts rounded to an integer, even though the game internally computes with non-integer amounts. (As I mentioned before, a good argument can be made for the idea that the interal unit of computation is 0.01 HP: namely, the infamous ranger oneshot bug does 231 / 100 points of damage, which is just the amount you would expect if the game internally uses signed 32-bit integers in which one unit represents 0.01 hit points.) This explains why a normal hit of 165 points is sometimes accompanied by a crit of 188 and sometimes a crit of 189; clearly the underlying values of the normal hits were actually also different, but they both happened to round to 165.

It’s hard to resist the feeling that not all these outcomes are equally frequent; for example, normal hits of 165 and 170 seemed more common than the intermediate values. But we don’t really have enough data to be sure, and it’s slow to collect it as you have to wait several minutes before you can spawn a new dummy.

In any case, let’s try to estimate something about the critical bonus damage. If your normal hits were for 165 points and your crits were for 188, you might compute 188 / 165 = approx. 1.1394 and then say that your crits were 13.94% greater than your normal hits. But in fact, we just saw that we don’t really know the exact values of our hits; if the combat log says 165, we can only say that the correct amount was somewhere in the range [164.5, 165.5), and likewise 188 can be from anywhere in the range [187.5, 188.5). So the actual ratio crit/normal can be anywhere between 187.5 / 165.5 = 1.1329 and 188.5 / 164.5 = 1.1459; so the critical bonus damage could be anywhere between 13.29% and 14.59%.

We can obtain a lower and upper bound like this from every row of our above table. As it turns out, the highest lower bound, 14.16%, comes from (169, 194); and the lowest upper bound, 14.41%, comes from (167, 190). So all we can really say about the critical bonus damage in this case is that it’s somewhere between 14.16% and 14.41%.

But, and this is a big but — my gear and perks at the time actually gave me 633 critical damage rating, and the resulting critical bonus damage from that is 17.3% (and indeed the GUI said the same thing).

So we’d expect our crits to be 17.3% more powerful than our normal hits, but in fact they turned out to be somewhere between 14.16% and 14.41% more powerful. I have no idea how to explain this. As we’ll hopefully see in a later post, the same phenomenon occurs over a wide range of tests with different values of critical damage rating and combat rating.

At least we can probably safely conclude that we have no default 50% bonus in critical hits (where the critical bonus damage from our stats would then be applied on top of it); though as we’ll hopefully see in a later post, something of that sort does turn up if you equip a weapon.

Straw dummies from the Veteran vendor

Having seen the disturbing variance in the mitigation of straw dummies from Fate on the testlive server, a natural next question is whether other straw dummies have the same problem. So I did some tests with the dummy that you can buy on the live server with veteran tokens. This was again with an unarmed guardian, but the gear here was slightly different than in the testlive experiments from the previous section, consisting of a mixture of T4 plate armor. The Attributes / General tab showed 132.2 dps, of which 1.0 is weapon damage of bare hands and the reset is from combat rating; of this there is 1044 generic combat rating (28.5 dps), the rest is from strength (1253 str = 3759 combat rtg = 102.7 dps).

Here are the outcomes after 50 straw dummies. The most common outcome was that my normal hits were for 164 points, crits were for 200, and in defensive stance this decreased to 150 and 186. But on almost half the dummies, the hit amounts were slightly different:

Defensive stance

Neutral stance

Number of dummies
Normal

Critical

Normal

Critical
150 186 164 200 26
151 186 164 200 13
151 187 165 200 4
151 187 165 201 4
152 187 165 201 1
152 188 165 201 1
152 188 166 202 1

So we can see that these dummies also vary somewhat in mitigation, but not as much as the ones from Fate on the testlive server.

We can also try to estimate the critical bonus damage %, same as in the previous section. From the neutral stance experiments, we find that the critical bonus damage must be in the range [21.3%, 21.9%]; but from the defensive stance experiments, we find that it must be in the range [23.3%, 23.8%]. This strikes me as very bizarre — it’s as if the switch to defensive stance had a smaller effect on the critical bonus damage than on the normal part of the hit.

Of course, to make matters even more bizarre, my critical damage rating was 952, which should mean 26.0% critical bonus damage — well above our estimates from the previous paragraph.

We can similarly try to estimate bounds on the ratio from the hits in defensive stance and corresponding hits in neutral stance. From normal hits, we find that the ratio should be in the range [91.5%, 92.0%]; but from critical hits, we find that the ratio should be in the range [93.1%, 93.5%]. So again it seems as if switching from neutral to defensive stance had a bigger effect on the normal part of a critical hit than on its critical part.

And much like before, neither of these ranges is quite what I would expect from reading the tooltip — the tooltip for defensive stance says “−10% Damage Multiplier”. So we’d expect that a hit in defensive stance would be 90% of the corresponding hit in neutral stance, but here we see that it’s actually more like 92% or 93%. On the other hand, the DPS as shown in the Attributes / General tab has indeed decreased by exactly 10%: from 132.2 to 119.0. In fact this might point to a hint why our hits have decreased by less than 10%; from some of my other experiments (which I’ll hopefully describe in a future post) I got the impression that the hit amount is a linear function of the form hit_amount = const1 · DPS + const2, where const2 is not 0 (as one might expect), but greater than 0. So decreasing DPS by 10% of course decreases hit_amount by less than 10%, since the second term remains the same as before.

Straw dummies in the guild cities

Your guild city likely has a pair of permanent straw dummies somewhere. My understanding is that they are caused by having a barracks, though IME they don’t necessarily spawn near the barracks — our city is on the western plot in Poitain and the dummies are next to the library, not the barracks. Anyway, naturally I was curious if those dummies have the same problems with changing mitigation as the ones from Fate or the veteran vendor. Of course, you can’t simply spawn new dummies in the guild city, so I started switching between various instances of Poitain and riding around the playfield, hoping to find some guild cities without walls, or with gaps in the walls, or with doors left open, so I could whack at their target dummies and see how much damage they take.

I’ve tested dummies in more than 10 cities (and each has 2 dummies), and the amount I was hitting for was exactly the same in all of them. In neutral stance, normal hits were 164 points and critical ones were 200 points; in defensive stance, they were 150 and 186, respectively. These are the same amounts as in the most frequently occuring outcome of the veteran dummy tests in the previous section.

So I guess this means that it’s safest if I do all my future testing on guild city dummies. One downside of this is that I’ll have to limit myself to testing on the live server, since our guild city on testlive keeps disappearing.

The next step will hopefully be to do some more extensive experiments with unarmed hits that will vary combat rating and critical damage rating in a systematic way. In fact I’ve already done some experiments of this sort but it was on the straw dummies from Fate, before I noticed the problems with randomized mitigation. After that, I can start doing experiments with white hits while holding a weapon; but this will be more annoying due to the variance in the amount you hit for if you have a weapon equipped.

(Next post in the series: Hit amount as a function of DPS.)