## A few notes on combat mechanics

## 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.

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 2^{31} / 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* = *const*_{1} · *DPS* + *const*_{2}, where *const*_{2} 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.)

I tried a few times to test dps for different classes (Guard, HoX, Sin, Necro and lately BS and ToS), and i ended to do the tests only on City Strawman. I noticed the differences with the Veteran Strawman, but I was like “f*ck it…” instead of trying to understand Funcom 🙂 I’m not a wise man, and math is a rather fair then extraordinary skill to me.

In the end, the most conclusive tests for me were done on mobs in Epic Kheshata… But only with my Guard I was able to run extensive dps tests there.

I did some testing on strawmen.. actually the crit rating in the GUI is not showing the correct numbers. Easily tested by equipping a caster dagger which as you say give a whooping increase in crit rating. However this crit rating does not apply to spells. It only applies to the dagger hits. So if you mix dagger hit and spells, the dagger hits get a larger percentage crits compared to the spells you cast. All with the same gear and same GUI crit rate.

Seems the internal calculations are separate for spells and melee (as you propose). However you can have TWO different critrating at same time (these are not shown in gui).