Weapon and Guard Proc Rates

**Vanshilar** · 12-16-2011, 10:15 PM

In the coming months I plan to post results of testing done on proc rates and damages of various weapons and guard effects. I've already started doing some but felt that it would be better to have it all in a single thread rather than a separate thread for each. I'm aware that there have already been other efforts to gather data on proc rates, such as here, but this will be primarily for high-quality information i.e. large sample sizes, rather than speculation. By "large" I mean in the thousands or tens or hundreds of thousands. Other than the specific dice used for damages, I will try to keep speculation to a minimum. This will likely not be completed for a very long time, so feel free to look at other sources like the above link if data on them is not yet available here.

As with my other game mechanics projects such as renown, monster stats, and run speed, updating this will depend on my available time, interest, relevance, and other factors, so it may or may not be frequent.

The testing method will for the most part be to take videos of the combat log while using items with the proc effect, and then going through the videos and counting up how often the proc occurred relative to whatever causes it (getting hit, hitting something, etc.). Each cause and each proc is tagged with the frame of the video where it was first observed, allowing for double-checking and verifying the accuracy of the count. In some cases the videos will be made available, although I don't intend to upload all the videos to Youtube due to bandwidth and space considerations.

This first post will be on weapon procs. These are effects which occur when you successfully hit a victim. The chart below is a summary of known effects and results of experimental data on them, if available:

For weapon effects, I didn't test if the effects proc on hit (i.e. may end up being 0 damage due to DR) versus proc on damage (i.e. victim actually takes damage from hit), so those are interchangeable for weapon effects until I test them; it's just to differentiate between this and proc on crit effects.

Code:

Effect                 	ProcOn	Proc%	Dam/Hit	AvgDam	Stdev	Formula 	GS?	Found on
Cacophony              						         	No	Epic Elyd Edge
Cloudburst             	Hit	9.0%	4.50	50.01	2.58	10d3+30 	No	Cloudburst, Fang of Siberys
Corrosive Salt         						         	Yes	Epic Cutthroat's Smallblade (Tier 3), Polycurse Dagger, calomel weapons
Crushing Wave          						         	Yes	new cannith challenge weapons, calomel weapons
Curse Vector           						         	No	Polycurse Dagger
Deception              						         	No	Too many to list; can also be cannith crafted
Disintegration         	Hit	2.0%	9.15	457.62	22.11	15d20+300	Yes	Epic Chimera's Fang, Epic Midnight's Greetings, Epic Noxious Fang
Earthgrab              	Hit	4.0%	N/A	N/A	N/A	N/A     	Yes	Epic Ratkiller (Tier 3)
Elemental Mastery      						         	Yes	
Enervation             						         	Yes	
Epic Trap the Soul     						         	No	Epic Souleater
Freezing Ice           						         	Yes	
Giant Slayer           						         	No	Epic Ancient Vulkoorim Dagger
Greater Disruption     						         	Yes	possibly Epic Hammer of Life?
Greater Incineration   						         	No	Epic Elemental Greataxe of Fire (Tier 3), Epic Garos' Malice (new)
Greater Shocking Blow  						         	No	Epic Charged Gauntlets
Improved Deception     						         	No	Epic Midnight's Greetings
Incineration           	Hit	2.0%	5.68	283.86	16.27	8d20+200	Yes	Epic Hellfire Crossbow, Epic Xuum, (old garos' malice?)
Lightning Strike       	Hit	1.5%	9.15	610.00	25.79	20d20+400	Yes	Epic Flint, Epic Kron'zek's Cruelty, Epic Storm
Magma Surge            						         	Yes	Epic Elemental Greataxe of Fire (Tier 3)
Nightmares             						         	No	Terror, Tharaak Wraps
Peals of Thunder       						         	No	Fang of Siberys
Polycurse              						         	No	Polycurse Dagger
Radiance               						         	Yes	
Radiant Blast vs undead	Hit	1.0%	7.58	757.85	32.97	20d25+500?	No	Epic Wraps of Endless Light
Radiant Blast vs others	Hit	1.0%	3.80	380.23	22.67	10d25+250?	No	Epic Wraps of Endless Light
Ravager                						         	No	Ring of the Ravager, Colethenis's Belt (set effect)
Rock Shattering        						         	No	Earthshatter Warhammer
Shocking Blow          						         	No	Charged Gauntlets, Greater Bold Trinket
Slay Living            						         	Yes	
Slicing Winds          	Hit	2.0%	7.44	372.15	8.17	3*(8d10+80)	No	Breeze (new Abbot)
Steam                  						         	Yes	
Sundering Ooze         						         	Yes	
Tchurvul's Touch       						         	No	Tchurvul's Kukri
Tharaak Corrosion      						         	No	Tharaak Wraps
Thief Acrobat          						         	No	Morah's Band, Morah's Belt (set effect)
Trap the Soul          						         	Yes

It's just copy-paste from my Excel file on this, so let me know if you have suggestions on improving the formatting.

If you would like to help, the best way is probably to suggest what weapons have these effects, since the limiting factor will likely be getting my hands on them. I'm not looking for an exhaustive list, but more the ones that would be more readily available. For quite a few I could in theory craft green steel weapons for them, but I'd rather not waste large mats. If you have procs that are not listed here, feel free to suggest them as well.

----------

Each entry gives the likely information first, followed by the experimental information. For example, a likely proc rate may be given as 9.0% even though the experimental data was 9.06%. For each entry, "likely" means what I think are the most likely values given the experimental data, whereas "tested" means the direct results from data. The "Tested with" is the item used to test the proc; technically the results are only valid for that item only, since it's *possible* (though unlikely) that other items have the same name effect but the actual effects are different (for example, two different effects both named "lightning strike"). In most cases though the effect should be the same for all items that have it.

Cloudburst
Found on: Cloudburst, Fang of Siberys
Tested with: Cloudburst
Likely Average Damage per hit: 4.5 (electric)
Likely Proc rate: 9.0%
Likely DC: N/A
Likely Average Damage per Proc: 50
Likely Damage Formula: 10d3 + 30
Tested Average Damage per Proc: 50.01
Tested Standard Deviation: 2.58
Tested Proc Rate: 9.06%
Tested DC: N/A
Sample size: 127063
Procs: 11507

Disintegration
Found on: Epic Chimera's Fang, Epic Midnight's Greetings, Epic Noxious Fang
Tested with: Epic Noxious Fang
Likely Average Damage per hit: 9.15 (untyped)
Likely Proc rate: 2.0%
Likely DC: N/A
Likely Average Damage per Proc: 457.5
Likely Damage Formula: 15d20+300
Tested Average Damage per Proc: 457.62
Tested Standard Deviation: 22.11
Tested Proc Rate: 2.03%
Tested DC: N/A
Sample size: 161350
Procs: 3276

Earthgrab
Found on: Epic Ratkiller, Green Steel
Tested with: Epic Ratkiller
Likely Average Damage per hit: N/A
Likely Proc rate: 4.0%
Likely DC: 35
Likely Average Damage per Proc: N/A
Likely Damage Formula: N/A
Tested Average Damage per Proc: N/A
Tested Standard Deviation: N/A
Tested Proc Rate: 3.80%
Tested DC: 35
Sample size: 358295
Procs: 13617

Greater Sunburst
Found on: Wraps of Endless Light (level 24), Celestia
Tested with: Wraps of Endless Light (level 24)
Likely Average Damage per hit: 5.1 (light)
Likely Proc rate: 2.0%
Likely DC: N/A
Likely Average Damage per Proc: 255
Likely Damage Formula: 10d10+200
Tested Average Damage per Proc: 255.21
Tested Standard Deviation: 8.96
Tested Proc Rate: 2.00%
Tested DC: N/A
Sample size: 136385
Procs: 2728 (2634 with damage recorded)

Incineration
Found on: Epic Xuum, Epic Hellfire Crossbow
Tested with: Epic Xuum
Likely Average Damage per hit: 5.68 (fire)
Likely Proc rate: 2.0%
Likely DC: N/A
Likely Average Damage per Proc: 284
Likely Damage Formula: 8d20+200
Tested Average Damage per Proc: 283.86
Tested Standard Deviation: 16.27
Tested Proc Rate: 1.96%
Tested DC: N/A
Sample size: 106597
Procs: 2088

Radiant Blast vs undead
Found on: Epic Wraps of Endless Light (from Mabar festival)
Tested with: Epic Wraps of Endless Light
Likely Average Damage per hit: 7.6 (light)
Likely Proc rate: 1.0%
Likely DC: N/A
Likely Average Damage per Proc: 760
Likely Damage Formula: 20d25+500
Tested Average Damage per Proc: 757.85
Tested Standard Deviation: 32.97
Tested Proc Rate: 0.95%
Tested DC: N/A
Sample size: 7063
Procs: 67

Radiant Blast vs non-undead
Found on: Epic Wraps of Endless Light (from Mabar festival)
Tested with: Epic Wraps of Endless Light
Likely Average Damage per hit: 3.8 (light)
Likely Proc rate: 1.0%
Likely DC: N/A
Likely Average Damage per Proc: 380
Likely Damage Formula: 10d25+250
Tested Average Damage per Proc: 380.2
Tested Standard Deviation: 22.7
Tested Proc Rate: 1.01%
Tested DC: N/A
Sample size: 35804
Procs: 361

Slicing Winds
Found on: Breeze (new version), Elemental Rapier of Air
Tested with: Breeze (new version)
Likely Average Damage per hit: 7.44 (slash)
Likely Proc rate: 2.0%
Likely DC: N/A
Likely Average Damage per Proc: 372
Likely Damage Formula: 3*(8d10+80)
Tested Average Damage per Proc: 372.15
Tested Standard Deviation: 8.17
Tested Proc Rate: 1.99%
Tested DC: N/A
Sample size: 112117
Procs: 2236

**Vanshilar** · 12-16-2011, 10:15 PM

Reserved for when I post about guard proc rates.

**Vanshilar** · 12-16-2011, 10:16 PM

Reserved for when I post about attack proc rates such as doublestrike and glancing blow magical damage.

**Vanshilar** · 12-16-2011, 10:16 PM

Reserved for when I post about other proc rates.

**Vanshilar** · 12-16-2011, 10:17 PM

Cloudburst:
Testing for Cloudburst was by using the item Cloudburst (old version) on the training dummy. Repeatedly. The data was taken from 9 videos which totaled 24.2 hours in length. The sample size is the number of hits (i.e. misses were excluded) and was 127063, and 11507 procs were observed. This gives a 95% confidence interval for the proc rate of (8.9%, 9.2%), so the proc rate is most likely 9%. It can also proc on glancing blows, but is subject to the glancing blow magical effects proc rate.

Overall, the proc does occur fairly frequently, so despite the somewhat low proc damage of 50 or so, it still has a respectable average damage per hit.

The observed proc damages were:

Code:

Damage	Count
40	0
41	2
42	11
43	33
44	100
45	298
46	539
47	953
48	1284
49	1660
50	1772
51	1585
52	1334
53	922
54	545
55	280
56	126
57	50
58	12
59	1
60	0

The average of this is 50.01 and the standard deviation is 2.58. This matches very well with 10d3 + 30, which would be an average damage of 50 and a standard deviation of 2.58.

Earthgrab:
Testing was done using the Epic Ratkiller on the dummy. The data was taken from videos that totaled 63.8 hours in length. Yes, of hitting the training dummy over and over. The sample size was 358295 and 13617 procs was observed, giving a 95% confidence interval of (3.74%, 3.86%). The sample size was a bit overkill but I was using it to test magical damage proc rates for glancing blow and didn't have anything else (other than Cloudburst) on hand to test with. Earthgrab can also proc on glancing blows, but is subject to the glancing blow magical effects proc rate.

After doing this testing, I tested it out on a guildie in the PVP pit and it turns out that Earthgrab has a save on it, with a DC of 35. So the reason why the tested proc rate was 3.8% was probably because the training dummy would save when it rolled a 20. Hence, the proc rate of Earthgrab is likely actually 4.0%.

**Vanshilar** · 12-16-2011, 10:25 PM

I tested some guards effects. Again, the method was to take videos of them and then tabulate the results afterwards. In this case, because the dummy doesn't hit me very often, I got a level 1 char to hit me repeatedly in PvP. The videos totaled 32.5 hours of footage across 34 sessions.

It turns out that how the guards proc depends on the order that you equip them. Also, they do not proc if the victim is already dead. For example, if you equip a lightning guard item, then equip a disintegration guard item, the lightning guard has a chance to proc first, and then, only if the target survives the lightning guard, the disintegration guard has a chance to proc. From a practical standpoint it means you should equip guards that can increase damage or debuff first, followed by other guards. For example, if you equip freezing ice guard first, and then lightning guard, if you get a hit where both of them proc, the freezing ice guard will freeze the target first, rendering him helpless and thus take 50% more damage, and then the lightning strike will have an additional 50% more damage. If you equip the lightning guard first and then the freezing ice guard, then the lightning guard will proc first at regular damage, and then the freezing ice guard will make the monster helpless to everything after the lightning guard proc.

The order of guards equipped for the tests was: Epic Ratkiller (for unbalancing), GS with lightning storm guard, Epic Helm of the Red Dragon (for magma surge guard), Cloak of Night from Mabar (for nightmare guard and phantasmal killer guard), and dragontouched armor with freezing ice guard.

The unbalancing doesn't kill the target. Its sample size is all hits, and the sample size of later guards is unaffected by it. The lightning guard kills the level 1, so while its sample size is all hits, that decreases the sample size for the other effects. The sample size for magma guard is all hits minus the number of lightning guard procs, and because it also kills the level 1 outright, all later guards have to have the number of magma surge guard procs subtracted from them. Thus the sample size for the nightmare guard is the total number of hits minus the number of lightning guard procs and the number of magma surge guard procs.

It turns out the phantasmal killer effect of the Mabar Cloak will only proc when the nightmare guard procs. What this means is that its proc rate is actually the product of two different rolls, one for whether or not the nightmare guard procs, and a second roll for given that the nightmare guard procs, whether or not the PK guard should also proc. For the phantasmal killer part of the nightmare guard, out of the 52 PK procs that I specifically looked at on this, the level 1 was still alive after the nightmare guard's damage, so the PK guard will only proc if the guy is still alive after taking the nightmare guard damage. Thus, the sample size for the PK effect is the total hits minus the lightning guard procs, magma surge guard procs, and nightmare guard procs that outright killed the target. And lastly, the sample size of freezing ice guard is the total hits minus all the deaths from the above guards. Thus, you will see the sample size decrease as it moves from the earlier guards to the later guards.

In the PVP pit, when a player tries to damage another player, the DR will only decrease up to half of the incoming damage, rounding down. So even though my barbarian has 6 DR/-, when the level 1 does 5 damage, only 2 of the damage will be mitigated and the level 1 will deal 3 points of damage. This also means that when it's 1 point of damage, it will go through as if there were no DR. What this means is that every hit was guaranteed to do damage, so I couldn't distinguish between whether these guard procs are on-hit or on-damage (the latter being a hit where damage is done), since none of the hits did 0 damage due to DR. I'll have to go do some further testing on that. By the way, so a "hit" means where the level 1 actually did roll a hit, i.e. excludes swings where the guy missed because of blurry, and excludes swings where the guy missed because he didn't roll high enough to overcome my AC.

Unbalancing
Out of 39287 total hits, there were 3855 procs. So the tested proc rate was 9.81%, with a 95% confidence interval of (9.52%, 10.11%), so the proc rate is most likely 10%. The effect has a duration of 20 seconds. I didn't see any sign that there's a save to it.

Lightning Storm Guard
Out of 39287 hits, there were 561 procs. So the tested proc rate was 1.43%, with a 95% confidence interval of (1.32%, 1.55%), so the proc rate is most likely 1.5%. The observed damages were:

Code:

The average was 611.06, and the standard deviation was 25.93. This fits well with the proc rate and damage that Kinerd did previously for lightning strike, so the most likely damage dice is 20d20 +400.

Magma Surge Guard
The sample size for this was the total 39287 hits minus the 561 lightning procs which killed the level 1 and thus prevented the magma surge guard proc from occurring, so the sample size was 38726. Out of this, 772 magma surge guard procs were counted, for a tested proc rate of 1.99%. Thus, the proc rate is likely 2%. The observed fire damages and the count of how often that amount occurred were:

Code:

Damage	Count
45	1
46	2
47	1
48	3
49	2
50	6
51	1
52	5
53	6
54	4
55	7
56	10
57	11
58	14
59	15
60	19
61	18
62	21
63	17
64	21
65	27
66	28
67	29
68	33
69	23
70	32
71	22
72	33
73	30
74	31
75	25
76	22
77	21
78	25
79	31
80	25
81	18
82	19
83	14
84	7
85	14
86	12
87	13
88	10
89	7
90	12
91	8
92	6
93	5
94	5
95	1
96	1
97	1

The average was 71.84, with a standard deviation of 10.13. This makes it fairly close to 3d20+40. Because the guy died soon as he got hit with a proc, I didn't test how long or how many hits this inflicts. Also, the combat log said he was immune to magma, and the slow effect was never observed; I'm guessing though that this is because the slow effect only applies when he's still alive, so it said he was immune because he already died. Anyway it means that the slow part of the effect wasn't tested.

Nightmare Guard
The sample size was 37954, and 7601 procs were observed, for a tested proc rate of 20.03%. Thus, the likely actual proc rate is 20%. The observed damages were:

Code:

Damage	Count
5	0
6	1
7	1
8	6
9	11
10	36
11	43
12	70
13	111
14	142
15	238
16	294
17	337
18	402
19	471
20	514
21	612
22	567
23	554
24	543
25	514
26	447
27	402
28	343
29	286
30	208
31	146
32	106
33	79
34	55
35	34
36	16
37	8
38	3
39	1
40	0

The average was 22.49, with a standard deviation of 5.09. This matches well with the dice given in the description of 5d8, which has an average of 22.50 and a standard deviation of 5.12, so it's probably the dice used for this. (Yes, the description does give the dice, but it's worthwhile to confirm whether or not the description actually matches up with the numbers used in the game).

Nightmare Guard (Phantasmal Killer effect)
Procs of the phantasmal killer effect on the Mabar Cloak of Night were only observed when a nightmare guard damage proc occurred, and only when the person survived that damage. The sample size was the total hits minus the number of lightning guard procs, magma surge guard procs, and nightmare guard procs that killed the level 1 guy, so basically the total hits minus (total deaths - PK guards) since no other damages were used. So the sample size for this was 36514. Out of those, 316 procs were observed, for a proc rate of 0.87%, with a 95% confidence interval of (0.78%, 0.97%). No saves were reported in the combat log, so I can't really tell if this is because there's no save, or because there is a save but it's not reported in the combat log. At any rate though, the proc rate doesn't really seem to be settling down to an intuitive number, although the closest proc rate is 1%. I'll likely test this further.

Freezing Ice Guard
The number of hits that didn't result in the death of the level 1 guy, and thus allowed for a freezing ice guard proc, was 36198, so this was the sample size. 1850 procs were observed, for a tested proc rate of 5.11%, with a 95% confidence interval of (4.89%, 5.34%), so it likely has a proc rate of 5%. It does have a save on it, though, but the save was higher than what I could test of 23, so the DC on it is 24 or higher; I'll test with someone who has better saves later. Nevertheless, the procs that I'm counting are when the level 1 tries to make a save ("You attempt to save versus frozen."), as opposed to when the save fails. When it procs, the duration is 9 seconds.

**Kinerd** · 12-17-2011, 04:46 PM

Nice!

Did you get any Cloudbursts on glancing blows?

**Vanshilar** · 12-21-2011, 10:53 PM

Testing for incineration was done via an epic Xuum on the training dummy. The data comes from videos that total 1337 minutes (22.3 hours) in duration. There were a total of 106597 attacks. Out of those, 2088 had incineration procs, for a tested proc rate of 1.96%, so the actual proc rate is likely 2%. The somewhat-sorted damage values, taking into account the dummy's helpless state, is below:

Code:

The average was 283.86 and the standard deviation was 16.27. This fits dice 8d20+200 pretty well, so that's the likely formula.

**Vanshilar** · 12-21-2011, 11:16 PM

This testing was done using the Cloudburst (for the shocking burst effect) and the epic ratkiller with a force damage ritual, to test how often glancing blows had magical procs. The victim as usual was the training dummy. For the Cloudburst, the "shocking" part of "shocking burst" was used, since burst effects do not proc on glancing blows, only the regular magical part will proc. For the epic ratkiller, it was the force damage from the eldritch ritual that was used to count.

The goal is to count up how often magical effects will proc on glancing blows. For those who are not familiar with this, magical effects such as flaming don't automatically proc on two-handed weapon's glancing blows (although they automatically proc on every regular attack). Instead, there is a chance for them to proc. This chance starts off at 0% but can be modified by the THF feats and by certain enhancements such as warforged great weapon aptitude and barbarian's frenzied berserker prestige line. Magical burst/blast effects that depend on a crit or a roll of 20 do not proc on glancing blows at all, or at least has not been documented.

The data comes from a total of 155.2 hours of video. I don't intend on uploading them because it'll take forever, but they pretty much follow what was done for the mabar wraps here. Basically it's just hitting the training dummy over and over, and counting up how many glancing blows there were and how many of them had magical effects. The test parameters were THF + ITHF feats, THF + ITHF + GTHF feats, and some mix of them along with the warforged great weapon aptitude enhancement series, and the barbarian frenzied berserker prestige enhancement series.

The summary of results is below:

Code:

Samples	procs	Rate	Conditions	Notes
42300	2575	6.087%	ITHF     	Supposed to be 6.0%
51578	4179	8.102%	ITHF, WF 1	Supposed to be 8.0%
43497	4299	9.883%	ITHF, WF 2	Supposed to be 10.0%
68234	6115	8.962%	GTHF     	Supposed to be 9.0%
65482	7025	10.728%	GTHF, FB 1	Supposed to be 11.0%
95700	12284	12.836%	GTHF, FB 2	Supposed to be 13.0%
103436	15567	15.050%	GTHF, FB 3	Supposed to be 15.0%

Basically, the results match up with the current Turbine descriptions for them. The feats will each provide a 3% chance to proc, each tier of WF great weapon aptitude will provide a 2% chance to proc, and each tier of barbarian FB will provide a 2% chance to proc.

**bhgiant** · 12-25-2011, 11:13 AM

Do you have a subscribe button? I've subscribed to the thread but I feel more recognition is in order.

**AMDarkwolf** · 12-25-2011, 11:59 AM

With all the time you spend making the vids then analyzing them, when do you actually get time to PLAY?

And thanks for the effort to figure out exact rates, its appreciated.

**Glenalth** · 12-25-2011, 02:30 PM

Thanks for compiling all of this in one spot.

**Diyon** · 12-25-2011, 02:49 PM

+1

You are awesome. I look forward to more. No more more needs to be said.

**jejeba86** · 12-26-2011, 10:07 AM

Outstanding

**Shade** · 12-27-2011, 01:34 PM

Thanks for doing this man.
I added and verified all your data on the wiki.

I'd like to see you do Greater Incineration next as some anon source edited the wiki on it, from 4% to 5%, which seems odd since a dev mentioned it was double regular incin (4%)..

You can easily get the epic elemental greataxe of fire which has it. Just takes a few hours of mostly easy challenges.

Else the Epic Garos Malice has it. (base in non epic snith, seal in epic snitch, shard in big top)

**Glenalth** · 12-27-2011, 02:47 PM

Originally Posted by Shade

Thanks for doing this man.
I added and verified all your data on the wiki.

I'd like to see you do Greater Incineration next as some anon source edited the wiki on it, from 4% to 5%, which seems odd since a dev mentioned it was double regular incin (4%)..

You can easily get the epic elemental greataxe of fire which has it. Just takes a few hours of mostly easy challenges.

Else the Epic Garos Malice has it. (base in non epic snith, seal in epic snitch, shard in big top)

I blame SirGog

http://forums.ddo.com/showthread.php?t=351909

I did a test to 50 procs and wound up at 5% as well (somewhere around 5.05) but it's not really enough to know for sure in either case.

**Kinerd** · 12-27-2011, 08:06 PM

Originally Posted by Glenalth

I blame SirGog

http://forums.ddo.com/showthread.php?t=351909

I did a test to 50 procs and wound up at 5% as well (somewhere around 5.05) but it's not really enough to know for sure in either case.

Well, 104 procs in 2000 hits is 5.2% ± 1.0% at 95% confidence. If we say your 50 procs were exactly 5% (knowing that the rate was actually higher), that gives us another 50 procs in 1000 hits, or 5.1% ± 0.8% at 95% confidence. It's not a slam dunk for 5% over 4%, but it's pretty compelling imo.

**sirgog** · 12-30-2011, 08:48 PM

Originally Posted by Glenalth

I blame SirGog

http://forums.ddo.com/showthread.php?t=351909

I did a test to 50 procs and wound up at 5% as well (somewhere around 5.05) but it's not really enough to know for sure in either case.

Yeah the testing my friend did does not conclusively prove 5%. However, I'd heard 5%/200+8d20 from a source I trusted before organising the tests, and so I personally am convinced it is that.

**karl_k0ch** · 12-31-2011, 06:48 AM

Finally, I can +1 you again, Numbercruncher of Doom!

nice work.

How reliable are your Likely Damage Formulas? I remember when Kinerd cracked Lighning Strike, he provided a somewhat thorough reasoning on the formula.
Your propositions are shorter, which I interpret as a brevity in presentation, not reasoning.
Are there other likely candidates for the damage formulas?

**Vanshilar** · 01-06-2012, 06:15 PM

I tested disintegration on the training dummy via an epic noxious fang. The videos totaled 56 hours. In all, there were 161350 non-miss hits, and disintegration occurred 3276 times, for a tested proc rate of 2.03%. The 95% confidence interval on the proc rate is (1.96%, 2.10%), so it's likely really 2%. The observed damages, taking into account the helpless state of the dummy, were:

Code:

The average is 457.62 and the standard deviation is 22.11, so this matches pretty closely with 15d20 + 300 (which has an average of 457.5 and a standard deviation of 22.33).

The videos, as well as the counted number of hits and procs from them, are in the following table:

Code:

Name	Hits	Procs	Proc%
Total	161350	3276	2.030%
Video1	25431	543	2.135%
Video2	28959	563	1.944%
Video3	17937	365	2.035%
Video4	23453	506	2.158%
Video5	26874	505	1.879%
Video6	17953	370	2.061%
Video7	20743	424	2.044%

The count started after an initial action (such as casting the house P trinket). This is just to mark an initial location where the data could be dependable, since for example, prior to this marker, the dummy may not be taking helpless damage. Anyone can go through the video and verify my numbers if they want.

Originally Posted by karl_k0ch

How reliable are your Likely Damage Formulas? I remember when Kinerd cracked Lighning Strike, he provided a somewhat thorough reasoning on the formula.
Your propositions are shorter, which I interpret as a brevity in presentation, not reasoning.
Are there other likely candidates for the damage formulas?

Yes, there are other possible dice, so I'm just giving what I think are likely ones based on the tested information. What's reliable though is the tested average and standard deviation, and not necessarily the given dice, because there are multiple dice that may fit. The problem is basically to determine A (number of dice), B (sides on each die), and C (constant offset) in the formula AdB + C given the data. I've only been giving average and standard deviation, which would only determine up to two of the variables, but are generally what people are interested in anyway. For example, both 19d16 and 15d18 + 19 have an average of 161.5 and a standard deviation of 20.09, so those two statistics are not enough to uniquely determine the dice.

To do so, I would have to use a third statistic, such as kurtosis (which is based on (x_i-x_mean)^4 while standard deviation is based on (x_i-x_mean)^2), which essentially measures how peaked a distribution is; a uniform distribution for example is very flat and so would have a low kurtosis score. But the final problem is that because of the central limit theorem, once the number of dice exceeds a certain amount, they all look pretty close to a normal distribution, and so it requires a huge sample size to determine the difference between two. So I basically just choose "common sense" numbers that people would typically choose. Rule of thumb is also that generally, for AdB + C, A*B = C (or C is 0). So you can see that for 15d20 + 300, 15*20 = 300. Similarly, for proc rates, I'll generally determine it down to within a half percent, i.e. 1.0% or 1.5% or 2.0% etc. Although I know as I write this, the next effect Turbine comes out with will have a 1.783% chance of 17d19 + 262 damage. I just know it.

In theory I could use more exotic techniques such as Bayesian model selection, probably using the Metropolis-Hastings algorithm, to determine what is the most likely candidate set (A, B, C) given the data. A plus is that I could probably reuse some of the code from school (although I'd probably have to rewrite it extensively to fit this problem). However, I'm not sure if the work to do that is worth it, i.e. if enough people are interested in the actual dice formulae and think that just knowing the average and standard deviation isn't enough. If so I could look into that, but it would come at the expense of being slower at determining the average and standard deviation for the remaining untested procs. Of course, Turbine can always just directly release that information, but like the renown system, monster stats, and other game mechanic data, it seems like they prefer for players to figure it out and generally stay mum about specifics on how those things work.

Thread: Weapon and Guard Proc Rates

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