A Statistical analysis of Charm Duration

[bcbrown]

Originally Posted by DeathsSilkyMist [You must be logged in to view images. Log in or Register.]

I made a streak calculator:

This is an excellent example of using Monte Carlo methods to generate an exponential or geometric distribution. Good work!

[charleski]

Ok, I levelled up to 53 and got Boltran's to test against a higher-level mob: Corundium, one of the L50 golems guarding the passage in the Overthere wall. An earlier attempt to use a guard at the East Cabilis gate failed miserably as it seems these are now 'newbie guards' and resist virtually everything. Many thanks to @bcbrown (Lakemist) for his help in acquiring these data (it would have been almost impossible to do solo).

TLDR: Charisma is now has a very significant effect.
Initial cast is disregarded and stats computed solely with regard to charm breaks.
Input data 1:
File: L53 Corundium CHA115.txt
Total trials: 92
p charm success (per tick): 0.7737
Wilson Score lower bound: 0.6609
Wilson Score upper bound: 0.8847
Input data 2:
File: L53 Corundium CHA226.txt
Total trials: 457
p charm success (per tick): 0.9454
Wilson Score lower bound: 0.9176
Wilson Score upper bound: 0.9726

probability difference: 0.1717

Newcombe-Wilson difference interval: -0.1161, 0.1144
Significant at 99% level

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You'll notice that the number of trials is far fewer than in the previous example with the EJ spurbone. This was largely because attempting to keep the mob charmed with a CHA of 115 was almost impossible. A charm was attempted 32 times for each condition (CHA 115 or 226). With CHA 115 the maximum charm length was 10 ticks, and charm frequently broke after only 1 or 2 ticks, meaning we had to keep it rooted while I medded up to cast another expensive (400mana) Boltran's. With CHA226 the maximum charm duration was 60 ticks and I was frequently able to med up to full in between charm breaks.

Another notable feature is that in both conditions I noticed a significant number of resists on the initial cast of charm. There were 13 initial resists with CHA115 and 10 initial resists with CHA226 (out of 32 attempts for each). This difference was not statistically significant, but a lot higher than seen in my previous data set on the EJ Spurbone (2 resists out of 30 attempts at CHA115; 0 resists out of 18 attempts at CHA226).

Clearly some charisma modifier has been switched on when attempting to charm this L50 mob. This was either turned off for the lower-level mobs, or had such a weak effect that its presence was insignificant. For comparison, I plotted the 95% interval ranges for the orc pawn, EJ spurbone and L50 Corundium, all at a CHA of 115. There is obviously a very non-linear effect at play here:
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The question now is whether this is a function of the absolute mob level or the level difference between mob and caster. Since this is a static and repeatable mob, I'll go back and repeat the test when I get to 60, whioch might provide some answer.

I've updated the parsing programs (attached) to accommodate Allure and Boltran's, and also added a boolean switch in each of them which allows you to include the success or failure of the initial charm cast in the statistics. For the purposes of this analysis, this was turned off.

[DeathsSilkyMist]

Originally Posted by charleski [You must be logged in to view images. Log in or Register.]

Ok, I levelled up to 53 and got Boltran's to test against a higher-level mob: Corundium, one of the L50 golems guarding the passage in the Overthere wall. An earlier attempt to use a guard at the East Cabilis gate failed miserably as it seems these are now 'newbie guards' and resist virtually everything. Many thanks to @bcbrown (Lakemist) for his help in acquiring these data (it would have been almost impossible to do solo).

TLDR: Charisma is now has a very significant effect.
Initial cast is disregarded and stats computed solely with regard to charm breaks.
Input data 1:
File: L53 Corundium CHA115.txt
Total trials: 92
p charm success (per tick): 0.7737
Wilson Score lower bound: 0.6609
Wilson Score upper bound: 0.8847
Input data 2:
File: L53 Corundium CHA226.txt
Total trials: 457
p charm success (per tick): 0.9454
Wilson Score lower bound: 0.9176
Wilson Score upper bound: 0.9726

probability difference: 0.1717

Newcombe-Wilson difference interval: -0.1161, 0.1144
Significant at 99% level

[You must be logged in to view images. Log in or Register.]

You'll notice that the number of trials is far fewer than in the previous example with the EJ spurbone. This was largely because attempting to keep the mob charmed with a CHA of 115 was almost impossible. A charm was attempted 32 times for each condition (CHA 115 or 226). With CHA 115 the maximum charm length was 10 ticks, and charm frequently broke after only 1 or 2 ticks, meaning we had to keep it rooted while I medded up to cast another expensive (400mana) Boltran's. With CHA226 the maximum charm duration was 60 ticks and I was frequently able to med up to full in between charm breaks.

Another notable feature is that in both conditions I noticed a significant number of resists on the initial cast of charm. There were 13 initial resists with CHA115 and 10 initial resists with CHA226 (out of 32 attempts for each). This difference was not statistically significant, but a lot higher than seen in my previous data set on the EJ Spurbone (2 resists out of 30 attempts at CHA115; 0 resists out of 18 attempts at CHA226).

Clearly some charisma modifier has been switched on when attempting to charm this L50 mob. This was either turned off for the lower-level mobs, or had such a weak effect that its presence was insignificant. For comparison, I plotted the 95% interval ranges for the orc pawn, EJ spurbone and L50 Corundium, all at a CHA of 115. There is obviously a very non-linear effect at play here:
[You must be logged in to view images. Log in or Register.]

The question now is whether this is a function of the absolute mob level or the level difference between mob and caster. Since this is a static and repeatable mob, I'll go back and repeat the test when I get to 60, whioch might provide some answer.

I've updated the parsing programs (attached) to accommodate Allure and Boltran's, and also added a boolean switch in each of them which allows you to include the success or failure of the initial charm cast in the statistics. For the purposes of this analysis, this was turned off.

Charisma does have an effect on the initial cast of charm, and golems tend to have higher MR. That coupled with your significantly less data for the 115 CHA testing could explain the difference. I'd advise testing on a mob with less MR, as MR will affect charm breaks quite a bit. That specific mob you are testing is going to break quite a bit probably due to it's MR whether or not CHA affects charm breaks, which can muddy the data.

There probably isn't a level 50+ special check of some kind, there's no evidence of that in the EQEMU code. Unless someone has a P99 patch note or some in-era evidence of that.

[charleski]

Originally Posted by DeathsSilkyMist [You must be logged in to view images. Log in or Register.]

Charisma does have an effect on the initial cast of charm

I found no evidence of that. Resist rates on the initial cast were equally high in both conditions.

That coupled with your significantly less data for the 115 CHA testing could explain the difference. I'd advise testing on a mob with less MR, as MR will affect charm breaks quite a bit. That specific mob you are testing is going to break quite a bit probably due to it's MR whether or not CHA affects charm breaks, which can muddy the data.

The number of trials compiled only affects the sensitivity of the test. The relationship between sensitivity and number of trials is effectively an inverse square law:
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Sensitivity is, as a rough estimate, around twice the value shown in the graph. So the 1100 trials used for the EJ Spurbone gave a little under 2% sensitivity. But it rises rapidly for lower numbers of trials (this is one of the benefits of the Wilson Score). This test produced 92 tick-trials for the CHA115 condition and 457 for the CHA226 condition, and after adjusting for the change in p_hat this gives a sensitivity estimate of around 10%, comfortably under the difference that was found. So I feel confident in the result.

The goal here was to test on a mob with a fixed level that was easily accessible to allow repeatability. If you can think of another candidate with lower MR, please let us know.

There probably isn't a level 50+ special check of some kind, there's no evidence of that in the EQEMU code. Unless someone has a P99 patch note or some in-era evidence of that.

I think that, after 10+years of operation, it would be an error to assume that the code running p99 is identical to the EQEMU base.

[ewjax]

Originally Posted by charleski [You must be logged in to view images. Log in or Register.]

Ok, I levelled up to 53 and got Boltran's to test against a higher-level mob: Corundium, one of the L50 golems guarding the passage in the Overthere wall. An earlier attempt to use a guard at the East Cabilis gate failed miserably as it seems these are now 'newbie guards' and resist virtually everything. Many thanks to @bcbrown (Lakemist) for his help in acquiring these data (it would have been almost impossible to do solo).

TLDR: Charisma is now has a very significant effect.
Initial cast is disregarded and stats computed solely with regard to charm breaks.
Input data 1:
File: L53 Corundium CHA115.txt
Total trials: 92
p charm success (per tick): 0.7737
Wilson Score lower bound: 0.6609
Wilson Score upper bound: 0.8847
Input data 2:
File: L53 Corundium CHA226.txt
Total trials: 457
p charm success (per tick): 0.9454
Wilson Score lower bound: 0.9176
Wilson Score upper bound: 0.9726

probability difference: 0.1717

Newcombe-Wilson difference interval: -0.1161, 0.1144
Significant at 99% level

[You must be logged in to view images. Log in or Register.]

You'll notice that the number of trials is far fewer than in the previous example with the EJ spurbone. This was largely because attempting to keep the mob charmed with a CHA of 115 was almost impossible. A charm was attempted 32 times for each condition (CHA 115 or 226). With CHA 115 the maximum charm length was 10 ticks, and charm frequently broke after only 1 or 2 ticks, meaning we had to keep it rooted while I medded up to cast another expensive (400mana) Boltran's. With CHA226 the maximum charm duration was 60 ticks and I was frequently able to med up to full in between charm breaks.

Another notable feature is that in both conditions I noticed a significant number of resists on the initial cast of charm. There were 13 initial resists with CHA115 and 10 initial resists with CHA226 (out of 32 attempts for each). This difference was not statistically significant, but a lot higher than seen in my previous data set on the EJ Spurbone (2 resists out of 30 attempts at CHA115; 0 resists out of 18 attempts at CHA226).

Clearly some charisma modifier has been switched on when attempting to charm this L50 mob. This was either turned off for the lower-level mobs, or had such a weak effect that its presence was insignificant. For comparison, I plotted the 95% interval ranges for the orc pawn, EJ spurbone and L50 Corundium, all at a CHA of 115. There is obviously a very non-linear effect at play here:
[You must be logged in to view images. Log in or Register.]

The question now is whether this is a function of the absolute mob level or the level difference between mob and caster. Since this is a static and repeatable mob, I'll go back and repeat the test when I get to 60, whioch might provide some answer.

I've updated the parsing programs (attached) to accommodate Allure and Boltran's, and also added a boolean switch in each of them which allows you to include the success or failure of the initial charm cast in the statistics. For the purposes of this analysis, this was turned off.

This is really excellent work, thanks for pulling this together and sharing! Coincidentally, recently some of us were mulling over similar questions about charm duration and discussing it in the Enchanter channel in our guild discord, and I thought I might share some thoughts / ideas here:

1) Probability of Charm Duration

If the charm-break check is being performed every tick, then I believe the math associated with that check is given by:

pd(n) = (1-p)^n

where

pd(n) = probability that charm duration will achieve 'n' ticks
p = probability that charm will fail on any given check
n = number of successive charm break checks

This equation generates this graph, which matches exactly with both the PREDICTED graphs generated by OP, as well the MEASURED histograms also generated by OP. Really cool that the measured histogram data matches the prediction so nicely.

2) Inferring Mob Level from Max Melee Values

To help quantify the level difference topic, OP might be able to tighten up charmed-mob level estimates by using this equation, which correlates mob level with its observed max melee values:

Mob Level <= 30: Level = MaxMelee / 2.0
Mob Level >= 30: Level = (MaxMelee + 60) / 4.0

This works reasonably well on most exp mobs up thru Kunark, and some of Velious, although exceptions begin to creep in here and there (giants, spectres, some Hole mobs, some Juggs in Seb, etc)

But you might be able to use this to tighten up your estimate of mob level, and thus the assessment on impacts from level difference.

3) Suggestions for other higher level charm targets

Agree, Corundium is tough, his charm break data seems to vary quite a bit from other mobs, to the point I have wondered if he has some special case coding going on or something.

Suggest the two level 50 giants in FM as possible candidates (although they are often camped by exp grinders).

https://wiki.project1999.com/Mentrax_Mountainbone
https://wiki.project1999.com/Eldak_Howlingbear

I have used them for levelling, I will see if I can run some tests and share the data here.

4) Other Discussion

If we hypothesize that p, the probability of charm break on any given tick, is a function of the three variables mentioned, i.e.

p = f(level diff, CHA, MR)

then the challenge is to try to measure that, using your handy parsing code, or infer it from reading the EQEmu source code and hoping that is representative of the P99 source code.

Trying to infer it from the EQEmu source code is pretty tough. My opinion, that code is a snake pit, mostly uncommented, full of special cases and difficult to understand code. I've tried to read it and it's tough sledding. But maybe other folks might have better luck.

[Goregasmic]

If you want to test mobs of a particular level loramin came up with this list, post #49

https://www.project1999.com/forums/s...=437358&page=5

Some quest mobs might be tougher than usual so might want to check them out on the wiki first.

I know chardok has some static-level 53s like di'zok cryptmaster you could borderline charm with boltran. Shouldn't be too long to get a bunch of samples in at 53 but unlike the low level mobs that are too tame to let charisma make a difference, it is possible the 53s are too unruly to see a noticeable difference too.

My chanter is 85% into 59. I'll be able to do some testing relatively soon.

[kjs86z2]

all that matters is FT8

[kjs86z2]

the nerd boners are raging

[Duik]

Originally Posted by kjs86z2 [You must be logged in to view images. Log in or Register.]

the nerd boners are raging

Thats called a brainer.

[Goregasmic]

I don't think golem MR matters since it was the same for all tests? If anything, with no tash and high MR it helps mitigate the possibility that charisma is hidden behind already squelched resists. You'd just have to keep in mind you'll get lesser returns on mobs with low MR if tash already nullified all potential resists.

It is known mob level and MR has an effect on charm duration, here I think the level difference really shows and makes some "room" for charisma to do something. I hypothesized you might see no return on charisma on very low level mobs since the level difference is so big it nullifies any possible resists anyway. On a higher mob with resists that aren't buried under tash/level difference charisma could help. It seems to follow the logic of AC mechanics too so it wouldn't be a wild idea.

It is also known charm duration seems to nosedive past 50 due to level gap closing in. This tracks with what we already knew; past that point you can't squelch the mob's resists entirely.