Magic Accuracy and INT

[CDF]

Talking about applicability and generalizability... "wut."

Why not a different INT critical point for INT-based enfeebling vs. elemental magic? As I recall (actually I was apparently the only person to look at it critically), pchan's other data with elemental magic provided another source of corroboration of the critical point being around d(INT) = 10. At least there was really nothing to suggest that the critical point could be higher.

Here's the summary of lodeguy's data regarding INT and elemental magic (Burn). Obviously no confidence band, but note the estimated slope of the blue line was +0.9% per INT, so this could have been merely Type I error. Mentally extrapolating this line shows the relative implausibility of having the critical point as high as +15.

http://4.bp.blogspot.com/_rgArRdhzZw...tRate_Burn.png

[Klutz]

Everyone put on your thinking caps. It's time to articulate the simplest terms in a such a way that makes you look like a professional while at the same time criticizing others.

This kind of thinking is what makes the best of BG the best!

[Callisto]

My proposed formula would be dINT/8^3 - Enfeebling skill/3 * π = YOUGAY

[Wrish]

I further looked into the spreadsheet, and there are additional data points - one each at even higher INT for blm and pup. They comport with what we know about INT vs. m.acc., but why leave out two of ten relevant experiments?

No clue what you are talking about. PUP/RDM tests have dint=9,15 and 23. Try more, fail less.

My query is over why your Elvaan PUP/RDM did not test at the naked INT value of 55 INT, for a dINT of -3... while your Elvaan BLM/rng was ever so cautious to test at 55 INT despite a naked INT of 58. Reaching and measuring a baseline for magic hit rate validates the testing and interpretive methods - something Kaeko keenly pointed out as missing from the data (even in the worksheet entitled "sea").

The "code" you quoted of me just shows how your data reinforces the m.acc versus m. hit rate slope change at 50% hit rate, regardless of source of m.acc (skill or INT). Otherwise the PUP tests would appear to show dINT at all tested values having severely diminished effect. You don't need to and shouldn't have us all take for granted that the same 50%-hit-rate inflection point applies to enfeebling when you can pinpoint it with data.

[Kaeko]

Talking about applicability and generalizability... "wut."

Why not a different INT critical point for INT-based enfeebling vs. elemental magic? As I recall (actually I was apparently the only person to look at it critically), pchan's other data with elemental magic provided another source of corroboration of the critical point being around d(INT) = 10. At least there was really nothing to suggest that the critical point could be higher.

Here's the summary of lodeguy's data regarding INT and elemental magic (Burn). Obviously no confidence band, but note the estimated slope of the blue line was +0.9% per INT, so this could have been merely Type I error. Mentally extrapolating this line shows the relative implausibility of having the critical point as high as +15.

http://4.bp.blogspot.com/_rgArRdhzZw...tRate_Burn.png

(post not directed at CDF just to everyone else)
This is the other pchan related data set involving elemental magic for anyone that is wondering. This is also what oldWiki generally says since Pchan edits oldWiki.

http://bluegartr.com/forum/showthread.php?t=78828

EDITS:

Here are the relevant lines from this thread regarding the idea that dINT=10 was the cutoff in this other Pchan data set:

There are some borderline cases here from the standpoint of statistical significance, such as macc and INT. Checking the residuals, the Alkalurops data (row 84) seem "extreme." Interestingly, the level adjustment effect is not close to significance (are rows 76-78 for a different level qiqirn than the other rows?).

Of course, the identification of delta(INT) = 10 as a critical point was done informally. Let's try applying the model for samples where delta(INT) <= 10. (I removed the level effect from the model.)

....

INT is indeed more efficient below delta(INT) 10 than above.

Using the MACC scores, there is a statistically significant lack of fit to all twelve samples (p-value .0026... compared to the saturated model) even accounting for level difference (p-value .0701).

So, it may be worth checking model fit to the data where delta(INT) <= 10 and where delta(INT) >= 10. Start with the first case where delta(INT) <= 10:

....

And for the second case with delta(INT) >= 10:

....

While superficially the MACC score is not really different in either case, there is a lack of fit to the data given delta(INT) >= 10. Checking the residuals, row 84 (Alkalurops) stands out like a sore thumb (std. residual above 3). Removing the Alkalurops data gives the following result:

[Vodou]

To me methodology is secondary to whether all of this is valid data at all, given the sheer difficulty of repeating these exact conditions.

What "exact" conditions are you trying to repeat? Time of day? HP of caster? et al? The OP stated the conditions. If someone repeats the tests, the result will either be the same or it will not. If it is, it validates the theory. If it doesn't, it demonstrates that either the theory is incorrect or the subsequent tests were conducted differently than the OP stated.

Whether it's Kparse or ffrep or some old parser, the results would probably be nearly identical and, where occasionally erroneous, not suggestive of systematic bias.

The OpenOffice spreadsheet I just now see is a step in that direction toward verifiability and credibility. I'm importing with Excel and that seems to strip all formulas, but after initial spot checking it seems to pass.

Your posts continue to be too transparent. There are no issues of either verifiability or credibility that can be solved by having every single data point posted on a spreadsheet along with an attached screenshot of each event. Theories are not proven by knowing exactly how the person derived his theory and by seeing every data point accumulated.

They are proven (or dis-proven) by independent testing.

If someone wants to try to verify or discredit the theory, repeat the tests or create tests that will demonstrate the theory.

[Klutz]

My proposed formula would be dINT/8^3 - Enfeebling skill/3 * π = YOUGAY

Oh god I lol'd.

[pchan]

I further looked into the spreadsheet, and there are additional data points - one each at even higher INT for blm and pup. They comport with what we know about INT vs. m.acc., but why leave out two of ten relevant experiments?


My query is over why your Elvaan PUP/RDM did not test at the naked INT value of 55 INT, for a dINT of -3... while your Elvaan BLM/rng was ever so cautious to test at 55 INT despite a naked INT of 58. Reaching and measuring a baseline for magic hit rate validates the testing and interpretive methods - something Kaeko keenly pointed out as missing from the data (even in the worksheet entitled "sea").

The "code" you quoted of me just shows how your data reinforces the m.acc versus m. hit rate slope change at 50% hit rate, regardless of source of m.acc (skill or INT). Otherwise the PUP tests would appear to show dINT at all tested values having severely diminished effect. You don't need to and shouldn't have us all take for granted that the same 50%-hit-rate inflection point applies to enfeebling when you can pinpoint it with data.

If you cast bind with no INT/skill from gear you will be at lower cap (5% magic hit rate). From what I remember, magic evasion was 243, due to test I (246-3int). This means that the base skill of pup/rdm put me at 142 skill (with troque and cape) and 56 INT, which gives 140 magic accuracy exactly. This gives 50%-51.0% hitrate : I'm therefore below the cap, so I have to up my int or magic acc to get above the cap. Balrahn gives +4 mac, range gives 2 mac, aumented earring gives +2, so +8 total. 142 skill and 8 mac is what is listed in the test of PUP/RDM. Naked it would then give 150 magic accuracy, or ... 50%-46.5%=3.5% hit rate. I'm still below the cap. I need 3 magic accuracy to reach the cap exactly, so anything below 62 INT is a useless test. I decided to start slightly above 62 due to the other constraint of having low str (pup/RDM has 70 so i need at least -8 str), this would be hard to to do w/o errant legs which gives -7 str but also +7 INT. After that i still had to reduce str so used other gear end ended up at 67.


On a side note, my test do confirm the relation 1 mac = 0.5% magic hit rate, or else the above reasoning would probably lead to different hit rates. With 67 INT, 142 skill, 8 mac, you predict 50%-42%=8% which is exactly what the first test on PUP gives. My goal was not to test this anyway, I already said I admitted the mac part and would study the variation of dint, since we knew the evolution post dint=10 was not super documented.

[pchan]

I take it parser distinguishes between resist and "no effect"

K parser records "no effect" "successfull" and "#times", so getting the resist rate is just a matter of doing :

[ (#times - "noeffect")-"successful" ] / [ #times - "noeffect" ] ). And yes I checked beforehands that "resist" are not counted as "no effect", but are counted in "#times#).


For day weather : there are none. Only day bonus/mallus can have an effect, since I don't pay attention to this. I don't think it can have a serious effect on the hit rate, but if you think it does, first you'd need to prove if weather affects mac and secondly how much (100% of the time ? 1/3 of the time ? how much magic accuracy ?).

[pchan]

I further looked into the spreadsheet, and there are additional data points - one each at even higher INT for blm and pup. They comport with what we know about INT vs. m.acc., but why leave out two of ten relevant experiments?

Are you going to repeat this for every test listed in the spreadsheet ? The "sea" page has 8 tests of huge sample and 1 test of 700 sample size with was done on a tough mob.. I stopped using tough mobs since I had to nuke them to know their level. Level 75 mobs are much easier to target.

[Kaeko]

K parser records "no effect" "successfull" and "#times", so getting the resist rate is just a matter of doing :

[ (#times - "noeffect")-"successful" ] / [ #times - "noeffect" ] ). And yes I checked beforehands that "resist" are not counted as "no effect", but are counted in "#times#).


For day weather : there are none. Only day bonus/mallus can have an effect, since I don't pay attention to this. I don't think it can have a serious effect on the hit rate, but if you think it does, first you'd need to prove if weather affects mac and secondly how much (100% of the time ? 1/3 of the time ? how much magic accuracy ?).

This is something people can harp on since we don't really conclusively know if enfeebling magic hit rate is affected by day/weather; however, there is nothing saying it doesn't either. It doesn't necessarily debunk anything either. It's just something you have to note and everyone should be aware of regardless of their belief that it does/does not affect hit rate.

[Argettio]

Looks like the actual discussion started off while I was away for the weekend (Titties, clubs, stuff).

Has any thing important been said? I read the first page I missed and got bored around the point some guy was suggesting Pchan re-does his tests on an HNM...

[Kaeko]

I would personally like to hear Pchan respond to CDF (Robonosto) since he's probably the best person to decifer the statistics side. Based on his first post, there is some stuff worthy of discussion.

His post was here
http://bluegartr.com/forum/showpost....&postcount=141

[pchan]

I would personally like to hear Pchan respond to CDF (Robonosto) since he's probably the best person to decifer the statistics side. Based on his first post, there is some stuff worthy of discussion.

His post was here
http://bluegartr.com/forum/showpost....&postcount=141

The data of the JP guy doesn't validate the model int=0.5 mac past dint=10, just saying. He finds 3.3% increase only between dint=10 and dint=20, while the model would predict 5%. 5% doesn't even lie within both confidence intervals. The only points that confirm the 1 int=0.5% are the data points for dint>20. I tried to google translate the page, but it's hard to understand what he did, and he doesn't give data. I assume he casts burn and register the # of lands and # of resist, which both give an estimate for p (# resist gives (1-p)^2).

[CDF]

It was actually Water being used. I had to refresh my memory (original source). Data table is toward the top.

Also, the Wald 95% CI for the difference of two proportions between Δ(INT) 10 and Δ(INT) 20 is (0.465%, 6.1%). One could argue that if the critical point were really Δ(INT) = 15, you should then expect a 7.5% increase (instead of 5%) between Δ(INT) 10 and Δ(INT) 20.

At the moment, I don't really see how one could reconcile this result and your result, but I haven't considered too deeply other factors that might explain this discrepancy (aside from the critical point for elemental magic is different than that for enfeebling).

[pchan]

It's funny that when you look at the 1/8 resist rates, and calculate their errors, you find that the range dint : 10 > 20 matches with the previous model while the range 20 > 30 doesn't (using the table from you link with partial resists), although the error is much higher due to weak sample size. Maybe it's the explanation. You might want to to wait that all the estimations for all the partial resists reach a low enaugh value to validate the test. Having 4 different possible states for the spell is probably adding a lot of noise compare to a spell that has 3 states.

[CDF]

All inference is based on the assumption that the probability of no resist, p, is the "fundamental" parameter. This assumption is shown to be reasonable based on a few lines of evidence cited in this thread and elsewhere.

For the water data, direct estimation of the binomial parameter p (probability of no resist) is possible (based on the above assumption), so you wouldn't care about conclusions using an alternative estimator like (1-("#no of full resist"/n)^(1/3). We care only about estimating the probability of no resist (and changes in that probability when INT changes).

Also, for a given sample size there is no additional "noisiness" from 4 levels of resist vs. 3 levels. Obviously, the levels of partial resist represent a partitioning of the probability of partial resist, where (1-p) = p(1-p) + (1-p)^2 for 3 levels, or (1-p) = p(1-p) + p(1-p)^2 + (1-p)^3 for 4 levels.

Finally, it shouldn't be surprising that you might get different conclusions based on different estimators for the same data set. It's only from a frequentist perspective (repeating the same data collection and calculating the statistics many, many times) that the alternative estimator of p is an OK substitute for the direct estimator of p.

Using an alternative estimator based on solving for p from (1-p)^2 is OK when we don't have knowledge of the direct estimator (#no of success/total) because of practical limitations, but the direct estimator should be used when it is available.

[Byrthnoth]

Okay, so! I haven't been keeping up with the MAcc stuff nearly as well as I should considering I'm pretty much a mage everywhere. Some of what you guys are saying (I think) makes intuitive sense to me, but let me see if I can write it logically.

1) Based on the math you're doing, I think you'd predict that the detected accuracy of a spell would be dependent on the number of possible resist states.
Benefit: This would eliminate the need for a magic-specific MAcc Boost/Penalty to account for things like Bind vs. Stun accuracy, or Elemental Magic (4 states, 1, 1/2, 1/4, 1/8, 0) vs. Enfeebling magic (0-2 generally?), for instance.

2) You have one Magical Accuracy total based on your skill, INT (or MND), and your gear/buff MAcc. This is compared to one Magical Evasion, which is based on the target's INT, elemental resistance, an ethereal "magical evasion" trait which is likely a function of level, and possibly a monster specific bonus.
Benefit: By moving towards this equation we begin to understand how to optimize MAcc across spells.

3) Spell hit rate has a cap, but it might be over 95%. - This is something I've heard a few times in these threads, but not something I'm necessarily convinced of. If there are multiple states, then a spell with two states and a 95% hit rate would a 99.75% chance of full resist. At the same time, with Hit rate capped at 95% something with four resist states like Elemental magic would have only an 81% chance of going unresisted. I'd like to think my BLM sees numbers a little more impressive than that.

[mdkuser]

At the same time, with Hit rate capped at 95% something with four resist states like Elemental magic would have only an 81% chance of going unresisted. I'd like to think my BLM sees numbers a little more impressive than that.

caped hit rate means rate of NO RESIST is 95%. how you find 81% lol?

It all depends what you mean by "hit rate cap", that's where people are usually confused ( not to mention, there are situations where more macc increase rates of partial resists). I am pretty sure pchan parsed the maximum and minimum non-resist rate to be 95% and 5% ( unlike melee acc). This means a spell like sleepga has only 1/8000 chances of being full resisted in caped acc situations; its easy however to get partial resists even on lv -1 wild rabbits: gather 20 of them and spam sleepga, you will get half resists after a few tries.

The binomial model for partial resists is also the most simple from programming point of view: the game first checks if the spell lands ( proba p) or doesnt land ( 1-p). If it doesnt land it checks if it will be half resisted ( p) or more ( 1-p). etc.

[Nevex]

Has anyone ever run tests with -ga spells? Other than splitting the damage, it seems that their base accuracy is affected by the number of targets as well.

I.e. if you cast Poisonga on a bunch of level 30 mobs, while it normaly has near 100% hit rate, you'll notice quite a few resists in the course of few casts. Likewise this happens very often with any -ga nuke, too often to assume that 95% is the cap.