So that this post is not a complete waste of time, unlike the vast majority of hand-wringing and gloating cluttering TTTO over the past week post-banning (as opposed to the usual gloating and preening about acquired equipment and "accomplishments"), there were some more interesting results from lodeguy's experimentation that I did not address previously but are still interesting (they just didn't require any statistical techniques to analyze).
For direct-magic damage, does weakness to a certain element guarantee half-resists at worst?
Lodeguy demonstrated that there is a case where elemental weakness--specifically a Fire Elemental's weakness to water--guarantees half-resists for direct-damage magic at worst. He never observed anything worse than a half-resist casting Water magic over 1,000 times on a Fire Elemental. Remember that the usual distribution of resists is easily predicted (well, if you have some estimate of an "unresisted" rate to begin with), and that the proportion of quarter or "full" (1/8) resists when effective magic accuracy (no resist) is .30 is expected to be almost .50.
This observation probably does not apply to high-level Notorious Monsters with "known" elemental weaknesses. If it were true, there would be little incentive to maximize magic accuracy for such targets. I think players would generally accept the tradeoff of having few unresisted nukes in exchange for guaranteeing at least half-damage. But perhaps there is more to this phenomenon than what has been observed.
Again, I do not read Japanese so there may be something important in the discussion that I overlooked.
What is the maximum effective magic accuracy?
It is obviously 95% for direct-magic damage. Again, under the usual distribution of resists, the proportion of half resists when effective magic accuracy is 95% is .0475; for quarter resists, .002375. Note the rare quarter-resist event. A "full" resist with magic accuracy capped is even rarer, with hypothetical probability .000125, or basically a 1-in-10,000 event.
Now that that's taken care of, some idle thoughts on the duping-related bans.
Tears of a clown - my, my, how the ressentiment flies
It is obvious to me that the point of any carte blanche clause in a "terms of service" you may observe is so that the service provider has an easy out to rid itself of undesirables. I do not really care that SE reserves a prerogative to regulate its own product through banning of accounts.
Yet although SE certainly does not need to justify any bans or suspensions it metes out, the mere appearance of uneven application of "punishment" (regardless of the fact that punishment was unevenly applied) makes FFXI look even more of a joke than it already is.
That this exploit remained in place for over 18 months is enough of a joke. Never mind SE's execrable neglect of widespread RMT activity (considerably more pervasive than anything to do with Salvage) left unabated for years in a MMORPG whose conditions were extremely conducive to RMT activity (despite SE reserving carte blanche to terminate accounts), the "nerf" to Pandemonium Warden and Absolute Virtue in response to negative publicity, etc., etc.
And, anyone who thinks anyone at SE wasn't cognizant of the duping exploit at any time during the 18 or so months before the lead-up to patch-and-ban is an idiot. There is always some "snitch" who would report such a thing. I say snitch in the vein of someone who does the right thing mostly out of impure motives, like "seeing bitches get their comeuppance."
Face it, no one gives a fuck about the "integrity" of a consumer product/service like a MMORPG except immature 39-year-olds who deign to waste all their time fulminating about a trivial thing.
Of course, this doesn't stop idiots with no sense of proportion from riding SE's dick any chance they get. That SE should even pursue damages in court for duping in a video game to keep players "honest" is simply a farcical notion. Acting like SE is some poor besieged entity in a game rife with whining entitled players---most of whom, at the end of the day, despite crying about "intolerable" low drop rates in an endgame activity they voluntarily entered into, still waste their money on FFXI--is also a joke. SE and the "player community," you deserve one another.
At the end of the day, SE can merely point to your monthly credit card statements, cheater or not, and simply say, "monthly fee." Money is the prime mover, although SE sometimes seems not to act like it is.
Tuesday, January 27, 2009
Thursday, January 8, 2009
Mr. Decay
This post will be a potpourri of topics.
Chocobo racing - Crystal Stakes results
As of this post I've raced my (good) chocobo (SS/B/B/B) 112 times in the Crystal Stakes (C1) and obtained the following results:
1st: 52
2nd: 40
3rd: 16
4-8: 4
Total: 112
I haven't seen much information on results with other chocobo configurations, except from this one forum post (chocobo attributes unknown):
1st: 27
2nd: 12
3rd: 10
4-8: 7
Total: 56
Now, I have no idea how often this other chocobo faced competing PC chocobos, but seeing another chocobo's results helps to provide some more perspective.
Is B receptivity a good hedge if it means placing 2nd relatively more often than a chocobo with lower discernment, "all things being equal" (which never happens, but let's just finish this filler post)? One one hand, I'd rather place 1st more often at the expense of placing 3rd or lower more often, as in the long run the return could be better. (One way to think of it is that it's better to place 1st and 3rd in two races than 2nd both times.)
On the other hand, I don't like farming chocobucks.
Sure, you can calculate expected gains and losses of chocobucks per race, but I won't do it because it won't motivate me in any way to raise another chocobo.
Magic accuracy - does weather and day have an effect?
Earlier (see previous post), I observed that the (effective) magic accuracy of Paralyze seemed not to be (statistically) significantly affected when Paralyze was cast during Firesday and Iceday. I tried to search for more data sets, but I didn't find anything meaningful.
Lodeguy himself seems to have said neither day nor weather have an effect (too lazy to find the actual quote), but, really, since his goal was to measure changes in (effective) magic accuracy, whether or not there is a day/weather effect (that he didn't control for and is not practical to control for) doesn't matter all that much considering the effect, if it exists, processes only 1/3 of the time. (I haven't verified this myself though.)
Anyway, I guess I could operate under the assumption that weather and day do affect resist rates. But are the effects of day and weather on accuracy (if they exist) the same in magnitude as the effects of day and weather on damage?
If you wanted to test this assumption and you have a scholar, you could see whether single weather and day combined drastically increase the accuracy of nukes of the same element. (You could also check for the reduction in accuracy of nukes of the opposite element.)
Laziness dictates that I should do a basic statistical power calcuation to obtain the number of Bernoulli trials needed to observe that a possible 20% increase in effective magic accuracy is statistically significant, given a Type I error of 5%:
This conservative (but one-sided) power calculation (details omitted) indicates I need a total of 332 samples (166 for the trials without the effect of weather and day, and 166 for the trials with the effect) to observe statistical significance (using Fisher's exact test) with a probability of .8. And this probability assumes that this 20% increase (or reduction depending on your approach) is real.
But, I would have to make sure my effective magic accuracy, without the effect of weather and day, is somewhere above 50% and less than 75%. Based on lodeguy's data, one could figure this out for Earth Elementals (...) or, better, a Qiqirn ranger.
If weather has an effect on magic accuracy, why does Klimaform exist?
The English description of Klimaform states that the ability "[i]ncreases the magic accuracy for spells of the same element as the current weather." This statement does not really imply an existing accuracy bonus from weather before Klimaform, nor does it really imply no weather bonus before Klimaform.
Magic accuracy - revisiting data sets other than lodeguy's
A long time ago I looked at this data set and then just glossed over it while talking about lodeguy's results. But "intellectual honesty" compels me to attempt to explain the results of this other data set.
Actually I do not recall all the experimental details, but I "hope" the Ebony Puddings targeted were at the infamous Mount Zhayolm experience "camp." There, Ebony Puddings have a level of 79 or 80. (Incidentally, I noticed that these flans provide a experience point bonus of 5%, which I could not find corroboration for on FFXIclopedia.) Then that makes the observed data more "plausible."
First, it would be pretty obnoxious to say that the effect of magic accuracy increases with skill level without even acknowledging the imprecision of the estimates. If you are going to claim that, then you have to claim that one point of magic accuracy input gives an effective magic accuracy increase well above 1%, as shown below, using the nuke data from "Test III" and "Test IV" together (without the INT observations):
Not only can you not argue that macc is "better" than skill, you also cannot really say with a straight face that 1 point of magic accuracy input increases effective magic accuracy by some value well above 1%. That is just ridiculous on its face.
One possible explanation for the data is that the level 79 and level 80 Ebony Puddings were not targeted in roughly equal proportions; in the worst-case scenario, puddings of one level were inadvertently targeted exclusively for "Test III," and puddings of the other level were used exclusively for "Test IV." Since lodeguy provided some evidence of a level difference penalty (or bonus), we should be wary of such a phenomenon when collecting data.
For this data and experimental setting, a potential consequence of severe imbalance in the relative proportions of level 79 and level 80 Ebony Puddings targeted is a "distortion" of the true sampling distributions associated with the "skill" and "macc" effects, "true" meaning that the distributions should have a mean of 0.01.
This can be demonstrated through simulation as a demonstration of the concept. This is not a "proof" of anything, just a whimsical example. Suppose that the difference in level penalty between a level 79 and level 80 Ebony Pudding is 10% magic accuracy. Then, using the worst-case scenario I described above, I can generate approximate sampling distributions (with many, many assumptions) for the slopes associated with the main effects.
The most important assumption for this simulation is that 1 point of skill equals 1% effective magic accuracy, and 1 point of magic accuracy input equals 1% magic accuracy output (regardless of whether this is true in reality, which I think it is).
For elemental magic skill, the approximate sampling distribution has a mean of 0.0154 (not 0.01) and a standard deviation of .00245, which is close to the standard error from the actual data.
For magic accuracy input, the approximate sampling distribution has a mean of about 0.0133 (not 0.01) and standard deviation of about .00334. The standard error from the actual data is not close to .00334, but the concept still shows the "plausibility" of the data. Moral of the story: failing to control for real effects may have deleterious consequences.
As for the apparent (lack of) effect of INT below 50% effective magic accuracy ("Test II"), if 30 INT really corresponds to a 15% magic accuracy bonus (assuming any bonuses are cut in half because of the hit rate penalty), observing no improvement (or worse) is virtually guaranteed not to happen. At this point, I would just keep this result in mind but take it with a grain of salt.
Here's the R code I used to generate the above graphs:
Chocobo racing - Crystal Stakes results
As of this post I've raced my (good) chocobo (SS/B/B/B) 112 times in the Crystal Stakes (C1) and obtained the following results:
1st: 52
2nd: 40
3rd: 16
4-8: 4
Total: 112
I haven't seen much information on results with other chocobo configurations, except from this one forum post (chocobo attributes unknown):
1st: 27
2nd: 12
3rd: 10
4-8: 7
Total: 56
Now, I have no idea how often this other chocobo faced competing PC chocobos, but seeing another chocobo's results helps to provide some more perspective.
Is B receptivity a good hedge if it means placing 2nd relatively more often than a chocobo with lower discernment, "all things being equal" (which never happens, but let's just finish this filler post)? One one hand, I'd rather place 1st more often at the expense of placing 3rd or lower more often, as in the long run the return could be better. (One way to think of it is that it's better to place 1st and 3rd in two races than 2nd both times.)
On the other hand, I don't like farming chocobucks.
Sure, you can calculate expected gains and losses of chocobucks per race, but I won't do it because it won't motivate me in any way to raise another chocobo.
Magic accuracy - does weather and day have an effect?
Earlier (see previous post), I observed that the (effective) magic accuracy of Paralyze seemed not to be (statistically) significantly affected when Paralyze was cast during Firesday and Iceday. I tried to search for more data sets, but I didn't find anything meaningful.
Lodeguy himself seems to have said neither day nor weather have an effect (too lazy to find the actual quote), but, really, since his goal was to measure changes in (effective) magic accuracy, whether or not there is a day/weather effect (that he didn't control for and is not practical to control for) doesn't matter all that much considering the effect, if it exists, processes only 1/3 of the time. (I haven't verified this myself though.)
Anyway, I guess I could operate under the assumption that weather and day do affect resist rates. But are the effects of day and weather on accuracy (if they exist) the same in magnitude as the effects of day and weather on damage?
If you wanted to test this assumption and you have a scholar, you could see whether single weather and day combined drastically increase the accuracy of nukes of the same element. (You could also check for the reduction in accuracy of nukes of the opposite element.)
Laziness dictates that I should do a basic statistical power calcuation to obtain the number of Bernoulli trials needed to observe that a possible 20% increase in effective magic accuracy is statistically significant, given a Type I error of 5%:
Computed N Total
Actual N
Power Total
0.801 166
This conservative (but one-sided) power calculation (details omitted) indicates I need a total of 332 samples (166 for the trials without the effect of weather and day, and 166 for the trials with the effect) to observe statistical significance (using Fisher's exact test) with a probability of .8. And this probability assumes that this 20% increase (or reduction depending on your approach) is real.
But, I would have to make sure my effective magic accuracy, without the effect of weather and day, is somewhere above 50% and less than 75%. Based on lodeguy's data, one could figure this out for Earth Elementals (...) or, better, a Qiqirn ranger.
If weather has an effect on magic accuracy, why does Klimaform exist?
The English description of Klimaform states that the ability "[i]ncreases the magic accuracy for spells of the same element as the current weather." This statement does not really imply an existing accuracy bonus from weather before Klimaform, nor does it really imply no weather bonus before Klimaform.
Magic accuracy - revisiting data sets other than lodeguy's
A long time ago I looked at this data set and then just glossed over it while talking about lodeguy's results. But "intellectual honesty" compels me to attempt to explain the results of this other data set.
Actually I do not recall all the experimental details, but I "hope" the Ebony Puddings targeted were at the infamous Mount Zhayolm experience "camp." There, Ebony Puddings have a level of 79 or 80. (Incidentally, I noticed that these flans provide a experience point bonus of 5%, which I could not find corroboration for on FFXIclopedia.) Then that makes the observed data more "plausible."
First, it would be pretty obnoxious to say that the effect of magic accuracy increases with skill level without even acknowledging the imprecision of the estimates. If you are going to claim that, then you have to claim that one point of magic accuracy input gives an effective magic accuracy increase well above 1%, as shown below, using the nuke data from "Test III" and "Test IV" together (without the INT observations):
Analysis Of Parameter Estimates
Standard Wald 95% Confidence Chi-
Parameter DF Estimate Error Limits Square Pr > ChiSq
Intercept 1 -3.2974 0.6462 -4.5639 -2.0309 26.04 <.0001 skill 1 0.0143 0.0022 0.0099 0.0186 40.56 <.0001 macc 1 0.0179 0.0027 0.0126 0.0232 43.27 <.0001
Not only can you not argue that macc is "better" than skill, you also cannot really say with a straight face that 1 point of magic accuracy input increases effective magic accuracy by some value well above 1%. That is just ridiculous on its face.
One possible explanation for the data is that the level 79 and level 80 Ebony Puddings were not targeted in roughly equal proportions; in the worst-case scenario, puddings of one level were inadvertently targeted exclusively for "Test III," and puddings of the other level were used exclusively for "Test IV." Since lodeguy provided some evidence of a level difference penalty (or bonus), we should be wary of such a phenomenon when collecting data.
For this data and experimental setting, a potential consequence of severe imbalance in the relative proportions of level 79 and level 80 Ebony Puddings targeted is a "distortion" of the true sampling distributions associated with the "skill" and "macc" effects, "true" meaning that the distributions should have a mean of 0.01.
This can be demonstrated through simulation as a demonstration of the concept. This is not a "proof" of anything, just a whimsical example. Suppose that the difference in level penalty between a level 79 and level 80 Ebony Pudding is 10% magic accuracy. Then, using the worst-case scenario I described above, I can generate approximate sampling distributions (with many, many assumptions) for the slopes associated with the main effects.
The most important assumption for this simulation is that 1 point of skill equals 1% effective magic accuracy, and 1 point of magic accuracy input equals 1% magic accuracy output (regardless of whether this is true in reality, which I think it is).
For elemental magic skill, the approximate sampling distribution has a mean of 0.0154 (not 0.01) and a standard deviation of .00245, which is close to the standard error from the actual data.
For magic accuracy input, the approximate sampling distribution has a mean of about 0.0133 (not 0.01) and standard deviation of about .00334. The standard error from the actual data is not close to .00334, but the concept still shows the "plausibility" of the data. Moral of the story: failing to control for real effects may have deleterious consequences.
As for the apparent (lack of) effect of INT below 50% effective magic accuracy ("Test II"), if 30 INT really corresponds to a 15% magic accuracy bonus (assuming any bonuses are cut in half because of the hit rate penalty), observing no improvement (or worse) is virtually guaranteed not to happen. At this point, I would just keep this result in mind but take it with a grain of salt.
Here's the R code I used to generate the above graphs:
n = 10000
skill2 = rep(0,n)
macc2 = rep(0,n)
skill_se = rep(0,n)
macc_se = rep(0,n)
for (i in 1:n) {
success = c(rbinom(100,1,.59),rbinom(100,1,.72),rbinom(100,1,.72),rbinom(100,1,.79),rbinom(100,1,.90),rbinom(100,1,.90))
skill = c(rep(274,100),rep(274,100),rep(287,100),rep(284,100),rep(284,100),rep(295,100))
macc = c(rep(0,100),rep(13,100),rep(0,100),rep(0,100),rep(11,100),rep(0,100))
trials = data.frame(cbind(success,skill,macc))
model = glm(success ~ skill + macc, family=binomial(link="identity"),data=trials)
skill2[i] = coef(summary(model))[2,1]
skill_se[i] = coef(summary(model))[2,2]
macc2[i] = coef(summary(model))[3,1]
macc_se[i] = coef(summary(model))[3,2]
}
win.graph(width = 6, height = 4.5, pointsize = 12)
hist(skill2,freq=FALSE)
win.graph(width = 6, height = 4.5, pointsize = 12)
hist(macc2,freq=FALSE)
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