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Thread: AC Parse, CS3 & ID5 & PE & DI5

  1. #81
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    Default Re: Whoa...


  2. #82
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    Default Re: Whoa...

    <blockquote>Quote:<hr>

    When i do that in Excel I see the 200 - 600 bending start at 187 raw AC.

    <hr></blockquote>

    I'm stuck on the slope of the 0-100 line. I can see that the upper line passes through 187 - but I'm not sure it has intersected the first one yet. This still looks to me like a low 100's cap. I wish we had some additional data points between 100 and 200.


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  3. #83
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    Default Re: Whoa...

    Doesnt even look like theres a (soft) cap to me.. looks like a curve that we overlayed straight lines onto every 100 ac (note that for the values >= 200.. the increase is less each time).


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  4. #84
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    Default Re: Whoa...

    Sladen -



    Imagine that for every 1 AC you added, you mitigated 1% better. At 100 AC, you would mitigate 100%. If you plotted this on a graph, you would see a straight line from 1AC and 1% mitigation on up to 100/100. If the line isn't straight, if instead it "bends" at some point, then the point where the bend occurs is the softcap. The existance of a softcap doesn't imply an upper limit where AC no longer does any good - we'd call that a hardcap. The softcap is the point where we begin to see diminishing returns.



    In my fake example, let's say you got 1% mitigation up to 50 AC, and then after that each AC only gave you .5% mitigation. The softcap is 50, and now you'd only be at 75% mitigation at 100 AC.



    Demandred's graph clearly shows a steep slope at first, then a more gradual one - implying a softcap somewhere between 100 and 200.


    </p>Edited by: <A HREF=http://p201.ezboard.com/bmonklybusiness43508.showUserPublicProfile?gid=bla zyn>Blazyn</A> at: 5/19/05 4:39 pm

  5. #85
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    Default Re: Whoa...

    I played around some more with Neds excellent data, because this line vs curve thing was annoying me. There is of course a softcap of some form but what meaning would it have if the mitigation plot turns out to be a curve? Basically none, so there has to be an explanation.



    I started by looking at the frequency of max hits in Ned's parse:







    Clearly, this is not a straight line, but a curve of the form 1/x. So how can this lead to something that looks like a line in the mitigation plot? You got it, if you take the inverse of this curve you get:





    Which is clearly a line. So what does this have to do mitigation?



    The area under the graph in our first plot is the damage taken from max hits while mitigation basically is the damage we don't take, or mathematically, the inverse of the max hit distribution.



    But what about the other hits that are non max hits? They also contribute to mitigation, but it turns out we can simplify this quite a bit by noting that all but the min/max hits are aproximately a uniform distribution. So we deal with the min hits first. I do the same thing as I did with max hits:







    and then I form the inverse of this plot:





    In the next step I will subtract the inversed min plot from the inversed max plot. The explanation to this subtraction, is that min hits can't be mitigated. Then we have the the other hits that are non min/max hits. As mentioned earlier they also contribute to mitigation, but they will do this by an equal amount (remember I assumed a uniform distribution for these hits) at each ac point, so the only effect they will have is, some constant mitigation will be added to each data point. Since I already plotted the mitigation I will simply add a constant to each data point so that the estimated mitigation fits with the first data point in the previously posted plot.





    Now we can compare this with the initial mitigation plot, in where I simply used the average, min and max hits.





    Conclusion: The mitigation curve is basically determined from the max and min hit distributions. After reaching a certain AC the mitigation will be aproximately linear, but not completly, because the other hits, which I assumed were uniformly distributed, are not truly uniform.






















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  6. #86
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    Default Re: Whoa...

    I don't agree with the subtraction of 1/max from 1/min as being a valid estimator, because other hits in between can be mitigated to different extents (eg DI interval no. 2, if mitigated 5%, is going to end up as min damage, but anything more can't take it below DI1 either -- whereas DI 20 (=max hit) or DI 19 (next highest hit) will be effectively mitigated at all except the higest ACs).



    However, your insight on plotting the inverse of the % of max hits is VERY interesting -- and looks amenable to fitting to determine the exact softcap. By eye though, it does seem to confirm that the softcap is between 100 and 200 raw AC, i.e. less than 1067 displayed.... if THIS is the INCREASED softcap at 65, I shudder to think what it was before -- and suggests to me that this data really isn't showing the same thing as Brodda Thep's parses vs the HoH mobs -- unless CS3+ID5 really amounted to increasing this to around 300 raw AC (1325 displayed).


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  7. #87
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    Default Re: Whoa...

    Just plot without the 0 - 100 data.



    The 0 raw AC data is obviously skewed by some penalty no one bothered to tell us about.



    I'm pretty happy withe the notion that at 65 a person's softcap for AC is around 1200.



    The return over the cap is what has "reversed" the nerf. The cap itself is stupidly low.






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  8. #88
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    Default Re: Whoa...

    <blockquote>Quote:<hr>The area under the graph in our first plot is the damage taken from max hits while mitigation basically is the damage we don't take, or mathematically, the inverse of the max hit distribution.<hr></blockquote>



    Not mathematically, but logically yes.



    Just saying.



    You are correct however.


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    Default Re: Whoa...

    I'd go along with that. It'd be nice to see exactly how the Mitigation AA's affect the curves, but this makes AC worth something for us again.



    Curiously, this strikes me as a reflection of the situation for Tank classes at the time of the Nerf, in that at that point they'd been getting to the (then hard) cap and thereafter just loading up on HP, but after that AC was worth something again... our cap might not have been hard, but it was certainly not readily distinguishable from that until the current round of fixes.




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  10. #90
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    Default Re: Whoa...

    <blockquote>Quote:<hr>I don't agree with the subtraction of 1/max from 1/min as being a valid estimator, because other hits in between can be mitigated to different extents (eg DI interval no. 2, if mitigated 5%, is going to end up as min damage, but anything more can't take it below DI1 either -- whereas DI 20 (=max hit) or DI 19 (next highest hit) will be effectively mitigated at all except the higest ACs).<hr></blockquote>

    Well if you look at the end result you see the estimation seems to work and the reason is that only the min and max hit's change in Ned's parse while the other DI's stay roughly equal throughout each parse. Anyway the intention was not to get the exact mitigation plot, since there are much easier ways to do this (only average, max and min hit values are needed).



    I wanted to clarify for myself, the linear behaviour of the mitigation plot. I started to understand this when I saw that the inverse of max hit formed a line. I was still worried that the min hits would destroy the linear behaviour, but it turned out the min hit distribution was aproximately a line, which leads to a 1/x curve once we inverse it. So in the long run when we reach high ac values, the inversed min hit curve willl flatten out and the mitigation plot will behave linear after some certain point (soft cap).






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  11. #91
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    Default Re: Whoa...

    Hm. True. It appears to me that the 20-interval damage distribution is a kind of a "window" on a larger range of numbers - and that values that fall below the minimum get mapped to the minimum, and values above the maximum, to the maximum..




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  12. #92
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    Default Re: Whoa...

    <blockquote>Quote:<hr>values that fall below the minimum get mapped to the minimum, and values above the maximum, to the maximum<hr></blockquote>





    You've hit on something here. There really isn't a true 21 point DI.



    The DI is a creation, hence as you proved to me, the spikes at the top and bottom.



    Could it be our mitigation change included a change to the conversion factors of the real numbers to the 21 DI table?



    This also means that with a couple key strokes they could literally even out the distribution... Take 1/19 of hits over or under and put them here... This would open up a lot of game play and improve the combat system.


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  13. #93
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    Default Re: Whoa...

    I had a thought or 2 about what an accumulated normal distribution looks like. Take a look at this:



    (The top and bottom 'buckets' are actually "this value and further out" totals).



    Now increase the standard deviation further:



    Compare the bottom graph with Nedrom's graph for +200 AC ... I find it strikingly similar. Then, consider changing the Mean of the distribution:





    This is a bit of an aside with respect to AC parses, but IMO it gives a useful insight into what we actually see when we parse the data. It appears (to me) that the 'bell curve' we've been asking for has always been there, but as part of a larger range of values... perhaps someone with some formal statistical training can use this to take it further.



    (If anyone wants to play with this themselves, the OpenOffice spreadsheet I used for these is available here).


    </p>Edited by: <A HREF=http://p201.ezboard.com/bmonklybusiness43508.showUserPublicProfile?gid=anc aglon>Ancaglon</A>* at: 5/23/05 7:25 pm

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    Default Re: Whoa...

    If the damage distribution is indeed as above, then the Average damage taken is a valid measure of mitigation - the min and max percentages are an artifact of the binning up process.



    I then plotted (maxDmg-minDmg)/(avDmg-minDmg) against raw AC, and compared the gradients of the 2 sections. This shows that the gradient of the latter section is 2.8 times the gradient of the 1st segment -- which, to me, implies that our return on AC over the softcap is 1 per 2.8. The 'soft cap' implied this for an Iksar monk at level 65 is 118 worn AC -- for a Human monk this would be 150 worn AC.






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  15. #95
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    Default Re: Whoa...

    Ancaglon,



    Thanks.



    For whatever reason I get the lines to cross at about 187 RAW AC using my formula...



    I'm certain that RAW AC is capped at about 150-190AC.


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  16. #96
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    Default Re: Whoa...

    alrighty, been following this thread for awhile, and i don't mind telling you i don't understand at least half. You guys are doing awesome work, and i want to thank you for it.



    Anyone think we can come to an agreement on when to buy our migitation aa's so as to get the full effect. can we post it like this.

    (random guesses here)



    1200 - Luclin Def

    1350 - PoP

    1500 - OoW



    would be nice to have numbers, even if they are not 100% correct, and would kill alot of the new threads.


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  17. #97
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    Default Re: Whoa...

    im going to try to re-parse with CS3 over the next week


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  18. #98
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    Default Re: AC Parse

    will have cs3 1798 ac parse in the morning for you

    over the next few days ill include them with the other values of ac, i just have to let em run overnight



    i had a peek at the log file after 50k damage, the results are very interesting <img src=http://www.ezboard.com/images/emoticons/smile.gif ALT=":)">


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    </p>Edited by: <A HREF=http://p201.ezboard.com/bmonklybusiness43508.showUserPublicProfile?gid=ned rom2004>Nedrom2004</A> at: 5/25/05 12:39 am


  19. #99
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    Default Re: AC Parse

    Is there any reason to believe that the cap at 70 is the same as at 65 ?



    Reason I ask is, why do all the parses at lvl 65 if a large proportion of monks are lvl 70 ?


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  20. #100
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    Default Re: AC Parse

    Majority of monks on Emarr are lvl 66-68 from what Ive seen from doing /w all monk.


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  21. #101
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    Default Re: AC Parse

    <blockquote>Quote:<hr>This is a bit of an aside with respect to AC parses, but IMO it gives a useful insight into what we actually see when we parse the data. It appears (to me) that the 'bell curve' we've been asking for has always been there, but as part of a larger range of values... perhaps someone with some formal statistical training can use this to take it further.<hr></blockquote>

    Great work. I'm using MS office myself but I think I got your model right. I ran through the model and checked with the parse results and it's quite amazing how it predicts the hit distributions. Like look at this, using the parsed average hit (transformed to DI) in the model:







    The staples are 95% confidence intervals for the parse results and the model scores 20/20! Coincidence? Probably not. It turns out the std=9 model works great for 300-600 rAC but is less accurate from 0-200 as expected, since the softcap does something to the distribution, which leads to a different deviation.




    </p>Edited by: <A HREF=http://p201.ezboard.com/bmonklybusiness43508.showUserPublicProfile?gid=dem andred>Demandred</A> at: 5/25/05 4:30 am

  22. #102
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    Default Re: AC Parse

    Wow, that's pretty nice, considering that I just chose sd=9 'by eye' as an example from the graphs, increasing it by 2 each time, rather than trying to fit the distribution in any mathematical way. I suspect 9.5 or 10.0 might fit better (half of 19 or 20) but confidence intervals are a thing I don't remember how to use anymore <img src=http://www.ezboard.com/images/emoticons/wink.gif ALT=";)"> hence my plea to someone that does.



    I would guess that level 65's being used because it's where Brodda Thep's parses were done. The form of the equation that's used by Magelo (and which is pretty much spot on for everyone except Monks and Iksar <img src=http://www.ezboard.com/images/emoticons/wink.gif ALT=";)"> ) is this for an unbuffed melee class:



    DisplayedAC = trunc[(AvoidanceAC + MitigationAC) * (1000 / 847)]

    AvoidanceAC = AGIfactor + trunc[DefenceSkill * 16/9]



    (AvoidanceAC is set to 0 if the above total is less than zero).



    (AGIfactor above level 40 and for AGI 126-199 is trunc[(AGI+374)/10 ] , and for AGI 200-305 (possibly higher) is trunc[(AGI+1060)/20 ] ).



    and



    MitigationAC = trunc[DefenseSkill/3] + trunc[raw AC * 4/3]



    From what Kavhok wrote over in EQlive, the Monk bonus is equivalent to (Level+5) raw AC. Additionally, I estimate the Iksar bonus to be trunc[Level/2] worth of raw AC.



    So, just levelling up from 65-70 will only increase the Mitigation AC by a very small amount, due to the increased Defence skill and the level bonus(es). Avoidance AC increases by more (due to Defence skill) and so Displayed AC also rises. (The 18 pt rise in Defense skill from 252 to 270 amounts to +6 mitigation AC, +32 avoidance AC, and hence 44-45 displayed AC).


    </p>Edited by: <A HREF=http://p201.ezboard.com/bmonklybusiness43508.showUserPublicProfile?gid=anc aglon>Ancaglon</A>* at: 5/25/05 5:03 am

  23. #103
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    Default Re: AC Parse

    9 is the magic number :p. I didn't find anything better.


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  24. #104
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    Default Re: AC Parse

    <blockquote>Quote:<hr> Is there any reason to believe that the cap at 70 is the same as at 65 ?



    Reason I ask is, why do all the parses at lvl 65 if a large proportion of monks are lvl 70 ?

    <hr></blockquote>



    because...a majority of the complaints on this forum are for non-raiding casual monks.



    so i'm posting values for level 65.



    page 1 now has 1789 AC CS3 parse, ill post more when i get it



    AFIK...AC was not changed when OOW came out, so most likely caps were not changed from 65-70


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    </p>Edited by: <A HREF=http://p201.ezboard.com/bmonklybusiness43508.showUserPublicProfile?gid=ned rom2004>Nedrom2004</A> at: 5/25/05 7:15 am


  25. #105
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    Default Re: AC Parse

    If I apply the gradient of the 'post-cap' line to Nedrom's CS3 plot, and calculate its' intercept with the 'pre-cap' line, I get a value of 178 AC for Iksar, which translates to 210 AC for a Human - an increase in the cap of 60. ANy other parses he does in the 150-350 range will help nail this down.



    Speculating wildly, I would say CS1 increases cap by 10, CS2 by another 20, and CS3 by another 30.


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  26. #106
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    Default Re: AC Parse

    Ancaglon thanks. Ned thanks.



    CS3 looks worth 2% more mitigation at 1700AC.



    The line for mitigation as he decreases AC will be interesting to watch.


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  27. #107
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    Default Re: AC Parse

    <blockquote>Quote:<hr>Combat Stability: (3 skill levels) - Each skill level gives the character an increased ability to reduce the damage he takes in combat (damage mitigation). The first skill level increases the character's damage mitigation by 2%, the second skill level raises the damage mitigation increase to 5% and the third raises the increase to 10%.<hr></blockquote>



    Add that to the stated softcap value of 163 rAC, plus any misc gains from level 51 - 65 and you come out between 190 - 200 ish rAC. ( assuming of course the 2, 5, 10% increase stacks instead of being an increase based on a fixed number. )



    Interesting read, good luck tracking it down.


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  28. #108
    Iksar Admin OMFG I Post Too Much Nedrom's Avatar
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    Default Re: Whoa...

    added 1639 + cs3 parse


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  29. #109
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    Default Re: AC Parse

    Graph of inverse average damage with CS3 points: although this is only 2 points, the gradient is steeper than that without Combat Stability by a factor of 1.12 (i.e 12% better) -- this may be what's meant by "mitigating 10% better", rather than simply increasing the soft cap.




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  30. #110
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    Default Re: AC Parse

    ya, once ac increase you'll get closer to a 10% mitigation improvement. So basically no need to parse CS3 anymore, just go on with those other aa's :)


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  31. #111
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    Default Re: AC Parse

    I'd like to see at least one more CS3 run at about 200-300 raw AC to see if it really IS a straight line also, and to pin down the actual effect...


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  32. #112
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    Default Re: Whoa...

    added 1482 cs3 parse



    i got a new webserver this month and it blows ass, so my bandwidth has exceeded...who woulda thought...



    so anyway, i posted the numbers on the first thread at the top in the chart there



    pictures should be fixed tonight if my friend fixes my account


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    </p>Edited by: <A HREF=http://p201.ezboard.com/bmonklybusiness43508.showUserPublicProfile?gid=ned rom2004>Nedrom2004</A> at: 5/25/05 8:53 pm


  33. #113
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    Default Re: AC Parse

    Curiouser and Curiouser....

    Updated to include CS3/400ac. It seems to converge on the AC cap line....




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  34. #114
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    Default Re: AC Parse

    ill have the 1300 parse tomorrow morning


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  35. #115
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    Default Re: AC Parse

    Watch them merge at 300 rAC :)


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  36. #116
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    Default Re: AC Parse, now with CS3

    added 1325 AC CS3 parse


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  37. #117
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    Default Re: AC Parse

    Not quite... it still lies on a line that seems to lead back to where the pre-cap and post-cap lines cross.




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  38. #118
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    Default Re: AC Parse, now with CS3

    added 1167 parse


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  39. #119
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    Default Re: AC Parse, now with CS3

    Good grief. Now I have no clue what's going on.




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  40. #120
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    Default Re: AC Parse, now with CS3

    It apears that CS3 only raises the soft cap and not the return on Ac over the cap, thus, the diminishing return normalizes then begins to appear (only apprears) to decrease.


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