Value of ATK (graphs included) (Romidar, 2/3/04)

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Value of ATK (graphs included) (Romidar, 2/3/04)

Postby Valya Wanderfoot » Sun Sep 24, 2006 1:10 pm

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(2/3/04 2:05 pm)
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Value of ATK (graph of damage distribution)

Copying this from the general forum at the request of several board members. To pacify those who care, this is not presented as "discovery," it's presented as a demonstration for those who haven't seen it.

Sure, the pictures are worth 1000 words, but I'll sprinkle a few words in anyway - consider them free added value. Smile

We all know that ATK is valuable. We ask and answer a lot of questions about ATK. We're seeing now that ATK from strength actually works the same as "pure" ATK (a change from days past). However, unless someone is at least a little mathematically minded, explaining that it makes you "hit harder" can be difficult to understand and unsatisfying without knowing why.

As some know, my wife and I recently added a shaman to our mini-group (i.e., I 2-box a 65 paladin & 65 druid, she's 2-boxing a 65 ranger & 65 shaman). We added the shaman to our group mainly for slow & haste in LDoN, two things we were painfully lacking when it was "just us." One factor that we didn't really consider (though we knew of it, of course) was the shaman's ability to buff our stats and ATK.

I have two parses, both from logs that were done after the shaman had swift like wind - but one was taken before she had Ferine Avatar (we didn't bother with Avatar at all since she was levelling so quickly and it takes an expensive component). In other words, I have the same buffs in each parse, the same haste - but in one I have Ferine Avatar and in one I do not. Both parses were taken from 65th level Normal LDON adventures.

One other thing changed between parses - I went from no planar power (cap of 280 on melee stats) to PP4 (cap of 300), thus adding 20 points of dexterity and 20 points of strength.

First, the change in average slash (Windblade):

Before Ferine Avatar: 181 (2304 slashes)
After Ferine Avatar: 212 (1076 slashes)

Damage increase: 14.6%

Now, for a couple of pictures. We know that higher ATK changes the shape of the damage distribution, and the graphs below show the extent of that change with 140 ATK & 20 strength being added.

Before Ferine Avatar

Image

After Ferine Avatar


Image
It shouldn't be difficult to see the change in the damage distribution.

The first thing to note is the mode (most frequently occuring number) of the distribution. In the BEFORE condition, the mode is what we started calling the "magic number" about 4 years ago (2*DMG + Bonus). For Windblade at 65 that is 2*50 + 45 or 145. In the AFTER condition, the mode has actually changed to 341, or very close to 6*DMG + bonus. (341 appears to be the maximum non-special hit for Windblade.)

I should mention that in both conditions I already have some additional enhancements to ATK:

Spirit of the Predator
Speed of Vallon
Vengeance III (Ornate gloves)
Aura of Battle (stonewood bow)

In other words, that's around 150-200 more ATK than a self-buffed paladin with no Vengeance/AoB wold have (would check Lucy for actual numbers, but they're having SQL errors).

For that reason, my mean damage in the BEFORE condition is already higher than the magic number, and by a significant margin. A paladin with lower ATK would find their mean hit to be very close to the magic number (or even slightly below it).

In the second parse I was at 1505 ATK, much higher than I've ever been and it was "clear from watching my combat window" that I was hitting much harder than I had prior to then. Instead of seeing 300+ on rare occasions, they became common - and the maximum hit became the single most likely hit (if you had to bet on one particular number's appearing, that'd be the one to pick).

The comparison between these two graphs demonstrates about the difference you'd see between having a primal weapon and not having a primal weapon (for those of us without a shaman to keep FA on them all the time). It's a bit of hyperbole, but it's one of the few times that a single buff has such an impact that you can see and feel the difference (haste being the rare exception to that Smile ).

I have to say that my eyes nearly popped out when I saw the graphs of my parses - I had assumed that SOME of my perception was just confirmation bias (I'm a dyed in the wool skeptic, even of my own perceptions).

Bash (from 2-handed bash) also offers an interesting comparison:


Bash Before FA
Image


Bash After FA
Image


The differences should be pretty apparent. Note the complete lack of peak at maximum damage (36) on the Before graph and the very large peak on the After graph; maximum hasn't quite caught up to or surpassed the previous modal hit, but it is quite close.

For those who remember back when the level cap was 50 but our skills were those of a 42nd level paladin, what we saw then was the minimum hit becoming the modal hit. In other words, the most frequently occuring number when fighting a mob that was near 50th level was the minimum hit. (There were no pure ATK buffs, no Vengeance items and strength didn't work the same then - it didn't move the modal hit at all.) The picture below is one that came from our very early days of parsing - I was using a Falchion of the Koad'Vie against Seafury cyclopses (I was going a comparison between it, Ghoublane and Soulfire to show why the damage bonus made faster weapons so much better than slow weapons).

Falchion vs. Seafuries (50th level paladin)


Image

As you can see, minimum damage is actually slightly more likely than the "magic number." One thing we noted from the graphs back then is that adding even large amounts of strength added numbers at the right end of the graph (increased max hit), but was not more likely to make "magic number" bigger than minimum damage - or to change the distribution in other effective ways. I would be very curious to have a 50th level paladin take on the seafuries and get a look at the damage distributions with low & high strength to see whether the SHAPE of the distribution and the value of the mean hit changes.

I'm really looking forward to parsing my wife's archery damage now. Her ATK is approaching the 2k mark, though, so the difference MAY not be as pronounced as it was for me.

I thought others (particularly those who do eventually plan to have a primal weapon) might find the graphs at least 12% as engaging as I do. Smile
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