Gaffer wrote:theckhd wrote:As a side note, earmor and barmor won't be that hard to figure out. The base armor value of an item is fixed for a given ilvl. Given about a half an hour, I could either
A) plot barmor vs. ilvl and figure out what the functional dependence is, coming up with an analytical formula.
B) Write a simple lookup table
Alternatively, this info might already be on wowwiki - I haven't had time to check.
Information for previous expansions seems to be pretty readily available,
This was the closest I could find for Wrath though. Just seemed odd that I couldn't find anything more specific this late in the expansion.
I spent a little time this afternoon playing around, and I think I've come to some reasonably good conclusions about how the armor model works. If you want to play along at home,
here's the code.
Methodology: Take a bunch of (ilvl, armor) ordered pairs from both the current and cata wowhead databases, plot them and look for some sort of pattern. I've limited the scope of the investigation to chest pieces for simplicity.
First, let's consider the current (wolk) data:
Figure 1: Armor vs. Ilvl for plate chest items pre-Cataclysm
The "model" traces use the
wowwiki formula that gives a linear dependence on ilvl, with epic items having 25% more armor than their blue counterparts (in other words, epic = 1.25*blue).
The "epic" and "blue" traces are the actual data for current items, painstakingly copied over into matlab (by hand!) by yours truly. The "blue*1.25" and "blue*1.0345" traces are just scaled versions of the blue data set.
The first few things to note:
- The formula seems to do very well for classic and BC items, which means epics up through Sunwell gear (ilvl 159) and blues up to ilvl 115. The one exception is Carapace of Tuten'kash at ilvl 42, which we must assume has different itemization due to its low level and will ignore.
- The formula is blatantly wrong for Wrath items. The epic items fall far below the projected values from earlier expansions, and the blue items are far above the projected values, making the difference between a blue and an epic at a given ilvl much smaller.
- The "blue*1.25" curve seems to accurately reflect the relationship between epic and blue items in BC and clasic, but gives values that are too large for Wrath blues because of #2.
- Based on the ilvl 200 data point, an epic in Wrath only has about 3.45% more armor than a blue of equal ilvl. However, the region of overlap is small, and this relationship doesn't hold as we slide down the scale to the region of overlap between BC epics and early Wrath blues.
The implications here are fairly mundane. The developers obviously noted that the armor difference between blues and epics was going to grow dramatically with ilvl, and decided to change the formula to keep them more in line. Presumably, the function that converts ilvl to armor is piecewise, with the familiar linear relationship for items from BC and earlier, and a different function for Wrath items. The blue items in Wrath are defined by a function that gradually ramps them up to the level of early epics. Let's take a closer look at the Wrath epics, and this time, we'll include their Cataclysm armor values:
Figure 2: Armor vs. Ilvl for plate chest items pre- and post-Cataclysm, ilvl 200+
It seems here that the Wrath epics have a piecewise linear dependence. The items from 200-232 follow one linear function, while the items from 239 on follow a second, different linear function. As surmised in the EJ thread, this is probably because of feedback about armor scaling beyond the 232 limit spurred on by the introduction of heroic modes.
These items all see a slight increase in armor in Cataclysm, but retain their different formulas. So we're not seeing a Grand Unified Theory of Armor-Ilvl interaction in Cataclysm, at any rate.
The functional forms spit out by cftool, for those interested, are:
- Code: Select all
fit1a=1503+3.734*x
fit1b=306.7+8.842*x
fit2a=1961+1.882*x
fit2b=446.4+8.324*x
Now let's expand our view and look at the full ilvl range.
Figure 3: Armor vs. Ilvl for plate chest items pre- and post-Cataclysm, all ilvls
Very interesting! It seems that the linear function for pre-Wrath epics has been changed. It appears to be a piecewise function with four different linear curves (early classic epics, late classic epics, early BC epics, late BC epics).
It's hard to see from this plot, but the classic/BC blues have almost the same functional dependence (divided by 1.25). This is more clearly seen on the next plot. The wrath blues also seem to have a piecewise dependence in Cataclysm, with the breaking point somewhere around ilvl 179.
Finally, let's look just at the data from the Cataclysm site:
Figure 4: Armor vs. Ilvl for plate chest items post-Cataclysm, all ilvls
The red dots clearly show that the blues are simply following the same piecewise function as the epics, just smaller by a factor of 1.25. The teal dots show a similar pattern, but in this case the blues below ilvl 179 are about 11% behind (1.11), while the blues above 179 are about 3.45% behind (1.0345). The data point at ilvl 179 is a bit odd. If we assume it's 11% behind as I have in the teal curve, it's pretty linear (but much higher armor than the next few). If we assume it's 3.45% behind, it's a little too low. I'm not sure which I think is more likely - it's possible they made the piecewise cutoff 180 and didn't worry about the actual armor value since they never intended to have epics in that region and the blues would be normalized appropriately anyway.
Unfortunately, we only have three data points to work with for ilvl 270+ blues. However, I think it's reasonable to expect the same sort of dependence we see in Wrath. A sharp linear increase in armor to get us up to the next baseline, at which point it will change to a shallower linear dependence.
Finally, I decided to try and fit all of the sections of the piecewise function just for fun. Here's the result:
Figure 5: Armor vs. Ilvl for plate chest items post-Cataclysm, all ilvls
The functions are:
- Code: Select all
x1=40:58;
f1=58.87+11.9.*x1;
x2=59:87;
f2=499+4.162.*x2;
x3=88:108;
f3=-1300+24.86.*x3;
x4=109:130;
f4=1049+3.126.*x4;
x5=130:180;
f5=-959.2+18.58.*x5;
x6=170:235;
f6=1961+1.882.*x6;
x7=236:280;
f7=446.4+8.324.*x7;
The crossover points are only roughly estimated in most cases, and the 170-180 region is still a little bit of a mystery due to the 179 data point. Unfortunately, when I searched for blue plate chests with ilvls between 170 and 180, all it turned up was items at 179. An extra data point around 174 or so would really help. Perhaps we could extrapolate up from a green, but then we'd need to figure out whether the green->blue factor had changed at all across the domain, and I've already spent too much time on this today.
