The math behind ilvl explained

[Deleted]

Hello everyone, this is my first post ever and will be very math heavy, so please bare with me. I tried to search how did ilvl increase actually work and seeing no info anywhere, I decided to do the research myself. Here are the results of said research.

Index
1. A brief math introduction: Linear VS exponential growth
2. How itemlvl actually increases your power
3. Concluding remarks. BRF +5 ilvl, warforged.

1.A little bit of math So a lot of you may have thought, as I did in the past: "If I upgrade my head Ilvl by 10, it will take my Int/Str up by 10, and Sta up by 15, and the secondary stats by 20. And if the chest gets an upgrade, the chest would increase stats by 11-16-22 because chest is more powerful" and so on... well, this is actually FALSE. A 10 ilvl increase does not increase the stats the same amount, because ilvl is not linear

The only math you need to know to understand how Ilvl works is Newton's binomial theorem. What this basically means, is that if you increase by a 20% twice, you don't end up with 140%, but with 144%. (because the equation is not 100%+(20%*2), rather it's (100%+20%)^2

**While this difference is not significant in a short span, the more it mounts up the larger it is. If you do 2 50% upgrades, linearly you'd expect going from 100% to 200%, while exponentially you end up with 225%. And if you do more than 2 upgrades, exponential just pulls away wildly.

To sum it up, an exponential function does not increase at the same rate, the more you have the faster it increases



2.Ilvl impact So itemlvl for lvl 100 characters (sorry, I will not go into previous tiers because the statsquish made all sense go away, ilvl 230 epics being more powerful than ilvl 270 greens) works is by 15-ilvl gaps reflecting a 15% increase in power. (As per **, please notice a 60 ilvl increase is no such thing, but rather 4 15 ilvl increases).

The fixed "tiers" in power are:
615 (nm dungeons, lvl 100 follower mission rewards)
630 (hc dungeons)
645 (high ilvl follower rewards, invasion/raid mission satchel rewards)
655 (RF BRF, HM normal)
670 (BRF normal,HM heroic)
685 (BRF HC, HM mythic)
700 (BRF Myth)

As such, a BRF myth item is 15% more powerful than it's 685(heroic) counterpart, and 32% more powerful (not 30%, remember) than normal.
Please do note you have to use these 15-10 ilvl gaps. You do not compare a ilvl 691 to a 630, you compare it to a 685 because that's how exponential functions work.

3. Concluding remarks
What does this mean for you? Well it means that
-Every BRF item you got upgraded is now 5% more powerful.
-Every WF item you get is 6% more powerful than it's non WF counterpart.
-WF bonus is better the higher the ilvl, so WF>>>Socket at high ilvl

This post is subject to further editing for possible spelling/editing reasons.

Also, I realy hope this post belongs here and not in some other subforum dedicated to theorycrafting? >.<

[Weischbier]

Very worth the read. Absolutley true that most folks compare their gear with the lower tier gear.

Thanks for summing this up!

[ThePants999]

(As per **, please notice a 60 ilvl increase is no such thing, but rather 4 15 ilvl increases).

Why are you arbitrarily selecting 15 ilvls as a unit? Who's to say it isn't 3 20-ilvl increases... or more pertinently, 60 1-ilvl increases?

[Deleted]

Why are you arbitrarily selecting 15 ilvls as a unit? Who's to say it isn't 3 20-ilvl increases... or more pertinently, 60 1-ilvl increases?

Because the math works for 15-ilvl increments and not for 20. To further strengthen the evidence, RF-Normal-HC-Myth are 15 ilvl gaps

[fixx]

Random stat items with only one secondary stat dont quite follow the same math but that's nitpicking.

[Lynneiah]

Random stat items with only one secondary stat dont quite follow the same math but that's nitpicking.

People care about randon stat items with only one secondary stat?

[Vargur]

Used to be 13 ilvls between tiers and difficulties a few years ago. Then they added LFR, added "flex" and now increased the gap to 15.. there's only so much a player skill can address without proper gear to start with.

[Hindsgaul]

I love how you call it "math" - Yet you do absolutely no real math in your post

[Deleted]

Random stat items with only one secondary stat dont quite follow the same math but that's nitpicking.

It's an extreme of the more general rule that the more unbalance the two secondaries are, the lower the total, e.g.

665 Blast-Proof Cowl (124+172 = 294)
665 Acidic Jaws (154+154 = 308)

Needless to say the OP is wrong and there's nothing holy about 15 ilvl increases, but I think its correct that item stats are exponential wrt item level within an expansion.

EDIT: Here's some actual maths, primary attribute vs ilvl and the exponential constants uses:

https://docs.google.com/spreadsheets...GFhGeM/pubhtml

[Deleted]

A 15 ilvl increase is a 15% increase of stat budget (only talking about current raid gear). However that means that the stat formula looks something like:
Stats(New) = Stats(Old) * (1+0.15) ^ ([ilvl(new)-ilvl(old)]/15)

As such a 5 ilvl increase does not increase the stats by 5% but instead by (rounded on the second digit):
(1+0.15)^(5/15) -1 = 4.77% (and a WF by 5.75%)

I know some people would call this a 5% or 6% increase but it is an important distinction to make.

Further the statement: "WF bonus is better the higher the ilvl, so WF>>>Socket at high ilvl" is simplistic.
(Sure if we are talking about ilvls as high as idk ... 800? that is true but such gear doesn't exist.)

WF vs socket is a difficult decision and depends on two factors:

1.)Stat budget of the item (aka slot):
The base stat budget of a ring is smaller than a chest. Thus, a socket on ring will likely outperform a WF ring, while a chest or a weapon are the other way round.

2.) Itemization and scaling:
This depends on your class. If your class scales extremely well with a certain secondary stat sockets will stay competitive with WF because a socket lets you pick the stat you want.

Edit:
Btw you don't need to do curve fitting to get the values for the exponential function:
ln(1.15)/15 = 0.0093