Very nice section on runes. When I hit level 20 I didn't know what to buy and it helped a lot.

agree too much work! (:

SO MUCH WORK :p
+1

Dude, don't look at it FLAT way, seriously.

Let me give simple to follow example.

You have 100 AD and you buy 50 - you get 50% more, as 50 is 50% of 100, right?
You have 200 AD and you buy 50 - you get 25% more, as 50 is 25% of 200, right?
You have 400 AD and you buy 50 - you get 12,5% more, as 50 is 12,5% of 400, right?

We didn,t look at FLAT way, we wanted to compare our profit in percentage difference

It's easy to calculate when it's about total values, without unit or comas

The case is, that you want to look at your profit in percentage difference

To make it easier to follow, I'll cut off temporary unit (%) from damage reduction term

100 armor is 50 damage reduction (+50)
200 armor is 67 damage reduction (+17)
300 armor is 75 damage reduction (+8)

now, let's compare profit in percentage difference:

0 to 50 is infinite difference as 50 is infinite perfcent of 0.
50 to 67 is 34% more, as 17 is 34% of 50
75 to 67 is 12% more, as 8 is 12% of 67

So that doesn't onyl show each next armor point gives less damage reduction, but also percentage difference is progressivly lower. But it doesn't work for DAMAGE TAKEN

transformed differences at gaps:

100 to 50 (-50)
50 to 33 (-17)
33 to 25 (-8)

50 to 100 is 1/2
17 to 50 is 1/3
8 to 33 is 1/4

and each next 100 of armor gives us pattern, next would be 1/5 1/6 1/7 and so on.

Here is the tricky thing. Now if you give back unit (%) which already compared something (source of damage) to reverse it we need to compare differences to basic damage taken, not previous 100 armor gap.

This can be done by multiplying each next gap's differences

1/2 x infinity/0 = 1/2 x 1 = 1/2
1/3 x 1/2 = 1/6
1/3 x 1/4 = 1/12

to check if we have same result, we need to add each consequent component

for 1st gap it's: 1/2 + 0 (0 comes from basic reduction state) = 1/2
for 2nd gap it's: 1/3 + 1/6 + 0 = 2/6 + 1/6 = 3/6 = 1/2
for 3rd gap it's: 1/4 + 1/6 +1/12 = 3/12 +2/12 + 1/12 = 6/12 = 1/2

The think i talk about in my article is PERCENTAGE COMPARATIVE DIFFERENCE, and this one seem pretty constant value

I don't know how to explain advanced math in english but i guess NOW you see it

It doesnt matter if you look at the damage REDUCED or TAKEN. The point is still the same. You actualy wrote it there: "from 0 to 100 you gain 50% damage reduction, and from 100 to 200 you gain only 17%..." This sentence says this: In both cases you bought 100 additional armor/MR (from 0 to 100 and from 100 to 200) for some (and SAME) ammount of gold (lets call it X), but the finall effect is way different. First time its additional 50% and second time its only additioanl 17% reduction. Or from your point of view. In first case you payed X for 50% TAKEN DAMAGE, but in second case you payed additional X price to get 33% (=100-50-17) TAKEN DAMAGE. It is still the same from both sides of view (damage reduction or damage taken).

Why those 17% counts more? Imho 50% >> 17%. Look at it from economic side. If you pay only one X you get 50% reduction, if you pay 2x X you get 67% reduction. In total you get those 33% more like you wrote in your comment but for DOUBLE PRICE.

Who can buy 200+ armor/MR (excepts tanks) to still keeps solid damage output? You can buy maybe one of these, but deffinitely not both (that is pretty obvious stuff, but needed to be said).

Actualy I think there is some limit where buying more armor/MR is not worth it due to economic effectiveness. Lets say you will buy 50 armor/MR Z times, for the X price. I try to make a little table here.

Number of buys___armor/MR___reduction(%)___reduction gain from last buy

0___0___0___0
1___50___33___33
2___100___50___17
3___150___60___10
4___200___66___6
5___250___71___5
6___300___75___4
7___350___78___3
8___400___80___2

Ok, so now if you look at it you clearly see, that gaining up to 150 armor is still price effective because for every buy you get 33/17/10 more reduction. But if you continue to buy armor your gain is gettring terrible low. Imagine that I bought 3 pieces of armor/MR and you bought 6 of them. My price was 3x X, your 6x X, my damage reduction is 60%, your is 75%. So that means you for DOUBLE PRICE get only 15% more reduction than me. Got the point?

EDIT: It might be better to buy some HP item instead of additional armor/MR, because HPs are not limited and stacks lineary.

wrong again, you didn't read it carefully. I just wanted to show with this +5% reduction adding, that EACH NEXT PERCENT COUNTS MORE. Ok, say you get less and less damage reduction with each next armor point - but at the same time each less gained point counts more. With exact calculations i counted what the ratio is and... from 0 to 100 you gain 50% damage reduction, and from 100 to 200 you gain only 17% right? but that 17% counts MORE than previous 50% gained. Don't look at damage REDUCED but at DAMAGE TAKEN, that's the case.

At 100 from 0, you take 50% instead of 100% -> 1/2 times less than previously
at 200 from 100, you take 33% from 50% -> 1/3 times less than previously

But if you compare that 1/3 to previous 1/2 gained, total gain is 1/3 + (1/2*1/3) which is generally 1/3 + 1/6 = 2/6 + 3/6 = 1/2 more effect. Same as from previous case. That occurence goes further with 300 from 200 and 400 from 300. Damage taken comparative difference is the same. I should have made my calculations more clearer about what i was talking about, so Ty for the comment - that will make me add some more explainations to questions that people may ask :)

Its good, but...the part with armor/MR is weird. Let me explain.

Your basic idea is OK. You know how the math works. But the perspective with adding +5% is wrong.

0 -> 5 reduction ok
50 -> 55 reduction ok
90 -> 95 reduction TERRIBLE.

Count with me now. If you want to have 90% reduction you need 900 points of armor/MR. That is mission impossible (ok, its possible, but...). So your argument about getting two times less damage is just wrong. Most offtanks are playing with +/- 150 armor/MR. Thats pretty ok value, that can be achieved with few items (i.e. Nocturne with Wriggle's + Atma's + Wit's End + armor/MR runes). This value reduces +/- 60% of incoming damage and that is still ok.

Even the conclusion "Each armor point counts the same" is wrong. It is huge difference if you have 50 armor and buy additional 50 points (reduction before/after is 33%/50%) or if you have 150 armor and buy addional 50 points (reduction before/after is 60%/66%). The point is that you buy 50 armor for some gold, but in first case you get 17% more reduction and in second case you get only 6% reduction FOR SAME AMOUNT OF GOLD. Simply said every additional 1% of reduction is more expensive than the one before.

Last note: my signature... :-/

I've done a lot of gold efficency calculations on my own, few months ago, just for personal use. It's in my motherlanguage but WAY more detailed than the one you gave. Just in need to translate it all, also i need to add several more features. I predict that this guid will be like 2-3 times bigger when finished. But i want to make it contain all possible knowledge new people can find helpful on their own with LoL. Mostly because I'm extremly tired of that weak, easy to exploit meta-game that its very, very, very bad

thx for feedback, and stay tuned if interessted at my works

It needs work, but definitely has a lot of potential. Keep at it, you've got something great going.

Regarding what you want to do with items, I did some calculations about items stats and gold efficiency a while back. You can find them here, in a Google doc spreadsheet, if you're interested. It should be up to date, as of Hecarim patch, but let me know if there's anything wrong.

I admire your effort.

Nice to see people trying to help the newer community, especially with the hilarious builds we see on here sometimes. Good Job. +1

Reserved!