Blydden
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<Member>
Every time you post one of these, I will +Rep you.
This is just awesome.
I need to watch your stream more if you are going to do this live.
/fanboy
This is just awesome.
I need to watch your stream more if you are going to do this live.
/fanboy
Cervance
<Member>
<Member>
I took the trouble of getting my brain fried by your spreadsheet, and read a little more after that.
I vote for taking the stats from the least expensive items which contain them. Longsword, Dagger, Brawling Gloves. Then isolate the stats which don't have low tier items, like the %ArPen from Last Whisper.
Using just basic math I isolated the %ArPen from Last Whisper. Apparently 40% ArPen costs 630 gold!
2290g is the cost of Last Whisper. It has 40 AD, so I took 4 Long Swords, at 415g each and 1660g all together, and subtracted them from the total cost of the Last Whisper. That gives me 630g.
Do the same for the ArPen of Black Cleaver and the critical damage of Infinity Edge and compare those results to what runes give you.
In a completely unrelated realization, 1% AS beats 1 AD because abilities scale with AD, not AS. In your calculations, these abilities aren't taken into account, so AD will probably be worth less DPS than it actually is. Just something to keep in mind.
I vote for taking the stats from the least expensive items which contain them. Longsword, Dagger, Brawling Gloves. Then isolate the stats which don't have low tier items, like the %ArPen from Last Whisper.
Using just basic math I isolated the %ArPen from Last Whisper. Apparently 40% ArPen costs 630 gold!
2290g is the cost of Last Whisper. It has 40 AD, so I took 4 Long Swords, at 415g each and 1660g all together, and subtracted them from the total cost of the Last Whisper. That gives me 630g.
Do the same for the ArPen of Black Cleaver and the critical damage of Infinity Edge and compare those results to what runes give you.
In a completely unrelated realization, 1% AS beats 1 AD because abilities scale with AD, not AS. In your calculations, these abilities aren't taken into account, so AD will probably be worth less DPS than it actually is. Just something to keep in mind.
I dont think you can find a good way to compare the DPS stats. Maybe we should work our way around that by keeping the itembuilds in mind. Ie either find a way for the user to input his itembuild and then compare his deeps/gold from that point on. It might be smarter. I dont think you can program that in excel tho without major problems.
If you absolutely want to compare the stats tho i would recommend taking the lowest tier items and for stats like armorpen there might be a sensible way to calculate the gold cost for ad and off brutalizer or something along those lines.
I would still like to know why you wnat to evaluate a stat like that even after you posted those differentials which prove that the stats value is highly dependant on other DPS-factors.
Correct me if im wrong ;) it happens all the time (feel kinda tired right now so my thinking is likely to be off track)
If you absolutely want to compare the stats tho i would recommend taking the lowest tier items and for stats like armorpen there might be a sensible way to calculate the gold cost for ad and off brutalizer or something along those lines.
I would still like to know why you wnat to evaluate a stat like that even after you posted those differentials which prove that the stats value is highly dependant on other DPS-factors.
Correct me if im wrong ;) it happens all the time (feel kinda tired right now so my thinking is likely to be off track)
Chandro
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Cervance
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Congrats on fixing your math. I have one specific request, mister mathamagician Chandro. My experienced friend made it a point that Bloodrazors as a first item is awful.
My request is to compare the DPS of a Bloodrazor to that of an Inf Edge or Bloodthirster. At what point will it be a worthwhile item to buy?
My request is to compare the DPS of a Bloodrazor to that of an Inf Edge or Bloodthirster. At what point will it be a worthwhile item to buy?
Chandro
<Member>
<Member>
Thanks very much!
Here's the input I believe you wanted to see:
There's a lot to get from that picture, so if you have any questions, ask.
As for your friend, he actually has it backwards. The thing about δDPS/δM [the relative merit of the magic damage component on a Bloodrazor] is that it's as high as it will be when you have no items, because your magical DPS component only scales with one of the primary DPS stats: attack speed. Infinity Edge is, without question, a much better choice than BR later in the game, when the 3 DPS stats on an IE get multiplied across all of your other stats. But BR loses its weight later on because as all stats begin to grow, BR's major contributions become its attack damage and speed, neither of which are very significant.
So, as the numbers show, BR is a reasonably good choice as a first item. It's better for medium and high armor targets early game than IE or BT by reasonable margins across the board.
Here's the input I believe you wanted to see:
There's a lot to get from that picture, so if you have any questions, ask.
As for your friend, he actually has it backwards. The thing about δDPS/δM [the relative merit of the magic damage component on a Bloodrazor] is that it's as high as it will be when you have no items, because your magical DPS component only scales with one of the primary DPS stats: attack speed. Infinity Edge is, without question, a much better choice than BR later in the game, when the 3 DPS stats on an IE get multiplied across all of your other stats. But BR loses its weight later on because as all stats begin to grow, BR's major contributions become its attack damage and speed, neither of which are very significant.
So, as the numbers show, BR is a reasonably good choice as a first item. It's better for medium and high armor targets early game than IE or BT by reasonable margins across the board.
Nny00000
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<Member>
First thing first:
Your squishy armor is WAY too low.
No champion at level 18 (Which, based off HP levels, is what you're going by) has an armor below 61, let alone one of 50.
And only 13% of champions have an armor under 70. So 50 is just crazy.
The median and mode for armor at 18 is 77.5 (I use 78 in my spreadsheet for simplicity sake). If you want to break it into tiers (bottom 33% = squish, mid 33% = average, top 33% = tank) you get
squish: mean and median of 70.5
average: mean and median of 77.5
Tank: mean of 84.5, median of 83.5
(Note: Numbers are from http://leagueoflegends.wikia.com/wiki/List_of_champions%27_armor so haven't been updated since Riven added, but I doubt new champs will change it badly).
If I were you, I'd change it to
Squish: 70
Average: 115 (+50)
Tank: 185 (+100 armor)
I'd also probably drop tank MR. While the median and mode of MR is slightly less than the second tier (First tier: 30, second tier: 43.5, third tier: 52.5) (IIRC, both were around 40), I think it's probably easier to just use those tiers and guidelines for squish/average/tank.
The problem is, there aren't as many high MR items as armor (1 MR above +60 compared to 4 of armor [Two of which are +100]). So whereas armor was +50/+100, I think something like +35/+70. So I'd probably do like 75 for average, 120 for tank.
Moving to different subject:
A quick and easy way to know if adding attack or crit is better is to simply multiply your attack damage per percent of crit.
So, for instance, let's say you have 100 AD and you're wondering if you should build Cloak or Pickaxe while building towards IE.
Though Cloak would add the equivalent of 18 attack damage, making the Pickaxe (25 AD) better.
Meanwhile, if you had 200 AD, the cloak would now add 36 AD, making it better than the Pickaxe.
If you have IE, then that simply means multiply AD by Crit percent*1.5
So, if you have that 200 AD and an IE, Cloak would now add 54 AD, making it better than a BF Sword at half the price.
So you'd want to stack AD early, and go crit later.
ASPD isn't so easy, since champions with a higher base ASPD get more out of items with ASPD than those who have a lower ASPD. At that point, it is time to break out the spreadsheets.
While this is true, Bloodrazer still scales up later in the game due to another stat: Enemy HP.
Also keep in mind, the poster asked first item. An issue with your post is that you're comparing them at level 18, when a first item will be obtained a lot earlier than that.
Your squishy armor is WAY too low.
No champion at level 18 (Which, based off HP levels, is what you're going by) has an armor below 61, let alone one of 50.
And only 13% of champions have an armor under 70. So 50 is just crazy.
The median and mode for armor at 18 is 77.5 (I use 78 in my spreadsheet for simplicity sake). If you want to break it into tiers (bottom 33% = squish, mid 33% = average, top 33% = tank) you get
squish: mean and median of 70.5
average: mean and median of 77.5
Tank: mean of 84.5, median of 83.5
(Note: Numbers are from http://leagueoflegends.wikia.com/wiki/List_of_champions%27_armor so haven't been updated since Riven added, but I doubt new champs will change it badly).
If I were you, I'd change it to
Squish: 70
Average: 115 (+50)
Tank: 185 (+100 armor)
I'd also probably drop tank MR. While the median and mode of MR is slightly less than the second tier (First tier: 30, second tier: 43.5, third tier: 52.5) (IIRC, both were around 40), I think it's probably easier to just use those tiers and guidelines for squish/average/tank.
The problem is, there aren't as many high MR items as armor (1 MR above +60 compared to 4 of armor [Two of which are +100]). So whereas armor was +50/+100, I think something like +35/+70. So I'd probably do like 75 for average, 120 for tank.
Moving to different subject:
A quick and easy way to know if adding attack or crit is better is to simply multiply your attack damage per percent of crit.
So, for instance, let's say you have 100 AD and you're wondering if you should build Cloak or Pickaxe while building towards IE.
Though Cloak would add the equivalent of 18 attack damage, making the Pickaxe (25 AD) better.
Meanwhile, if you had 200 AD, the cloak would now add 36 AD, making it better than the Pickaxe.
If you have IE, then that simply means multiply AD by Crit percent*1.5
So, if you have that 200 AD and an IE, Cloak would now add 54 AD, making it better than a BF Sword at half the price.
So you'd want to stack AD early, and go crit later.
ASPD isn't so easy, since champions with a higher base ASPD get more out of items with ASPD than those who have a lower ASPD. At that point, it is time to break out the spreadsheets.
Quoted:
As for your friend, he actually has it backwards. The thing about δDPS/δM [the relative merit of the magic damage component on a Bloodrazor] is that it's as high as it will be when you have no items, because your magical DPS component only scales with one of the primary DPS stats: attack speed. Infinity Edge is, without question, a much better choice than BRlater in the game, when the 3 DPS stats on an IE get multiplied across all of your other stats. But BR loses its weight later on because as all stats begin to grow, BR's major contributions become its attack damage and speed, neither of which are very significant.
While this is true, Bloodrazer still scales up later in the game due to another stat: Enemy HP.
Also keep in mind, the poster asked first item. An issue with your post is that you're comparing them at level 18, when a first item will be obtained a lot earlier than that.
Talkin' **** about a pretty sunset
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Here Comes The Loot
So, all of the theory having been tackled, I have added to my spreadsheet a large array of outputs illustrating partial differentials of all relevant DPS stats. The sheet looks something like this:
About my Sheet
I've had a spreadsheet configured for a while now that can take in an input of any of the [summoner's rift] DPS items and output the total DPS for several different champions at level 18 with all of their respective DPS bonuses running. The screencap shows the first two, Kog and Trist, although I should note that Kog's equation is broken, I still have no clue why. Conveniently, when I first constructed this version I made an intermediate section of the actual stats you are getting from items, really just so that I could keep an eye on items' stats for updates. However, now that we have partial differential calculations from my previous post, based on these +stats, direct formulation of the partial differentials is a lot easier.
Problem 1: Before We Can Proceed
We need some kind of neutral way of comparing the DPS stats. Specifically, it must be independent of circumstantial DPS situations, since that's exactly what we're trying to use it for. This is hard to explain so let me ask an example question: "Exactly how much AD do we consider to be equal in value to 10%AS?" So far I've thought of two possibilities and I'd like for people to say which they prefer or suggest alternatives.
1) We could compare stats by their runes. The pros here are that we could compare most of the stats we'd want to compare, namely AD, AS, Cc, Cd, P#, and Mp#. The cons would be that it is well-documented that each rune is not equal in value. Therefore we'd probably be introducing a bias into our weights, but I'm not sure if that logic holds or only seems so via circular logic.
2) We could compare stats by lowest- or highest-tier items, via gold costs. The pros on this are that, I think, we'd be taking the most relevant way of comparing stats: what's more relevant in deciding what stat to buy next than the cost of that stat? The cons are that we can't compare every stat anymore; crit damage and flat armor pen cannot be found alone in any item. So, if we went with this, we would have to either scrap the ability to compare armor pen to other stats, which I think we don't want, or try to find an objective weight for flat armor pen based on what items do have it. Any intelligent thoughts on this matter would be most helpful.
Unfortunately I really can't go on from here because our partial differentials as they stand, as you can see in the screencap, are incomparable. δS/δDPS=395 while δD/δDPS=3.2... woop-de-doo, getting 100% more attack speed is better than getting 1 more attack damage; shocking news. And simply dividing by 100 wouldn't be accurate because no one's saying (or at least, no one has proven) that 1% AS and 1 AD are equivalent. So we're almost there, we just need to compare these stats objectively in order to see how they perform.
10/26/2011: Progress!!
I had the spreadsheet operational with our partial derivatives with respect to the 9 variables from the day after I posted this, and, after some discussion, I scaled down the simplest 3, AD, AS, and CC, to their respective weights based on low-tier items (specifically, the constants generated by purchasing 500g worth of items). Strangely, with these numbers, I found that AS beat the other 2 stats in virtually every conceivable scenario. This seemed highly implausible so I let it sit and thought about it.
Today I had my breakthrough: I'm a dumbass. When I scaled the three partial derivatives to 500g worth of items, I forgot one crucial thing. I forgot to run the AS coefficient through the standard AS equation (in this case, simply needed to multiply it by .625), and so the coefficient was nearly double where it should have been for all outcomes. Wow.
So, I now have the spreadsheet quite working for our three primary DPS stats (primary because they're comparable with the least bias introduced) and it's giving so very solid results, i.e. results we could manual expect from simple scenarios, and enlightening results from those more complicated. This is the kind of output we get from the sheet: Say I input one Infinity Edge and one Brutalizer.
At this point I'm looking for feedback again. If anyone has specific circumstances they'd like tested, whether they be simple item comparisons, or course-of-action evaluations like I just showed, I'm happy to answer. I'll be tinkering with the spreadsheet a bit more and then I will probably open it up to the public for use (incidentally, what would be the best way to give you guys my spreadsheet? individual e-mails could work if there's no good and safe method of file hosting I can use).
Bear in mind the shortcomings of this mathematical modelling. I am precisely modelling the act of right-clicking on someone with no outside factors. No moves are being used other than direct stat-boosters (like Tristana's Q), not to mention general moves that scale to AD, (like Cait's Q or MF's Ult). Because of these reasons, AD is almost always going to be more worthwhile than this spreadsheet would suggest, but not necessarily so much more that it surpasses other variables. And, of course, it almost always comes down to individual playstyles anyway.
Any and all input (with intent to conduce growth and discussion) is always welcome. Please comment and let me know what you think or what you'd like answered.