Enhancement Diversification Calculator & Guide

Enhancement Diversification Calculator & Guide

Feeling Confused? Bemused?

Enhancement Diversification got you down?

Are you looking for a complete breakdown of Enhancement Diversification?

Do you want to know the formula/method used in calculating how it affects your enhancements?

How about a tool to help you visualize the process?

Worried because the in-game information about this is a complete and misleading mess?

Well worry no more!

Because now you can have the formula, the breakdown, and the tool all in one convenient place.

Think that's great?

Well what if I told you it's all free? Yes, that's right. Free for your enjoyment, edification, and enlightenment.

I'm afraid I can't consider myself as "confused" by any stretch of the imagination, your formula has me intrigued. I've toyed around with it, and I've convinced myself that it works as designed.

Now I'm a little more curious as to WHY it works. For a while I thought that reaching a certain level of enhancement percentage simply lopped a bit off the values for each enhancement. Apparently it's not quite as straightforward, as there appears to be a "bonus" on top of that, as well, this "reduction base."

The way I enterpret is like this: "Pre-ED Total * Reduction Multiplier" is actually the flat percentage lopped off each enhancement. Since the "Pre-ED Total" is a simple sum of the slotted enhancements, it's pretty easy to split it up into each individual enhancement's value, multiplied by the reduction modifier, thereby illustrating my stated inference.

However, the calculations seem to be geared so that "too much" is taken off the enhancements. It is my assumption that for this reason, a bonus percentage is given, I assume to make up for the difference acuqired by using these steep percentages. It's basically a flat bonus overtop of the bonus your enhancements give to "make up the difference, somewhat," as it were.

If my deductions are correct, then it only seems to beg the question: Why bother? Why not simply institute more appropriate or more gradual percentages and simply not bother with this flat bonus?

It would be pretty easy to model this formula as a linear function, where your pre-ED enhancement values are the the variable, though with a few limitations. At a glance, it would appear to me that the base and multiplier actually have opposing effects. Because both of them are pretty severe and change in pretty big steps, one assumption would be that this is done to keep the equation relatively ballanced. But it still doesn't tell me why such complication was even needed.

I'll need to examine this further, but I'm pretty sure that either I'm missing something big, or the formula could simply have been made... Well, simpler.

Quote:

Originally Posted by Arcanaville Samuel_Tow is the only poster that makes me want to punch him in the head more often when I'm agreeing with him than when I'm disagreeing with him.

Yeah as for why it work... well I'm not sure, it just took a bit of work to derive some of the values, and some pushing to get others.

I tend to agree though... if you want to maximize effectiveness at about 55%, then why not just limit to 3 SOs and be done with it. I'm not really sure why all the complication either. Perhaps just someone trying to "cement" their job.

OK, I figured it out. It kept me up until 6 AM or thereabout, but I figured it out. Now, bear with me, as this will take some math that's heavy in appearance, but is actually very (very, VERY) simple mathematical analysis, about the very vasis of the field. I will apologise if I use any terms incorrectly, as I don't know the proper mathematical terms in English.

Let's model your formula as a two-dimensional function, where our variavle is your pre-ED total. Looking at it realistically, it's the only value that varies without interruption. Your reduction base and reduction modifiers will be interpretted as numerical parameters, and your ED total as the value of the function. Essentially:

<font class="small">Code:[/color]<hr /><pre>y(x) = b + a*x</pre><hr />

Where x is your pre-ED total, b your reduction modifier, a your reduction multiplier and y(x) (as a function of x) your ED total. Now is a very simple linear function, describing a simple two-dimensional line. Something like this. Incidentally, that is the graph of the function

<font class="small">Code:[/color]<hr /><pre>y(x) = 2 + 2*x</pre><hr />

Now, in a linear function, both paramaeters - a and b - are coefficents of two different things. The parameter a is the angular coefficent - it represents the angle (measured counter-clockwise) at which the graph is offset from the abcissa (the horizontal x coordinate axis). Translating that into an actual angle is a little bit more complex and requires a bit of trigonometry, but that is irrelevant to the matter at hand. What is important, however, is that as a increases, the angle of the graph increases, and so the entire graph rotates counter-clockwise around the point where it intersects the ordinate (the vertical y coordinate axis). Mathematically, this is a circular rotation around the point where x=0, or the point where the graph intersects the ordinate. Effectively, changing the a parameter does this. Those three functions are as follows:

<font class="small">Code:[/color]<hr /><pre>
y(x) = 2 + 2*x
y(x) = 2 + 3*x
y(x) = 2 + 4*x
</pre><hr />

What does this mean in relation to us? Well, the angle of a graph basically represents the productivity of the action it describes - in this case the ratio of percetnage put into powers and net percentage gained at the end. A coefficent above 1 (or an angle greater than 45°) describes overunity - for each 1% put into a power, you gain MORE than 1% net. A coefficent of 1 (or an angle of exactly 45°) describes an even gain - for each 1% slotted, you gain 1% net. Unsurprisingly, a coefficent less than 1 (or an angle smaller than 45°) describes a diminished return - for each 1% you invest, you get less than 1% net.

Basically, the ED formual, as stated, starts with a coefficent of 100%, or 1.0, and then goes down through 0.9, 0.7 and 0.15. I feel it is quite obvious what this means - with each step the coefficent decreases, so you get less and less return on your enahncements with each consequent step.

So what is the purpuse of the reduction base, our b, then? Why not stick to just a reduction modifier? The answer to that is actually quite simple, but first let me explain what the b coefficent does. In simple terms, b just adds a flat value to the y of each and every point, effectively "raising the graph up." Mathematically, this is defined as a linear translation, colinear with the ordinate. Changing the b parameter effectively does this. Those three functions are as follows:

<font class="small">Code:[/color]<hr /><pre>
y(x) = 2*x + 2
y(x) = 2*x + 3
y(x) = 2*x + 4
</pre><hr />

What does this mean to us? Well, it alters the speed of our gain again, but it does so in a different way. Instead of a percentage increase or decrease to our gain in relation to our investment, think of it as property tax, or a raise. So as b increases, now for each 1% you slot, you get exactly b% more on top of that, net. And when b decreases, for each 1% you slot, you get b% less, net. So as for a positive b (b&gt;0), you get a bonus on top of your slotting, and for a negative b (b&lt;0), you get a tax. When b equals 0 (b=0), there is no change.

But why is this necessery? Well, the reduction base is pit in there to fix what would otherwise be a very serious problem - a big drop in the gain at each reduction point. Without a reduction base, you would suffer not only a diminished return, but a flat decrease in enhancement values, meaning that actually sltotting more % into your power would actually give you a net total of less % post-ED. It would look something like this. Note how the Moderate section of the graph is actually net less than the Mild, and almost net less than the Unaffected ones. Note, furthermore, how the Sever section is net less than all of the others, and by a significant margin. What this means is that slotting ANYTHING in the Severe section would not only give you diminishing returns, it would actually give you a smaller percentage than slotting most anything into in the Unaffected section. This would be bad, and were it made like that, it would have killed the game.

The ED formula is a complex function. It is actually comprised of four seperate linear functions. What was needed for this complex function to be effective was for it to be uninterrupted. If you look at the "bad" graph, you will note that horizontally, where one sectin ends, the other begins, but it begins a lot lower. Well, one way to line all of the sections with each other is to "raise them up" until their ends meet. That is what the reduction base does. It brings the next section up to "start" from where the previous one ends. Because the new section has a different angle coefficent (or a different a), the gain is diminished, but the starting point is the same as where the previous section ended. This insures an uniterrupted increase of net % for each % slotted. There are no instantanious jumps.

In its final form, the graph of the ED formula looks like this. I've coloured the sections as close as I could to the colour scheme given in the guide, with green being Unaffected, yellow - Mild, orange - Moderate and red - Severe. You can tell how the Mild, Moderate and Severe sections have been "raised up" until their ends met. This tells me that the reduction base is not, in fact, a bonus or a means to "make up" for the percentages. It is a required translation to keep the complex function uninterrupted. They are also calculable as a function of x and a. It's a little complicated and quite unimportant, though, so I don't want to bother with it.

I also came up with the answer to another, less technical problem - why did the developers tell us there were two reduction points when in fact there were three. One look at the ED graph makes it pretty apparent. Visually, the length of both the Mild and Moderate sections taken together is still shorter than either the Unaffected or Severe sections. Indeed, the sum of the intervals of the Mild and Moderate sections is 30%, whereas the Unaffected has an interval of 70% and the Severe section can extend pretty high up. I've taken it up to 160%, which gives it a 60% interval. All calculations done on Schedual A enhancement, of course, but the calculations for the other Scheduals are no different.

Another interesting point is their reduction multipliers. Mild is 90%, or 0.9, and Moderate is 0.7. Compare that to the 0.15 multiplier of Severe and you see a marked difference. So, basically, on the grand scheme of things, Mild and Moderate are very similar in their numbers and very close together. If you look at the purpuse of the dveloper post that explained ED, you will see that it wasn't meant to give the number-crunchers a formula with which they could calculate. It was meant to give the casual players a relative referrence, so they knew more or less what to expect. So while there were, in fact, three reduction points, the middle reduction point was negligible for the purpuse of the explanation. It had an effect, sure, but not one big enough to bog down what was already a lot of numbers with. Most people don't like to see large fields of numbers. Heck, I don't like to see large fields of numbers. So the developers spared us one reduction point and melded two reduction sections together for ease of use without understanding.

That is my analysis of your Enhancement Diversification formula. I feel confident that I can visualise, predict and explain it, at least to myself. I'm open to any questions and willing to give any additional explanations, because I KNOW my math will scare a lot of people

Thank you for your time.

*edit* Because I'm stupid and I keep mixing reduction base with reduction modifier and vice versa. It should be correct now.

*edit2* Because I somehow turned 100% into 0.1, which is 10%. Thanks for pointing that out. This is embarassing

Quote:

Originally Posted by Arcanaville Samuel_Tow is the only poster that makes me want to punch him in the head more often when I'm agreeing with him than when I'm disagreeing with him.

Excellent post. It's a bit more technical than I wanted to get in my guide - which I simply wanted to be a "here's the forumula" and "here's how you use the formula" sort of thing and not a "here's where the formula comes from" thing.

I spotted one error in your writeup and that is that you refer to 100% as 0.1 when it's 1.0, but I think that's just a late night fat-fingering.

If you'd like I'm perfectly willing to take your writeup and your graphs and use it as an Appendix for the guide. I'd just need to know how you want to be credited. Let me know.

I've always been less concerned about the initial dev post and more concerned that the game itself does a terrible job of teaching the player the drawbacks of over-slotting - which is why I think simply limiting powers to a max of 3 +3 SOs worth of a single ability in a power would have worked better. And more people would get it.

When I try to install it as "Just Me" on a Win XP SP2 system, I get:

1: ALLUSERS property is not 1 - this MSM cannot be used for a per-user or fallback-to-per-user install

with an OK button

pressing OK brings me to an "Installation Incomplete" window, which does not allow me to complete the installation.

Install works fine if I install it for all users. Let me know if you need any more details to reproduce this.

[ QUOTE ]
Excellent post. It's a bit more technical than I wanted to get in my guide - which I simply wanted to be a "here's the forumula" and "here's how you use the formula" sort of thing and not a "here's where the formula comes from" thing.

[/ QUOTE ]

I apologise for complicating matter. It's just that when I saw two coefficents that basically change to counter each other (at least at first glance), I had to figure out why that had been done like that. I thought it was stupid, but it turned out it was required to keep the curve uninterrupted. Now I'm happy again

[ QUOTE ]
I spotted one error in your writeup and that is that you refer to 100% as 0.1 when it's 1.0, but I think that's just a late night fat-fingering.

[/ QUOTE ]

Fixed!

[ QUOTE ]
If you'd like I'm perfectly willing to take your writeup and your graphs and use it as an Appendix for the guide. I'd just need to know how you want to be credited. Let me know.

[/ QUOTE ]

Reall? Cool, I didn't expect many people would like it I'd be happy if you'd use it, as I really did put a lot of work, to say nothing of thought into it.

As this has to do exclusively with City of Heroes/Villains, I feel you should credit me as Samuel Tow. No need for going into a name that hasn't been used in relation CoH/CoV at all.

[ QUOTE ]
I've always been less concerned about the initial dev post and more concerned that the game itself does a terrible job of teaching the player the drawbacks of over-slotting - which is why I think simply limiting powers to a max of 3 +3 SOs worth of a single ability in a power would have worked better. And more people would get it.

[/ QUOTE ]

I agree. The game really does a poor job of showing you what you're doing wrong. For the witty, there is a simple way to test this - buy an extra enhancement and pretend to slot it into another slot. That'll give you a number of increase. Subtract that from the enhancement's actual value (which you can either simply know, or find out by pretending to slot it in a power that has none of that kind), and you get the percentage of loss on that enhancement. From memory, the loss for a seconf +3 enhancement is around 5% and from a third around 10%. Or at least thereabout.

But I'll agree - the game itself does a very poor job at telling you about ED. Even my workaround method only works once you get to SO levels, meaning it's very easy to not know about it and overslot on Training or Dual Origin enhancements. I was lucky in that I knew about it ahead of time, but many people aren't.

I have seen the suggestion that you simply limit enhancements to 3 and be done with it. That has a couple of interesting effects. Firstly, it gives you an even increase of gain between each of the three ehancements, while ED gives you diminishing returns. Secondly, I believe the original idea was that people may still want to slot things with 4, 5, 6 same enhancements, even despite the diminishing returns. I have it on pretty good authority that this was a wrong assumption, even though I have a friend who still 6-slots things, because he feels any benefit is a benefit. I think that was why it was left at possible 6-slot, but at a great penalty.

Oh, and I think I have forgotten to mention something - THANK YOU for that guide It's an excellent interpretation of the forumal, and it allowed me to understand what makes it tick. You have an excellent guide there.

Quote:

Originally Posted by Arcanaville Samuel_Tow is the only poster that makes me want to punch him in the head more often when I'm agreeing with him than when I'm disagreeing with him.

[ QUOTE ]
Install works fine if I install it for all users. Let me know if you need any more details to reproduce this.

[/ QUOTE ]

I have no idea, installers are sort of a mystery to me - I'm surprised I even ever got one to work. I know it's got a user install and an admin install it in (since they do by default), but beyond that I haven't got a clue.

Looking at it though, it seems to me that the problem is that I have to include some merge modules (MSMs) from Microsoft otherwise you won't have all the DLLs required to install, but one or more of those MSMs I guess can't install for single users. Since I don't create the MSMs, I just use them, I can't control that, and probably can't solve that error.

Nice work on the calculator C! Though the formulas have been around for a while my complete lack of knowledge of all things computer congratulates you on actually doing somethnig useful with them!

Ian Moore