MATH WARNING:

**THERE IS MATH HERE**

The difference is that while overall harm computes, well, the harm caused by a given damage constant, this formula calculates the minimum damage constant required to OHKO a pokemon with the given stats.

It is derived as follows:

Code:

```
(All variables are the same as in [URL="http://www.smogon.com/dp/articles/maximizing_defenses#overall"]Overall Harm.[/URL])
Damage = K/D + 2 + K/S + 2
Damage = K/D + K/S + 4
```

we can find the minimum damage constant required to OHKO:

Code:

```
H - (Damage) = 0
H = (Damage)
H = K/D + K/S + 4
```

Code:

```
H - 4 = K(D + S)/(DS)
[I]K = (DS(H - 4))/(D + S)[/I]
```

So, in the formula, K will equal the minimum attack constant of a physical attack followed by a special attack such that the combined damage from both attacks KOs the opponent.

Why, you may ask, is this formula better than Overall Harm?

I think it simplifies things. Rather than fiddling about with an extra variable, your Damage Constant, this formula eliminates unnecessary scalars and focuses on one thing: how much damage your pokemon can take (as opposed to how much a given attack will f*** your pokemon up).

Now, it's not too difficult from here to use the optimization and limitation formulas one would use to calculate the ideal EV spread.

What we'll do is make a formula for each stat which we'll plug in whenever we see a D, S, or H.

The formula is as follows:

Code:

```
E = Total EVs you're alloting to defenses
Eh, Es, Ed = HP, Sp.D, Def EVs, respectively
Sh, Ss, Sd = What each stat would be at your target level with 0 EVs
Eh + Es + Ed = E (A limiter to make sure we don't exceed
the allotted Durability EVs)
L = 4*(100/Level) (The reciprocal of the scalar of the rate
at which EVs add to each stat.
If you don't get it now, you will later. Basically,
Lv.50 makes it 8 and Lv.100 makes it 4.)
Then, we get:
H = Sh + Eh/L
S = Ss + Es/L
D = Sd + Ed/L
Now, we plug these expressions into
the Specific Durability formula, and get...
K = [U](Sd + Ed/L)(Ss + Es/L)(Sh + Eh/L - 4)[/U]
(Sd + Ed/L) + (Ss + Es/L)
Then, if you wanted to get all algebraic-y,
calculus-y about it, you might do this:
Let
E = (Total EVs available for distribution)/L
z = K
x = Ed/L
y = Es/L
Eh/L = E - x - y
x + y <=E ("<=" means "less than or equal to")
x >= 0
y >= 0
(These last three because the subscripts get confusing)
H = Sh
D = Sd
S = Ss
As such,
z(x,y) = [U](x + D)(y + S)(H + E - x - y - 4)[/U]
(x + D) + (y + S)
```

Here's a simplified example of what the surface might look like:

(And the optimum config would be the peak of that Math Mountain)

I'm sure there's a way to precisely find the optimum configuration without guess-and-check-ing, but it is beyond my Calculus skillz to figure it out. Or, alternatively, the different D, S, and H values seem to only transform the function, not change its symmetrical shape. That could be used to easily calculate with a VERY simple formula. Anyway, I must sleep, so that's all for now.

I really hope this is useful to the world of pokemanz, and I'd love it if you guys could give feedback/suggestions/further calculations regarding this new formula.

In the meantime, I shall snooze. Good luck.