Other Math model on optimaising Defense & SpD EVs distribution

[Fgdfgfthgr]

There are four math models here:
1.
Simple Balance between SpD and Defence
The simplified version of the fourth model. Work best for level 100 with all IV maxed. (but the conclusion shouldn't be different for lower levels)
Assume there is an imaginary enemy, it lands two hits on you. Two hits are identical, except one is physical and the other one is special. You would want to lower overall damage as much as possible.
For a given total spend in Defence, SpD and HP. It can show which combination will loss minimum percentage HP and how good it compares to all the other combinations. Enter your pokemon data and tweak the HP investment while observing the curve, find where you will get a minimum!
Recommend!
https://www.desmos.com/calculator/rsmv8suc1s

2.
3D Balance Between SpD, Defence and HP!
Now come in 3D! the x-axis is how much you will invest in Defence EVs, the y-axis is how much you will invest in HP EVs. SpD EVs is a depended on the other two variables as long as you give the total EVs spend so is not shown there.
Instruction:
TotalEVs is how much EVs you are going to invest into Defence, Spacial Defence and HP altogether.
SpeciesHP, SpeciesDf and SpeciesSpD is your pokemon's species HP, Defence and Spacial Defence Strength.
NaturaDf and NaturaSpD is the effect of nature of your pokemon, 1.1 for + nature, 0.9 for - nature.
On the right-hand side, you should see a slightly curved plane in a 3D space. And a blue point on it. Drag the point around, the three numbers on the point represent (Defence EVs, HP EVs, Total Damage Taken), try to minimise the third value! But don't forget EVs only work best at a multiple of 4!
https://www.geogebra.org/3d/n2mjnadn

3.
HP or Defense/SpD?
Should I invest my EVs into Defense/SpD or HP? This model gives you the answer.
https://www.desmos.com/calculator/nygykdze0g (Don't get tricked by all the equations! It's very easy to use if you enters the parameters correctly!)
Basically, it allows you to see for a given total amount of EVs spend in Defence and HP, which combination will give the most durable results against a given attack. (and how good they are compared to all other combinations)
Works the same for Special Defence.
For simple conclusion, adding EVs to Defence/SpD is almost always for countering the corresponding Attack/SpA. Unless the Pokemon has significantly lower HP Species strength than its Defence/SpD.

4.
Balance between SpD and Defence
Assume there is an imaginary enemy, it lands two hits on you. Two hits are identical, except one is physical and the other one is special. You would want to lower overall damage as much as possible.
https://www.desmos.com/calculator/ovfhtheuvu
For a given total spend in Defence and SpD, it can show which combination will loss minimum percentage HP and how good it compares to all the other combinations.

 

[Fgdfgfthgr]

Update: Included a floor() function to simulate the rounding when calculating the pokemon's HP and defence.

 

[Fgdfgfthgr]

Update: Made another model for balancing between Defence&SpD base points distribution.

 

[Fgdfgfthgr]

Update: Restrict functions range to avoid misunderstanding, as well as added the simplified version for " Balance between SpD and Defence" model.

 

[Fgdfgfthgr]

Well, this is a WIP 3D version of the model. https://www.geogebra.org/3d/n2mjnadn Will be improved, but if you can understand what the graph on the right-hand side is showing, feel free to use.
(warning:may run very slow on older computers)

 

[Fgdfgfthgr]

Pretty sure there is a better way...

 

[Nix_Hex]

I haven't looked at this in too much detail but so far it's really cool. I've tried to model this myself in the past but ended up putting it aside for whatever reason.

Something that none of the existing defense optimization apps cover is fixed HP. There are many cases of using specific HP numbers for hazards, weather damage, Life Orb, optimal Leftovers recovery, 101 HP subs, etc. It shouldn't be hard to make a model subset that treats HP as another constant and the only independent variables are then Defense and SpDef. Yet another more obscure situation would be aiming for a specific Download boost for your opponent.

 

[Fgdfgfthgr]

I haven't looked at this in too much detail but so far it's really cool. I've tried to model this myself in the past but ended up putting it aside for whatever reason.

Something that none of the existing defense optimization apps cover is fixed HP. There are many cases of using specific HP numbers for hazards, weather damage, Life Orb, optimal Leftovers recovery, 101 HP subs, etc. It shouldn't be hard to make a model subset that treats HP as another constant and the only independent variables are then Defense and SpDef. Yet another more obscure situation would be aiming for a specific Download boost for your opponent.

To be honest, I don't think it's possible to use desmos or geobebra to achieve your desired result. You should really do this yourself. Chose the correct HP EVs value you want that will give you the specific HP while having an overall low curve, and look at the curve to find the minimum. Guess that's all you can do.

 

[Fgdfgfthgr]

Update: Finished working with 3D model...

 

[MagikaripIsOP]

Quick question: when it comes to base stats, we have hp, def, and spdef.

Assuming you’re looking at base stats only, for a level 100 Pokémon with max IVs, would there be a formula to approximate total bulk using those 3 stats?

Something like hp+(def*.75)+(spdef*.75)? That’s a random example I came up with. I’m asking because I want to make an “adjusted base stats total”.

 

[Fgdfgfthgr]

Quick question: when it comes to base stats, we have hp, def, and spdef.

Assuming you’re looking at base stats only, for a level 100 Pokémon with max IVs, would there be a formula to approximate total bulk using those 3 stats?

Something like hp+(def*.75)+(spdef*.75)? That’s a random example I came up with. I’m asking because I want to make an “adjusted base stats total”.

It's really not that simple, but I can try to come up with an approximal curve that fits...please wait.

 

[Fgdfgfthgr]

Quick question: when it comes to base stats, we have hp, def, and spdef.

Assuming you’re looking at base stats only, for a level 100 Pokémon with max IVs, would there be a formula to approximate total bulk using those 3 stats?

Something like hp+(def*.75)+(spdef*.75)? That’s a random example I came up with. I’m asking because I want to make an “adjusted base stats total”.

HP/((1/Defence)+(1/SpD)+0.00017)
Try this out.

 

[MagikaripIsOP]

HP/((1/Defence)+(1/SpD)+0.00017)
Try this out.

it didnt seem to work, is that total stats or base stats?

 

[Fgdfgfthgr]

it didnt seem to work, is that total stats or base stats?

oh, wait...you are talking about base stats(EVs), not total stats. In that case, there is no simple formula because it differences in different pokemon. Please just use the model 2.