Resource "root" defenses

[gnore]

After pondering a way to quantify how much blissey's massive HP compensates for its dreadful Def, I term "root Def" & "root SpD" for the square root of the product of Def(or SpD) & HP. Approximating damage as .84*Power*Atk/Def & distributing maxHP to the denominator from %damage=damage/maxHP, a pokemon experiences ~ %damage equivalent to one whose HP & Def(or SpD) are both its root Def(or SpD).
Interestingly the 63 stat points gained through 252 EVs rarely translates into a full 63 root stats. Blissey as an outlier gains 87 Root Def from 63 Def EV stats. Dusclops gains 34 root stats in each of its defensive stats from 63 EV stats added to its HP. Full EV investment in both HP & a defensive stat guarantees a minimum 63 root gain. My brain is too exhausted to ponder if there's a mathematical reason or just coincidence.

some rDef & rSpD examples:

Blissey:
200 rDef / 538 rSpD (252 HP / 252+ SpD)
291 rDef / 446 rSpD (252+ Def)

Lugia:
405 rDef / 378 rSpD (252 HP / 252+ Def)

Regirock (& mirrored Regice):
447 rDef / 293 rSpD (252 HP / 252+ Def)
398 rDef / 346 rSpD (252 HP / 252+ SpD)

Registeel:
350 rDef / 399 rSpD (252 HP / 252+ SpD)

Suicune:
382 rDef / 328 rSpD (252 HP / 252+ Def)
301 rDef / 301 rSpD (uninvested)

Celebi/Jirachi:
364 rDef / 309 SpD (252 HP / 252+ Def)
284 rDef / 284 rSpD (uninvested)

Milotic:
333 rDef / 335 rSpD (252 HP / 252+ Def)

Tyranitar:
322 rDef / 309 rSpD (252 HP)

Swampert:
352 rDef / 295 rSpD (252 HP / 252+ Def)

Snorlax:
325 rDef / 344 rSpD (252 Def)

Dusclops:
290 rDef / 335 rSpD (252 HP / 252+ SpD)

Forretress:
334 rDef / 291 rSpD (252 HP / 252+ SpD)

Metagross:
328 rDef / 280 rSpD (252 HP)

Skarmory:
325 rDef / 296 rSpD (252 HP / 252+ SpD)

Hariyama:
307 rDef / 321 rSpD (252 Def / 252+ SpD)

Wailord:
302 rDef / 316 rSpD (252 Def / 252+ SpD)

Salamence:
278 rDef / 278 rSpD (252 HP)

Starmie:
258 rDef / 258 rSpD (252 HP)

Cloyster:
347 rDef / 251 rSpD (252 HP / 252+ SpD)

Slaking:
323 rDef / 271 rSpD (uninvested)

 

[Ajencis]

i've used a similar idea before when doing analysis of when to use tios vs tias in a post i'm too lazy to find. in this case i used simply the factor of defense stats and hp (without a square root). this may be an easier way to do it, taking the root has the advantage of being equivalent to having the "root def" in both stats, but this is not necessarily too useful because i'm not sure too many people have intuitive understandings of what, say, a 200 defence and hp stat looks like. the rdef also doesn't scale linearly - a pokemon with twice the rdef has four times the bulk, for instance. rdef does end up with smaller numbers, but i'm not sure that's overall too useful. would also be possible to multiply them together and divide by 1000 or something, idk.

thus,
0/0 def bliss has 36456 effective physical bulk
0/252 def bliss has 77469 effective physical bulk, just over twice as much
0/252 bliss takes about half as much from physical attacks as 0/0 bliss does

we can divide and round these to 36 and 77 respectively if we so desire


fun fact:
4/252 def lax has 105798 def
4/252+ spD lax has 161700 spD
252/144 def lax has 105848 def
252/112+ spD lax has 163488 spD

hp invest on lax is only very very very slightly more efficient than def invest (about 1% more efficient)

 

[gnore]

i've used a similar idea before when doing analysis of when to use tios vs tias in a post i'm too lazy to find. in this case i used simply the factor of defense stats and hp (without a square root). this may be an easier way to do it, taking the root has the advantage of being equivalent to having the "root def" in both stats, but this is not necessarily too useful because i'm not sure too many people have intuitive understandings of what, say, a 200 defence and hp stat looks like. the rdef also doesn't scale linearly - a pokemon with twice the rdef has four times the bulk, for instance. rdef does end up with smaller numbers, but i'm not sure that's overall too useful. would also be possible to multiply them together and divide by 1000 or something, idk.

thus,
0/0 def bliss has 36456 effective physical bulk
0/252 def bliss has 77469 effective physical bulk, just over twice as much
0/252 bliss takes about half as much from physical attacks as 0/0 bliss does

we can divide and round these to 36 and 77 respectively if we so desire


fun fact:
4/252 def lax has 105798 def
4/252+ spD lax has 161700 spD
252/144 def lax has 105848 def
252/112+ spD lax has 163488 spD

hp invest on lax is only very very very slightly more efficient than def invest (about 1% more efficient)

yeah, not rooting also lets you keep the numbers relative with the atk*pow from the numerator (though the .84 makes it tough to compare atk*pow to def*hp, which is why i liked the idea of rooting them; 42/50=7*3*2/5/5 does allow one to do some damage calcs with mental math by using ~def*hp like you said, though rounding the squared value loses more data & is much harder to then scale with stat modifiers). rooting atk*pow doesn't allow intuition because the range of move powers only barely overlaps its outliers with the range of ou lv100 atk stats. it does allow intuitive comparisons between rAtk*Pow clusters:
breloom stab mach is ~150*150
swampert neutral stab eq is ~200*200, ~ a wailord selfdestruct
gross stab mash ~250*250
gross cb stab mash is ~300*300
slaking cb stab edge ~350*350
medi cb focus is ~400*400
gross explosion is ~450*450
gross cb explosion is ~550*550

Edit:
sample mental calcs:

4 hundred ~ 405 (252+ Atk Metagross)
5 hundred = 250 Power Explosion / .5 Secondary Effect
7 hundred ~ 334 (252 HP Skarmory) * 2 Resisted
3 hundred ~ 316 (0 Def Skarmory)
(4*5 * 7*3) / (7*3 * 5*5) = 4/5, which is why Metagross needs a band to 1H Skarmory.

min roll is 17/20, so a min roll band is:
4/5 * 17/(4*5) * 3/2 = 17/25 * 3/2 = 51/50 for the KO.

also, ituiting root def is very nice with skarm, whose rDef of 325 is nicely only 9 off their original values of 334 & 316 each.
rounding them like in my example is also nice with skarm since 350-334=16 & 316-300=16.