Stat Ratings
IntroductionHereunder is a collection of ratings of a Pokemon, in particular:
Note that a Pokemon having high attacking stats but low defense and speed stats is NOT deemed to be offensive, as it can't do enough damage before it is KOed. An example of such a Pokemon is Camerupt. Physical Tankiness, Special Tankiness, Physical Sweepiness, Special SweepinessThe formulae for calculating the various components are as follows: Physical Tankiness (PT) = HP × Def ÷ 35
Special Tankiness (ST) = HP × SpD ÷ 35
Physical Sweepiness (PS) = Atk × (Atk × SF + 315) ÷ (Atk × (1-SF) + 315)
Special Sweepiness (SS) = SpA × (SpA × SF + 315) ÷ (SpA × (1-SF) + 315)
where HP is the normalized Base HP
Atk is the normalized Base Attack
Def is the normalized Base Defense
SpA is the normalized Base Special Attack
SpD is the normalized Base Special Defense
SF is the Speed Factor of the Base Speed
PT and ST are divided by 35 to normalize their values. A tankiness (physical or special) of 100 means that the Pokemon has average (physical or special) defense. A tankiness of more than 100 means it's pretty defensive (the more the better), while a tankiness of less than 100 means that it can't take hits well. A sweepiness (physical or special) of 100 means that the Pokemon has average (physical or special) offense. A sweepiness of more than 100 means it's pretty offensive (the more the better), while a sweepiness of less than 100 means it cannot attack well. Offense/Defense BalanceODB = 55 × ln(max(PS,SS) ÷ max(PT,ST)), rounded to one decimal place.
where max(a,b) returns the larger of a and b
ln(x) is the natural logarithm of x
If the ODB is negative, then the Pokemon's stats are geared towards defense. If the ODB is positive, then the Pokemon's stats are geared towards offense. If it is near zero, then the stats are balanced, having roughly the same amount of tankiness as it has sweepiness. A small chart can give us the degree of offense/defense:
Physical/Special BalancePSB = 55 × ln((PT × PS) ÷ (ST × SS)), rounded to one decimal place where ln(x) is the natural logarithm of x If the PSB is negative, then the Pokemon's stats are geared towards the special stats. If the PSB is positive, the Pokemon's stats are geared towards the physical stats. A small chart can give us the degree of physical/special disparity:
Overall RatingPart 1: The Rating Modifier The Rating Modifier (M) is used in the Overall Rating of a Pokemon, to reward Pokemon having outstanding PT, PS, ST, and/or SS. Each modifier increases slowly from 1 for a rating (tankiness or sweepiness) of 100, to 1.375 for a rating of 180 (about 2 standard deviations from the mean), to 2.5 for a rating of 260 (about 4 standard deviations from the mean). Modifier for PT (MPT) = (3 × PT^2 - 600 × PT + 81200) ÷ 51200, if PT > 100
= 1, otherwise
Modifier for PS (MPS) = (3 × PS^2 - 600 × PS + 81200) ÷ 51200, if PS > 100
= 1, otherwise
Modifier for ST (MST) = (3 × ST^2 - 600 × ST + 81200) ÷ 51200, if ST > 100
= 1, otherwise
Modifier for SS (MSS) = (3 × SS^2 - 600 × SS + 81200) ÷ 51200, if SS > 100
= 1, otherwise
M = MPT × MPS × MST × MSS
Part 2: The Overall Rating Formula Overall Rating = PT × ST × (PS + SS) × M ÷ (56 × (PT + ST)), rounded to the nearest whole number. The rating can be used as follows:
ExampleLet's say we are considering creating a hypothetical Pokemon having the following Base Stats: 52/117/93/80/67/101 First we find the normalized stats and the Speed Factor: HP: 52/4 + 18 = 31 Atk: 117 + 18 = 135 Def: 93 + 18 = 111 SpA: 80 + 18 = 98 SpD: 67 + 18 = 85 SF: 0.92 Now we find PT, ST, PS, SS: Physical Tankiness = 31 x 111 / 35 = 98.31 (average defense)
Special Tankiness = 31 x 85 / 35 = 75.29 (below average special defense)
Physical Sweepiness = 135 x (135 x 0.92 + 315) / (135 x 0.08 + 315)
= 135 x 439.2 / 325.8 = 181.99 (very high physical offense)
Special Sweepiness = 98 x (98 x 0.92 + 315) / (98 x 0.08 + 315)
= 98 x 405.16 / 322.84 = 122.99 (above average special offense)
Offense/Defense Balance: The higher from PT and ST is 98.31; that from PS and SS is 181.99. ODB = 55 x ln(181.99 / 98.31) = 55 x ln(1.851)
= 55 x 0.616 = 33.9
Looking at the chart, this translates to a Pokemon that is geared strongly towards offense. Physical/Special Balance: PSB = 55 x ln((98.31 x 181.99) / (75.29 x 122.99))
= 55 x ln(17891.44 / 9259.92)
= 55 x ln(1.932) = 55 x 0.659 = 36.2
Looking at the chart, this means that the Pokemon is geared strongly towards the physical stats. Overall Rating: Now, for the overall rating, we first need to find the rating modifier M, which is made up of four mini modifiers, one each for PT, PS, ST and SS. PT and ST are both not greater than 100, so MPT and MST are both 1. For PS, MPS = (3 x 181.99^2 - 600x181.99 + 81200) / 51200
= (3 x 33120.36 - 109194 + 81200) / 51200
= (99361.08 - 109194 + 81200) / 51200 = 71367.08 / 51200 = 1.394
For SS, MSS = (3 x 122.99^2 - 600x122.99 + 81200) / 51200
= (3 x 15126.54 - 73794 + 81200) / 51200
= (45379.62 - 73794 + 81200) / 51200 = 52785.62 / 51200 = 1.031
Hence M = 1 x 1 x 1.394 x 1.031 = 1.437
Finally, the overall rating! Note that ODB and PSB are not needed for the evaluation of the overall rating. Overall Rating = 98.31 x 75.29 x (181.99 + 122.99) x 1.437 / (56 x (98.31 + 75.29))
= 98.31 x 75.29 x 304.98 x 1.437 / (56 x 173.6)
= 3243867.61 / 9721.6 = 334
From the chart, a rating of 334 means that the stats are very good. |