A Much Better Rating Of A Pokemon Than BST

[X-Act]

Okay, so basically I've been researching on a good rating of a Pokemon that is neither too simple as to be useless (BST) nor too complex as to be uncalculable without a computer (this).

The rating is divided in two: what I call the tankiness of a Pokemon and the sweepiness of a Pokemon. The former uses HP, Def and SpD, while the latter uses Atk, SpA and Spe. These two numbers are important in their own right.

The tankiness of a Pokemon is defined by:

Tankiness = HP x Def x SpD / (Def + SpD)

where HP, Def and SpD are the normalized base stats (not the actual base stats!) of HP, Defense and Special Defense respectively. Tankiness is directly proportional to the overall defenses of a Pokemon.

The sweepiness of a Pokemon is defined by:

Sweepiness = AT x (SF x AT + 630) / ((1 - SF) x AT + 630)
 
where AT = Atk + SpA
      SF = Speed Factor of Spe

Again, normalized base stats are used here for Attack and Special Attack. The Speed Factor of a Pokemon can found from this chart, which is the only thing in the formula that depends on the actual base stat, but that is because the Speed stat is used differently than the other stats in the game. Sweepiness is directly proportional to the overall attacking prowess of a Pokemon.

Finally, the overall rating of a Pokemon is

Rating = Tankiness x Sweepiness / 1000, rounded to the nearest whole number

The division by 1000 is only there so as not to have a rating with 6 or 7 digits.

For an idea of what a rating means, here is a short table:

   Rating     The stats are   Pokemon with this rating
---------------------------------------------------------
950 or more   Exaggerated     Arceus, Giratina, Palkia, Rayquaza, Regigigas, Mewtwo, Slaking, Dialga, Lugia, Ho-oh, Kyogre, Groudon
 800 to 949   Too good        None
 700 to 799   Fantastic       Garchomp, Mew, Celebi, Jirachi, Manaphy, Shaymin, Salamence, Latios, Heatran, Dragonite, Latias
 600 to 699   Excellent       Entei, Darkrai, Tyranitar, Zapdos, Moltres, Raikou, Cresselia, Metagross, Azelf, Suicune, Articuno, Mesprit, Arcanine
 500 to 599   Very good       Uxie, Gyarados, Deoxys-D, Charizard, Electivire, Togekiss, Typhlosion, Infernape, Kingdra, Registeel, Porygon-Z, Deoxys, Milotic, Magmortar, Lapras, Walrein, Feraligatr, Mamoswine, Swampert, Deoxys-S, Blastoise, Flygon
 450 to 499   Quite good      Blaziken, Venusaur, Sceptile, Lucario, Torterra, Vaporeon, Meganium, Crobat, Regirock, Regice, Empoleon, Espeon, Luxray, Snorlax, Magnezone, Yanmega, Starmie, Hippowdon, Glaceon, Lickilicky, Umbreon, Porygon2, Exeggutor
 400 to 449   Good            Leafeon, Golduck, Gardevoir, Gallade, Ninetales, Tentacruel, Scyther, Jolteon, Nidoqueen, Poliwrath, Rapidash, Heracross, Aerodactyl, Politoed, Honchkrow, Machamp, Nidoking, Flareon, Rhyperior, Weavile, Gliscor, Houndoom, Tangrowth, Gengar, Ampharos, Pinsir, Kangaskhan, Muk, Drapion, Magmar, Scizor, Toxicroak, Ursaring, Abomasnow, Drifblim, Roserade, Floatzel, Electabuzz, Cradily, Skuntank, Claydol, Altaria, Exploud
 350 to 399   Average         Kabutops, Mismagius, Tauros, Glalie, Phione, Wailord, Miltank, Shiftry, Probopass, Dusknoir, Froslass, Hypno, Ludicolo, Ambipom, Rampardos, Donphan, Armaldo, Pidgeot, Bronzong, Dewgong, Manectric, Staraptor, Victreebel, Slowbro, Slowking, Omastar, Clefable, Whiscash, Xatu, Lopunny, Weezing, Raichu, Vileplume, Bellossom, Swalot, Deoxys-A, Hariyama, Gastrodon, Relicanth, Aggron, Alakazam, Tropius, Huntail, Gorebyss, Stantler, Lanturn, Lumineon, Octillery, Grumpig, Golem
 300 to 349   Below Average   Vespiquen, Zangoose, Absol, Dodrio, Golbat, Girafarig, Primeape, Seaking, Spiritomb, Magneton, Cacturne, Breloom, Rhydon, Seviper, Cherrim, Venomoth, Kingler, Piloswine, Carnivine, Crawdaunt, Purugly, Cloyster, Banette, Sharpedo, Bastiodon, Electrode, Hitmonchan, Granbull, Torkoal, Fearow, Camerupt, Steelix, Lunatone, Solrock, Hitmontop, Mantine, Skarmory, Vigoroth, Sandslash, Rotom, Hitmonlee, Jumpluff, Arbok, Noctowl, Forretress, Mr. Mime
 250 to 299   Poor            Jynx, Misdreavus, Quagsire, Persian, Qwilfish, Chimecho, Pelipper, Seadra, Castform, Mightyena, Mothim, Kecleon, Dragonair, Dusclops, Dunsparce, Wormadam-S, Bibarel, Wigglytuff, Wormadam, Wormadam-G, Linoone, Gligar, Pupitar, Marowak, Sealeo, Furret, Masquerain, Metang, Sneasel, Gabite, Azumarill, Sunflora, Raticate, Chatot, Swellow, Grotle, Medicham, Croconaw, Monferno, Marshtomp, Machoke, Wartortle, Shelgon, Tangela, Ponyta, Prinplup, Bayleef, Ivysaur, Charmeleon, Quilava
 200 to 249   Bad             Combusken, Munchlax, Parasect, Sudowoodo, Ninjask, Murkrow, Togetic, Grovyle, Volbeat, Illumise, Haunter, Porygon, Magcargo, Lairon, Lickitung, Plusle, Gloom, Minun, Ariados, Roselia, Pachirisu, Wobbuffet, Wailmer, Blissey, Yanma, Kricketune, Delcatty, Weepinbell, Beautifly, Butterfree, Poliwhirl, Dustox, Corsola, Sableye, Beedrill, Dugtrio, Mawile, Kadabra, Nidorina, Flaaffy, Nidorino
199 or less   Horrible        Everything else

Let's give an example: suppose we need to find a rating for Scylant's base stats.

Syclant's base stats are 70/116/70/114/64/121.

The normalized base stats are:

HP: 70/4 + 18 = 35.5
Atk: 116 + 18 = 134
Def: 70 + 18 = 88
SpA: 114 + 18 = 132
SpD: 64 + 18 = 82
Spe: 121 + 18 = 139 (not needed)

Speed Factor for 121 base speed = 0.98.

Sum of Attack Stats = 134 + 132 = 266.

Tankiness = 35.5 x 88 x 82 / (88 + 82) = 1506.87.
Sweepiness = 266 x (0.98 x 266 + 630) / (0.02 x 266 + 630) = 266 x 890.68 / 635.32 = 372.92.

Rating = 1506.87 x 372.92 / 1000 = 562 (Stats are very good).

Another example: Revenankh. :)

Revenankh's base stats are 90/105/90/65/110/65.

The normalized base stats are:

HP: 90/4 + 18 = 40.5
Atk: 105 + 18 = 123
Def: 90 + 18 = 108
SpA: 65 + 18 = 83
SpD: 110 + 18 = 128
Spe: 65 + 18 = 83 (not needed)

Speed Factor for 65 base speed = 0.49.

Sum of Attack Stats = 123 + 83 = 206.

Tankiness = 40.5 x 108 x 128 / (108 + 128) = 2372.34.
Sweepiness = 206 x (0.49 x 206 + 630) / (0.51 x 206 + 630) = 206 x 730.94 / 735.06 = 204.85.

Rating = 2372.34 x 204.85 / 1000 = 486 (Stats are quite good).

 

[Time Mage]

First, let me make this clear: I like this a lot. So, consider that every criticism or commentary I'm going to make after this doesn't mean that I don't like this, they are only things I think would make this even better.

- The speed rating: The idea is simple, and effective. I just don't have a complaint about it, but I don't understand why you're using all pokémon in this sample. Being Smogon a competitive site, and being CAP a project centered around the competitive side of pokémon, including NFE pokémon in the list doesn't make ense, since you are not going to encounter them, save some odd exceptions like Light Orb Pikachu or Scyther. So, to make the ratings better, I think it would be a good idea to exclude the NFE from the list.

- The purpose: I guess the goal of this is to use it instead of BSTs in the BST range poll, right? If that's the case, I agree, this is much better, no questions. However, does it have another purpose? The Tankiness and Sweepiness ratings seem to suggest that. Sadly, I can't find a good use for those ratings. Why? Because they are too unspecific. Taking into account both special and physical stats is better for a general idea, but when designing a pokémon, many times one focuses on the physical or special aspects of them, and that specialization, while not yielding ratings as high as those attained with even-ish stats, is in fact better. Anyway, for a new kind of "BST totals", this is awesome.

- The math: Could you explain how did you obtain the Sweepiness formula? The Tankiness one seems obvious, but I can't figure out the Sweepiness one. Specially that 630 constant you've added.


Ah, I almost forgot! Did you find a better way to determine the "Style" of a pokémon? The one we have now works well in one direction (if the highest defense stat is X% higher than the highest offense stat, there's no way the pokémon could be offensive), but doesn't in the other (as you showed, a pokémon with very high HP and defenses X% lower than the highest attack stat can still be defensive, like Wailord).

 

[Aldaron]

I'm noting a severe bias towards offensive Pokemon. Is there a particular reason for this?

 

[Stall]

I'm noting a severe bias towards offensive Pokemon. Is there a particular reason for this?

I'm not sure I see that. Deoxys-A is 3 categories down from all the other forms, after all.

 

[Aldaron]

Hmm, I should say fast Pokemon as well. High Offense High Speed Pokemon over HP high Defenses Pokemon?

 

[X-Act]

First, let me make this clear: I like this a lot. So, consider that every criticism or commentary I'm going to make after this doesn't mean that I don't like this, they are only things I think would make this even better.

Okay.

- The speed rating: The idea is simple, and effective. I just don't have a complaint about it, but I don't understand why you're using all pokémon in this sample. Being Smogon a competitive site, and being CAP a project centered around the competitive side of pokémon, including NFE pokémon in the list doesn't make ense, since you are not going to encounter them, save some odd exceptions like Light Orb Pikachu or Scyther. So, to make the ratings better, I think it would be a good idea to exclude the NFE from the list.

Because NFE's ratings can also be found using this method. I didn't want to discriminate against Unown and Luvdisc, since they are also Pokemon, even though nobody uses them. And they aren't even NFEs, and certain NFEs are better than them. So banning NFEs from the list is kinda discriminating.

- The purpose: I guess the goal of this is to use it instead of BSTs in the BST range poll, right? If that's the case, I agree, this is much better, no questions. However, does it have another purpose? The Tankiness and Sweepiness ratings seem to suggest that. Sadly, I can't find a good use for those ratings. Why? Because they are too unspecific. Taking into account both special and physical stats is better for a general idea, but when designing a pokémon, many times one focuses on the physical or special aspects of them, and that specialization, while not yielding ratings as high as those attained with even-ish stats, is in fact better. Anyway, for a new kind of "BST totals", this is awesome.

I could also write similar formulae for "physical tankiness", "special tankiness", "physical sweepiness" and "special sweepiness" if you like, and a "physical rating" and a "special rating" would them also be possible. Would you like that?

- The math: Could you explain how did you obtain the Sweepiness formula? The Tankiness one seems obvious, but I can't figure out the Sweepiness one. Specially that 630 constant you've added.

The interesting thing is that I did something very different at first, and then, when I simplified the equation, it turned out to be divided into an expression involving the defensive stats and one involving the offensive stats. So I thought to divide it neatly in two. The 630 is because I roughly assumed that 630/(Atk+SpA) is the number of hits needed to KO the opponent, and I needed that to give a meaning to the Speed stat.

Ah, I almost forgot! Did you find a better way to determine the "Style" of a pokémon? The one we have now works well in one direction (if the highest defense stat is X% higher than the highest offense stat, there's no way the pokémon could be offensive), but doesn't in the other (as you showed, a pokémon with very high HP and defenses X% lower than the highest attack stat can still be defensive, like Wailord).

I was thinking about that as well, but its formula is not yet finished.

I'm noting a severe bias towards offensive Pokemon. Is there a particular reason for this?

Cresselia is high in the list. Blastoise is also quite high.

 

[Aldaron]

Yea, that's true, just that the general trend I am seeing is that bulky Sweepers are at the top end, as opposed to offensive tanks or something like that.

Probably insignificant. I ran calcs for 100 HP / 50 Atk / 100 Def / 50 SpA / 100 SpD / 50 Spe and got 318, while 50 HP / 100 Atk / 50 Def / 100 SpA / 50 SpD / 100 Spe gave me 309, so yea, it probably doesn't mean too much.

 

[dekzeh]

Charizard/Walrein/Registeel/Feraligatr being 'Very Good' and Lucario/Hippowdon/Vaporeon being 'Quite Good' seems a little odd...

Not to mention Entei and Arcanine being 'Excellent'.

I know that this is due to the fact this thing doesn't take in account the Movepool/Typing etc and that's exactly why it just seems kinda useless to me.

 

[Jenigmat]

Well, if you can rate things on all of their various components, you can come up with a way to combine them. You can't deny the fact that things like Luke or Hippo are made much better by movepool or ability. And when you think about it, in terms of stats Entei and Arcanine actually are Excellent.

 

[Hyra]

Can I request an applet / something for this? Although it is nice to not need a computer, it is nicer to not need a calculator while at the computer.

 

[EconBiscuit]

Charizard/Walrein/Registeel/Feraligatr being 'Very Good' and Lucario/Hippowdon/Vaporeon being 'Quite Good' seems a little odd...

Not to mention Entei and Arcanine being 'Excellent'.

I know that this is due to the fact this thing doesn't take in account the Movepool/Typing etc and that's exactly why it just seems kinda useless to me.

This is just taking into account the Base stats that a pokemon uses as a more accurate descriptions.

You couldn't produce a formula based on movesets/typing e.t.c it's completly unfeasible the nearest thing we have to this is the Tiers and look how much arguements derive from that. Be content with what X-Act has done if the next gen comes out and they are given a bigger movepool, who'll be laughing then?

Anyways X-act has yet again done a wonderful job and we should be thanking him, not trying to shoot down the hard work he has put into it.

 

[Aldaron]

Second Hyra's request.

 

[X-Act]

Charizard/Walrein/Registeel/Feraligatr being 'Very Good' and Lucario/Hippowdon/Vaporeon being 'Quite Good' seems a little odd...

Not to mention Entei and Arcanine being 'Excellent'.

I know that this is due to the fact this thing doesn't take in account the Movepool/Typing etc and that's exactly why it just seems kinda useless to me.

Imagine a Pokemon having 115/115/85/90/75/100 base stats. Excellent stats across the board, right? 115/85/75 defenses are above average. 115/90/100 attacking prowess is very good.

Oh wait, that Pokemon exists. It's called ENTEI.

Now imagine another Pokemon with 90/110/80/100/80/95 stats. Pretty good stats once again: 110/100/95 attacking stats are quite great, and 90/80/80 defenses are slightly above average.

But wait... this Pokemon exists too. It's called ARCANINE.

Then another Pokemon with 108/112/118/68/72/47 came in. Very solid defensively, but it lacks in the special defense department. Very good in the physical offense, but it lacks in the special offense. It also is very slow. So this Pokemon has its upsides and downsides... and hence it's simply 'quite good'. Who cares that it's called HIPPOWDON?

Okay, seriously, I'm disappointed that such a post was made yet again. Let me regurgitate again what I said countless times before: Arcanine's and Entei's problems aren't the stats. They are excellent, they are impressive. Their problems are their typing and movepool, especially for Entei's case.

 

[Kindred]

Could we see a list for the Tanking stats of pokemon exclusively? And the Sweeping stats?

 

[X-Act]

Since Time Mage seems to have wanted this:

Physical tankiness (PT) = HP x Def

Physical sweepiness (PS) = Atk x (SF x Atk + 315) / ((1 - SF) x Atk + 315)

Physical rating (PR) = PT x PS / 1000

Special tankiness (ST) = HP x SpD

Special sweepiness (SS) = SpA x (SF x SpA + 315) / ((1 - SF) x SpA + 315)

Special rating (SR) = ST x SS / 1000

Tankiness = PT x ST / (PT + ST)

Sweepiness = PR + SR (very near)

 

[Time Mage]

Since Time Mage seems to have wanted this:

Thanks a lot. I'm going to do some number-crunching and then I'll propose a new form of obtaining the style with this. For the preliminary calcs I've done, it might work very well.

 

[dekzeh]

Imagine a Pokemon having 115/115/85/90/75/100 base stats. Excellent stats across the board, right? 115/85/75 defenses are above average. 115/90/100 attacking prowess is very good.

Oh wait, that Pokemon exists. It's called ENTEI.

Now imagine another Pokemon with 90/110/80/100/80/95 stats. Pretty good stats once again: 110/100/95 attacking stats are quite great, and 90/80/80 defenses are slightly above average.

But wait... this Pokemon exists too. It's called ARCANINE.

Then another Pokemon with 108/112/118/68/72/47 came in. Very solid defensively, but it lacks in the special defense department. Very good in the physical offense, but it lacks in the special offense. It also is very slow. So this Pokemon has its upsides and downsides... and hence it's simply 'quite good'. Who cares that it's called HIPPOWDON?

Okay, seriously, I'm disappointed that such a post was made yet again. Let me regurgitate again what I said countless times before: Arcanine's and Entei's problems aren't the stats. They are excellent, they are impressive. Their problems are their typing and movepool, especially for Entei's case.

My post got kinda misunderstood.
What I mean, I think it's pointless to 'rate' pokemon due to their stats since movepool/typing/trait are MUCH more important.

I do understand how this this works and I do know their stats are better, I just think that looking from a competitive perspection, that's kinda useless.

But I do appreciate the effort you did into this for the people who actually care, it's just my opnion that pokemon isn't only numbers.

 

[X-Act]

I agree fully. But I said that this is just a better alternative to BST. BST means absolutely nothing. This at least means _something_.

 

[moi]

Well, since Aldaron bugged me, I've been working on getting something done that I should have done within a few more minutes. I'll also post an mIRC version eventually. I'll keep updates here.

 

[DougJustDoug]

I agree fully. But I said that this is just a better alternative to BST. BST means absolutely nothing. This at least means _something_.

This is not intended to measure the entire pokemon. This is simply a way of arranging the stats of a pokemon into tiers. Currently, most people create stat tiers by adding up the total of the stats and arranging them in descending order. As we all know the stat totals do not really signify anything important as it relates to the effectiveness of the pokemon. It doesn't even signify the effectiveness of the stats themselves!

Why is this relevant to the CAP project?.....

Because the CAP project uses the total stat sum as a early way to measure and poll when determining the stats for a new pokemon creation. If the stat total is essentially meaningless, then why are we wasting our time discussing and polling on it?

Because we don't have anything else.

Hence, X-Act's formula. It is "something else". I think it is "something better".

 

[Aldaron]

Agreed, I've been using this fantastic guide as a way to measure and compare certain spreads, and it has been very helpful.

Hopefully Castlevania will contribute that applet soon so that we can make the process even more efficient!

 

[chaos]

I think the algorithm needs work if a ridiculously offensive threat like Deoxys-A is lumped in "Average" with nonsense like Swalot and Huntail.

 

[X-Act]

I think the algorithm needs work if a ridiculously offensive threat like Deoxys-A is lumped in "Average" with nonsense like Swalot and Huntail.

Again I'm a bit disappointed with a comment such as this. :(

Deoxys-A is 'average' because it has the highest sweepiness in the game and among the lowest tankiness in the game. When all is said and done, if you give Deoxys-A only Tackle as a movepool, do you think it will fare well? It would be another Unown in that case.

Deoxys-A is an extreme case of a Pokemon where movepool is make-or-break for him. If its movepool allows him to OHKO things, then it would be uber (as it is now). If it doesn't, then it would be NU.

Since the rating only takes stats into account, and doesn't take movepool, typing or anything else into account, it just says that its rating is somewhere in between, or 'average'.

 

[chaos]

Yeah... and perhaps people are dissapointed with comments of yours too. There is no reason to say stuff like that in posts; does it really add anything?

The movepool argument is totally BS. "If I gave Snorlax only Tackle" "If I gave Garchomp only Tackle". Uh, yeah. What is the point again? Pokemon doesn't operate on this level. It's like you're assuming that Pokemon _don't have movepools_ which makes the algorithm completely out of touch with reality.

You don't even have to consider typing or the different movepools a Pokemon gets. You can assume a Pokemon gets a movepool that can somewhat make use of its stats; this is true for every evolved Pokemon in the game. Deoxys-A's ridiculous combination of attacking stats and speed aren't completely dependent on it's movepool. Even with an average offensive movepool, it still gets more out of its stats than the majority of Pokemon (which is why I have a problem with it being in the "Average" category)

I think my biggest problem is the equal weighting of "sweepiness" and "tankiness". The more a Pokemon excels at one, the less the other matters. Blissey's "sweepiness" should have little to no effect on it's actual placement because of how well it excels in the "tankiness" category. The reverse applies. Deoxys-A's defensive stats could be 0, it wouldn't effect the usefulness of the Pokemon whatsoever because of how much it excels in the other category. Claiming otherwise is just... I don't know, incorrect. Blissey's stat distribution is much more ideal than say, Kricketune, a Pokemon in the same "ranking". The rating of a Pokemon's stats in relation to "sweepiness" and "tankiness" looks more like

than

(awesome pictures, I know)

 

[X-Act]

I'll gladly research further on this so as to make it more optimal, if you will.

(Hopefully Shuckle doesn't end up having Fantastic stats though.)