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Feb 19th, 2008, 12:27:45 PM
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np: Biffy Clyro - Shock Shock
   
Join Date: Feb 2006
Posts: 4,679
Malta
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Analysis of Base Stats
I have been researching into how to give a rating to the base stats of a Pokemon since last November. All the stats except Speed were relatively easy to interpret, but Speed proved to be a tough nut to crack... until last week.
I would like to make it clear before I continue that this analysis concerns only the base stats of the Pokemon, and nothing else. It's not only base stats that make a Pokemon, but typing, movepool and ability as well (and the Pokemon-exclusive item if it has any). Leaving those other three things out when considering a Pokemon for usage in your team is naive, to put it mildly. With that out of the way, let's look at Arceus' base stats: 120/120/120/120/120/120 You might be thinking "this should surely rank highly in whatever base stats rating system you might care to invent". However, say the other Pokemon's base stats are all over 500. Then the above base stats wouldn't be looking terribly good, would they? This illustrates a point: a Pokemon's base stats are only good or bad compared to other Pokemon's base stats. And that is why the system which I devised attempts to give a rating to a set of base stats by comparing it to all the other Pokemon's base stats. To do this, I had to resort to... you guessed it... the damage formula, which, after removing all unnecessary stuff out of it (for the purposes of this), it gets to something like PercentDamage_i,j = 0.84 x Atk_i x MovePower / HP_j x Def_j where HP_n = 2 * (HP of Pokemon #n) + 141 Stat_n = 2 * (Stat of Pokemon #n) + 36 PercentDamage_i,j is the percentage damage that Pokemon #i deals to Pokemon #j. Now I actually want to see both the attacking and special attacking prowess of the Pokemon, and, to be fair, I wanted the Pokemon to deal a move with the same move power both using the Atk stat and using the SpA stat. So I added the special attacking percentage damage to this as well, and divided by 2, getting: Damage_i,j = (0.42 x MovePower / HP_j) x (Atk_i / Def_j + SpA_i / SpD_j) Now I actually don't care much about the percentage damage dealt. What I care about is whether the move OHKOes, 2HKOes, 3HKOes, 4HKOes, etc. This nifty little formula gives us the number of hits needed to KO a Pokemon: HTKO_i,j = ceil(1 / Damage_i,j) where ceil(x) is x rounded up. Simple, huh? (HTKO_i,j stands for the number number of Hits To KO.) Now, say Pokemon #1 can 2HKO Pokemon #2, while Pokemon #2 can OHKO Pokemon #1. It is obvious that Pokemon #2 would win the battle. So I defined the Hit Difference (HD) as: HD_i,j = HTKO_i,j - HTKO_j,i If HD_i,j is negative, then Pokemon #i would win against Pokemon #j. If HD_i,j is positive, then Pokemon #j would win against Pokemon #i. What if HD_i,j is zero? Then the faster Pokemon would win. This is where the Speed stat comes in! So here's the Win function: Win_i,j = 1, if (HD_i,j < 0) or (HD_i,j = 0 and Spe_i > Spe_j) Win_i,j = 0, otherwise It can be shown that the following are true for all i,j: HD_i,j = -HD_j,i HD_i,i = 0 Win_i,i = 0 Win_i,j = 1 implies that Win_j,i = 0 (The converse to this is NOT true, however.) Finally, the rating of the base stats of Pokemon i is defined as follows: Rating_i = Win_i,1 + Win_i,2 + Win_i,3 + ... + Win_i,498 The final complication that occurs when implementing this is to give a value for MovePower in the Damage_i,j formula, on which all the other formulae are then based. In my implementation, I used the value of 135, which is the value you get when using a 90-power STAB move. The result of the implementation was the following: Code:
Rank Name HP Atk Def SpA SpD Spe BST Rating ----------------------------------------------------------- 1 Arceus 120 120 120 120 120 120 720 497 2 Mewtwo 106 110 90 154 90 130 680 495 3 Lugia 106 90 130 90 154 110 680 494 4 Slaking 150 160 100 95 65 100 670 491 4 Regigigas 110 160 110 80 110 100 670 491 6 Palkia 90 120 100 150 120 100 680 490 7 Giratina 150 100 120 100 120 90 680 488 8 Ho-oh 106 130 90 110 154 90 680 486 8 Dialga 100 120 120 150 100 90 680 486 10 Kyogre 100 100 90 150 140 90 670 485 10 Rayquaza 105 150 90 150 90 95 680 485 12 Groudon 100 150 140 100 90 90 670 482 12 Garchomp 108 130 95 80 85 102 600 482 14 Latios 80 90 80 130 110 110 600 479 15 Tyranitar 100 134 110 95 100 61 600 476 15 Salamence 95 135 80 110 80 100 600 476 15 Darkrai 70 90 90 135 90 125 600 476 18 Cresselia 120 70 120 75 130 85 600 475 19 Mew 100 100 100 100 100 100 600 474 19 Celebi 100 100 100 100 100 100 600 474 19 Jirachi 100 100 100 100 100 100 600 474 19 Manaphy 100 100 100 100 100 100 600 474 19 Shaymin 100 100 100 100 100 100 600 474 24 Suicune 100 75 115 90 115 85 580 471 24 Latias 80 80 90 110 130 110 600 471 26 Raikou 90 85 75 115 100 115 580 469 27 Zapdos 90 90 85 125 90 100 580 468 28 Entei 115 115 85 90 75 100 580 467 29 Moltres 90 100 90 125 85 90 580 466 29 Heatran 91 90 106 130 106 77 600 466 31 Dragonite 91 134 95 100 100 80 600 465 32 Metagross 80 135 130 95 90 70 600 462 32 Uxie 75 75 130 75 130 95 580 462 34 Articuno 90 85 100 95 125 85 580 459 34 Deoxys 50 150 50 150 50 150 600 459 36 Snorlax 160 110 65 65 110 30 540 457 37 Registeel 80 75 150 75 150 50 580 455 38 Arcanine 90 110 80 100 80 95 555 454 38 Azelf 75 125 70 125 70 115 580 454 40 Deoxys-D 50 70 160 70 160 90 600 453 40 Mesprit 80 105 105 105 105 80 580 453 42 Lapras 130 85 80 85 95 60 535 445 43 Walrein 110 80 90 95 90 65 530 441 44 Milotic 95 60 79 100 125 81 540 439 45 Charizard 78 84 78 109 85 100 534 438 45 Typhlosion 78 84 78 109 85 100 534 438 45 Kingdra 75 95 95 95 95 85 540 438 45 Regirock 80 100 200 50 100 50 580 438 45 Porygon-Z 85 80 70 135 75 90 535 438 50 Regice 80 50 100 100 200 50 580 437 50 Magmortar 75 95 67 125 95 83 540 437 52 Swampert 100 110 90 85 90 60 535 436 53 Gyarados 95 125 79 60 100 81 540 435 53 Electivire 75 123 67 95 85 95 540 435 55 Infernape 76 104 71 104 71 108 534 434 56 Deoxys-S 50 95 90 95 90 180 600 431 57 Togekiss 85 50 95 120 115 80 545 430 58 Blaziken 80 120 70 110 70 80 530 428 58 Torterra 95 109 105 75 85 56 525 428 60 Lickilicky 110 85 95 80 95 50 515 427 61 Crobat 85 90 80 70 80 130 535 426 61 Hippowdon 108 112 118 68 72 47 525 426 61 Mamoswine 110 130 80 70 60 80 530 426 64 Sceptile 70 85 65 105 85 120 530 423 65 Flygon 80 100 80 80 80 100 520 422 66 Rhyperior 115 140 130 55 55 40 535 420 67 Feraligatr 85 105 100 79 83 78 530 419 67 Empoleon 84 86 88 111 101 60 530 419 69 Luxray 80 120 79 95 79 70 523 418 70 Blastoise 79 83 100 85 105 78 530 417 70 Vaporeon 130 65 60 110 95 65 525 417 70 Magnezone 70 70 115 130 90 60 535 417 73 Umbreon 95 65 110 60 130 65 525 415 74 Starmie 60 75 85 100 85 115 520 414 74 Yanmega 86 76 86 116 56 95 515 414 76 Lucario 70 110 70 115 70 90 525 411 77 Espeon 65 65 60 130 95 110 525 410 78 Meganium 80 82 100 83 100 80 525 408 79 Venusaur 80 82 83 100 100 80 525 406 79 Exeggutor 95 95 85 125 65 55 520 406 81 Porygon2 85 80 90 105 95 60 515 404 81 Glaceon 65 60 110 130 95 65 525 404 83 Leafeon 65 110 130 60 65 95 525 401 84 Golduck 80 82 78 95 80 85 500 400 85 Gallade 68 125 65 65 115 80 518 399 86 Flareon 65 130 60 95 110 65 525 398 87 Aerodactyl 80 105 65 60 75 130 515 396 88 Nidoking 81 92 77 85 75 85 495 395 89 Pinsir 65 125 100 55 70 85 500 394 89 Gardevoir 68 65 65 125 115 80 518 394 89 Tangrowth 100 100 125 110 50 50 535 394 92 Scyther 70 110 80 55 80 105 500 392 92 Machamp 90 130 80 65 85 55 505 392 94 Rapidash 65 100 70 80 80 105 500 391 94 Scizor 70 130 100 55 80 65 500 391 94 Jolteon 65 65 60 110 95 130 525 391 97 Slowbro 95 75 110 100 80 30 490 390 97 Muk 105 105 75 65 100 50 500 390 99 Toxicroak 83 106 65 86 65 85 490 389 100 Bronzong 67 89 116 79 116 33 500 388 101 Cradily 86 81 97 81 107 43 495 387 102 Ampharos 90 75 75 115 90 55 500 386 102 Slowking 95 75 80 100 110 30 490 386 104 Ursaring 90 130 75 75 75 55 500 385 105 Poliwrath 90 85 95 70 90 70 500 383 105 Tentacruel 80 70 65 80 120 100 515 383 105 Abomasnow 90 92 75 92 85 60 494 383 105 Weavile 70 120 65 45 85 125 510 383 109 Ninetales 73 76 75 81 100 100 505 382 109 Politoed 90 75 75 90 100 70 500 382 111 Heracross 80 125 75 40 95 85 500 381 111 Probopass 60 55 145 75 150 40 525 381 113 Nidoqueen 90 82 87 75 85 76 495 376 113 Gliscor 75 95 125 45 75 95 510 376 115 Kangaskhan 105 95 80 40 80 90 490 374 115 Exploud 104 91 63 91 63 68 480 374 117 Honchkrow 100 125 52 105 52 71 505 372 117 Armaldo 75 125 100 70 80 45 495 372 119 Kabutops 60 115 105 65 70 80 495 370 119 Shiftry 90 100 60 90 60 80 480 370 119 Drifblim 150 80 44 90 54 80 498 370 122 Skuntank 103 93 67 71 61 84 479 369 122 Wailord 170 90 45 90 45 60 500 369 124 Houndoom 75 90 50 110 80 95 500 368 125 Drapion 70 90 110 60 75 95 500 367 125 Rampardos 97 165 60 65 50 58 495 367 127 Dusknoir 45 100 135 65 135 45 525 366 127 Roserade 60 70 55 125 105 90 505 366 129 Magmar 65 95 57 100 85 93 495 365 130 Donphan 90 120 120 60 60 50 500 364 131 Mismagius 60 60 60 105 105 105 495 363 132 Miltank 95 80 105 40 70 100 490 362 133 Tauros 75 100 95 40 70 110 490 360 134 Gengar 60 65 60 130 75 110 500 359 134 Electabuzz 65 83 57 95 85 105 490 359 134 Gastrodon 111 83 68 92 82 39 475 359 137 Floatzel 85 105 55 85 50 115 495 358 138 Froslass 70 80 70 80 70 110 480 357 139 Gorebyss 55 84 105 114 75 52 485 356 140 Omastar 70 60 125 115 70 55 495 355 141 Aggron 70 110 180 60 60 50 530 354 141 Octillery 75 105 75 105 75 45 480 354 141 Huntail 55 104 105 94 75 52 485 354 144 Vileplume 75 80 85 100 90 50 480 353 144 Weezing 65 90 120 85 70 60 490 353 144 Relicanth 100 90 130 45 65 55 485 353 147 Victreebel 80 105 65 100 60 70 480 350 147 Altaria 75 70 90 70 105 80 490 350 149 Claydol 60 70 105 70 120 75 500 349 149 Glalie 80 80 80 80 80 80 480 349 149 Phione 80 80 80 80 80 80 480 349 152 Hariyama 144 120 60 40 60 50 474 348 153 Bellossom 75 80 85 90 100 50 480 347 154 Staraptor 85 120 70 50 50 100 475 346 154 Ambipom 75 100 66 60 66 115 482 346 156 Clefable 95 70 73 85 90 60 473 343 156 Manectric 70 75 60 105 60 105 475 343 158 Ludicolo 80 70 70 90 100 70 480 342 158 Swalot 100 73 83 73 83 55 467 342 160 Pidgeot 83 80 75 70 70 91 469 341 160 Spiritomb 50 92 108 92 108 35 485 341 162 Stantler 73 95 62 85 65 85 465 340 163 Xatu 65 75 70 95 70 95 470 339 164 Golem 80 110 130 55 65 45 485 338 164 Rhydon 105 130 120 45 45 40 485 338 164 Whiscash 110 78 73 76 71 60 468 338 167 Dewgong 90 70 80 70 95 70 475 337 167 Hypno 85 73 70 73 115 67 483 337 167 Torkoal 70 85 140 85 70 20 470 337 170 Lopunny 65 76 84 54 96 105 480 336 171 Vespiquen 70 80 102 80 102 40 474 335 172 Raichu 60 90 55 90 80 100 475 333 173 Tropius 99 68 83 72 87 51 460 328 174 Steelix 75 85 200 55 65 30 510 327 175 Bastiodon 60 52 168 47 138 30 495 326 175 Carnivine 74 100 72 90 72 46 454 326 177 Camerupt 70 100 70 105 75 40 460 322 178 Girafarig 70 80 65 90 65 85 455 321 178 Lumineon 69 69 76 69 86 91 460 321 180 Dodrio 60 110 70 60 60 100 460 320 180 Zangoose 73 115 60 60 60 90 458 320 182 Magneton 50 60 95 120 70 70 465 319 183 Primeape 65 105 60 60 70 95 455 318 183 Lanturn 125 58 58 76 76 67 460 318 185 Golbat 75 80 70 65 75 90 455 317 185 Kingler 55 130 115 50 50 75 515 317 185 Crawdaunt 63 120 85 90 55 55 468 317 185 Grumpig 80 45 65 90 110 80 470 317 189 Alakazam 55 50 45 135 85 120 490 314 189 Cloyster 50 95 180 85 45 70 525 314 191 Breloom 60 130 80 60 60 70 460 313 192 Absol 65 130 60 75 60 75 465 312 193 Purugly 71 82 64 64 59 112 452 307 194 Granbull 90 120 75 60 60 45 450 306 194 Seviper 73 100 60 100 60 65 458 306 194 Cherrim 70 60 70 87 78 85 450 306 197 Seaking 80 92 65 65 80 68 450 305 197 Sharpedo 70 120 40 95 40 95 460 305 197 Cacturne 70 115 60 115 60 55 475 305 200 Electrode 60 50 70 80 80 140 480 303 201 Venomoth 70 65 60 90 75 90 450 302 202 Piloswine 100 100 80 60 60 50 450 300 203 Banette 64 115 65 83 63 65 455 295 204 Fearow 65 90 65 61 61 100 442 294 205 Forretress 75 90 140 60 60 40 465 289 205 Skarmory 65 80 140 40 70 70 465 289 205 Rotom 50 50 77 95 77 91 440 289 208 Vigoroth 80 80 80 55 55 90 440 287 209 Persian 65 70 60 65 65 115 440 283 209 Dusclops 40 70 130 60 130 25 455 283 211 Mr. Mime 40 45 65 100 120 90 460 282 212 Jumpluff 75 55 70 55 85 110 450 281 212 Lunatone 70 55 65 95 85 70 440 281 214 Arbok 60 85 69 65 79 80 438 280 214 Hitmonchan 50 105 79 35 110 76 455 280 216 Sandslash 75 100 110 45 55 65 450 279 216 Mantine 65 40 70 80 140 70 465 279 216 Solrock 70 95 85 55 65 70 440 279 219 Hitmonlee 50 120 53 35 110 87 455 278 219 Misdreavus 60 60 60 85 85 85 435 278 221 Quagsire 95 85 85 65 65 35 430 277 222 Hitmontop 50 95 95 35 110 70 455 275 223 Qwilfish 65 95 75 55 55 85 430 273 224 Sunflora 75 75 55 105 85 30 425 272 225 Noctowl 100 50 50 76 96 70 442 268 226 Linoone 78 70 61 50 61 100 420 266 227 Chimecho 65 50 70 95 80 65 425 265 228 Mightyena 70 90 70 60 60 70 420 264 228 Bibarel 79 85 60 55 60 71 410 264 230 Dragonair 61 84 65 70 70 70 420 262 231 Deoxys-A 50 180 20 180 20 150 600 261 232 Pelipper 60 50 100 85 70 65 430 260 232 Gabite 68 90 65 50 55 82 410 260 232 Jynx 65 50 35 115 95 95 455 260 235 Castform 70 70 70 70 70 70 420 259 235 Seadra 55 65 95 95 45 85 440 259 237 Azumarill 100 50 80 50 80 50 410 257 238 Wigglytuff 140 70 45 75 50 45 425 255 239 Pupitar 70 84 70 65 70 51 410 254 240 Furret 85 76 64 45 55 90 415 253 240 Kecleon 60 90 70 60 120 40 440 253 242 Raticate 55 81 60 50 70 97 413 252 243 Dunsparce 100 70 70 65 65 45 415 251 244 Wormadam-S 60 69 95 69 95 36 424 250 244 Tangela 65 55 115 100 40 60 435 250 246 Sneasel 55 95 55 35 75 115 430 249 246 Wormadam-G 60 79 105 59 85 36 424 249 248 Gligar 65 75 105 35 65 85 430 248 249 Wormadam 60 59 85 79 105 36 424 247 250 Marowak 60 80 110 50 80 45 425 246 250 Masquerain 70 60 62 80 82 60 414 246 250 Sealeo 90 60 70 75 70 45 410 246 250 Mothim 70 94 50 94 50 66 424 246 254 Metang 60 75 100 55 80 50 420 245 255 Ivysaur 60 62 63 80 80 60 405 244 255 Shelgon 65 95 100 60 50 50 420 244 257 Munchlax 135 85 40 40 85 5 390 243 258 Machoke 80 100 70 50 60 45 405 242 259 Croconaw 65 80 80 59 63 58 405 241 259 Prinplup 64 66 68 81 76 50 405 241 261 Marshtomp 70 85 70 60 70 50 405 240 261 Illumise 65 47 55 73 75 85 400 240 263 Medicham 60 60 75 60 75 80 410 237 264 Volbeat 65 73 55 47 75 85 400 236 264 Grotle 75 89 85 55 65 36 405 236 266 Charmeleon 58 64 58 80 65 80 405 235 266 Quilava 58 64 58 80 65 80 405 235 268 Murkrow 60 85 42 85 42 91 405 233 269 Gloom 60 65 70 85 75 40 395 231 269 Sudowoodo 70 100 115 30 65 30 410 231 269 Swellow 60 85 60 50 50 125 430 231 269 Minun 60 40 50 75 85 95 405 231 273 Parasect 60 95 80 60 80 30 405 230 274 Ariados 70 90 70 60 60 40 390 229 274 Combusken 60 85 60 85 60 55 405 229 276 Porygon 65 60 70 85 75 40 395 227 277 Haunter 45 50 45 115 55 95 405 226 277 Wailmer 130 70 35 70 35 60 400 226 279 Wartortle 59 63 80 65 80 58 405 225 279 Monferno 64 78 52 78 52 81 405 225 279 Chatot 76 65 45 92 42 91 411 225 282 Bayleef 60 62 80 63 80 60 405 222 283 Ponyta 50 85 55 65 65 90 410 221 283 Lairon 60 90 140 50 50 40 430 221 285 Lickitung 90 55 75 60 75 30 385 219 286 Togetic 55 40 85 80 105 40 405 218 286 Magcargo 50 50 120 80 80 30 410 218 286 Kricketune 75 85 51 55 51 65 382 218 289 Kadabra 40 35 30 120 70 105 400 215 290 Delcatty 70 65 65 55 55 70 380 214 291 Sableye 50 75 75 65 65 50 380 213 292 Butterfree 60 45 50 80 80 70 385 212 293 Ninjask 61 90 45 50 50 160 456 211 293 Plusle 60 50 40 85 75 95 405 211 295 Wobbuffet 190 33 58 33 58 33 405 210 295 Grovyle 50 65 45 85 65 95 405 210 295 Mawile 50 85 85 55 55 50 380 210 298 Poliwhirl 65 65 65 50 50 90 385 209 299 Pachirisu 60 45 70 45 90 95 405 208 300 Blissey 255 10 10 75 135 55 540 206 301 Beedrill 65 80 40 45 80 75 385 201 301 Roselia 50 60 45 100 80 65 400 201 303 Flaaffy 70 55 55 80 60 45 365 198 304 Nidorina 70 62 67 55 55 56 365 197 304 Corsola 55 55 85 65 85 35 380 197 304 Beautifly 60 70 50 90 50 65 385 197 307 Graveler 55 95 115 45 45 35 390 194 308 Yanma 65 65 45 75 45 95 390 194 308 Dustox 60 50 70 50 90 65 385 194 310 Ledian 55 35 50 55 110 85 390 193 311 Dugtrio 35 80 50 50 70 120 405 190 312 Weepinbell 65 90 50 85 45 55 390 189 313 Nidorino 61 72 57 55 55 65 365 186 314 Spinda 60 60 60 60 60 60 360 185 315 Magby 45 75 37 70 55 83 365 183 315 Loudred 84 71 43 71 43 48 360 183 315 Lileep 66 41 77 61 87 23 355 183 318 Aipom 55 70 55 40 55 85 360 180 319 Pidgeotto 63 60 55 50 50 71 349 176 320 Luxio 60 85 49 60 49 60 363 175 321 Farfetch'd 52 65 55 58 62 60 352 168 321 Anorith 45 95 50 40 50 75 355 168 323 Elekid 45 63 37 65 55 95 360 166 324 Drifloon 90 50 34 60 44 70 348 165 325 Lombre 60 50 50 60 70 50 340 164 326 Buneary 55 66 44 44 56 85 350 163 327 Skiploom 55 45 50 45 65 80 340 162 328 Chinchou 75 38 38 56 56 67 330 159 329 Omanyte 35 40 100 90 55 35 355 155 329 Nosepass 30 45 135 45 90 30 375 155 331 Finneon 49 49 56 49 61 66 330 154 332 Growlithe 55 70 45 70 50 60 350 152 333 Vibrava 50 70 50 50 50 70 340 149 333 Snover 60 62 50 62 60 40 334 149 335 Staravia 55 75 50 40 40 80 340 148 336 Eevee 55 55 50 45 65 55 325 147 336 Teddiursa 60 80 50 50 50 40 330 147 338 Grimer 80 80 50 40 50 25 325 146 339 Seel 65 45 55 45 70 45 325 145 339 Nuzleaf 70 70 40 60 40 60 340 145 339 Clamperl 35 64 85 74 55 32 345 145 342 Kabuto 30 80 90 55 45 55 355 143 343 Cranidos 67 125 40 30 30 58 350 142 343 Stunky 63 63 47 41 41 74 329 142 345 Gastly 30 35 30 100 35 80 310 141 345 Staryu 30 45 55 70 55 85 340 141 345 Phanpy 90 60 60 40 40 40 330 141 345 Hippopotas 68 72 78 38 42 32 330 141 349 Shellos 76 48 48 57 62 34 325 139 350 Clefairy 70 45 48 60 65 35 323 138 350 Delibird 45 55 45 65 45 75 330 138 352 Chikorita 45 49 65 49 65 45 318 137 352 Buizel 55 65 35 60 30 85 330 137 354 Drowzee 60 48 45 43 90 42 328 136 354 Koffing 40 65 95 60 45 35 340 136 356 Squirtle 44 48 65 50 64 43 314 135 356 Unown 48 72 48 72 48 48 336 135 358 Rhyhorn 80 85 95 30 30 25 345 134 358 Houndour 45 60 30 80 50 65 330 134 358 Spoink 60 25 35 70 80 60 330 134 358 Turtwig 55 68 64 45 55 31 318 134 362 Goldeen 45 67 60 35 50 63 320 133 363 Slowpoke 90 65 65 40 40 15 315 132 364 Exeggcute 60 40 80 60 45 40 325 129 365 Mantyke 45 20 50 60 120 50 345 128 366 Venonat 60 55 50 40 55 45 305 127 366 Onix 35 45 160 30 45 70 385 127 366 Totodile 50 65 64 44 48 43 314 127 366 Piplup 53 51 53 61 56 40 314 127 366 Skorupi 40 50 90 30 55 65 330 127 371 Psyduck 50 52 48 65 50 55 320 125 372 Natu 40 50 45 70 45 70 320 124 373 Bulbasaur 45 49 49 65 65 45 318 122 373 Shieldon 30 42 118 42 88 30 350 122 375 Oddish 45 50 55 75 65 30 320 121 375 Doduo 35 85 45 35 35 75 310 121 375 Aron 50 70 100 40 40 30 330 121 378 Magnemite 25 35 70 95 55 45 325 115 379 Tentacool 40 40 35 50 100 70 335 113 379 Voltorb 40 30 50 55 55 100 330 113 381 Shuckle 20 10 230 10 230 5 505 112 382 Remoraid 35 65 35 65 35 65 300 111 382 Gulpin 70 43 53 43 53 40 302 111 382 Luvdisc 43 30 55 40 65 97 330 111 385 Cubone 50 50 95 40 50 35 320 110 385 Treecko 40 45 35 65 55 70 310 110 385 Swablu 45 40 60 40 75 50 310 110 388 Carvanha 45 90 20 65 20 65 305 109 389 Charmander 39 52 43 60 50 65 309 107 389 Cyndaquil 39 52 43 60 50 65 309 107 389 Chimchar 44 58 44 58 44 61 309 107 392 Mudkip 50 70 50 50 50 40 310 106 393 Pikachu 35 55 30 50 40 90 300 104 393 Machop 70 80 50 35 35 35 305 104 393 Gible 58 70 45 40 45 42 300 104 396 Snorunt 50 50 50 50 50 50 300 103 397 Larvitar 50 64 50 45 50 41 300 102 398 Mankey 40 80 35 35 45 70 305 101 398 Torchic 45 60 40 70 50 45 310 101 400 Baltoy 40 40 55 40 70 55 300 98 401 Spheal 70 40 50 55 50 25 290 97 401 Glameow 49 55 42 42 37 85 310 97 403 Abra 25 20 15 105 55 90 310 96 403 Dratini 41 64 45 50 50 50 300 96 403 Snubbull 60 80 50 40 40 30 300 96 406 Cacnea 50 85 40 85 40 35 335 95 406 Croagunk 48 61 40 61 40 50 300 95 408 Smoochum 45 30 15 85 65 65 305 94 408 Numel 60 60 40 65 45 35 305 94 410 Shroomish 60 40 60 40 60 35 295 93 410 Electrike 40 45 40 65 40 65 295 93 412 Beldum 40 55 80 35 60 30 300 92 413 Ditto 48 48 48 48 48 48 288 91 414 Vulpix 38 41 40 50 65 65 299 88 415 Barboach 50 48 43 46 41 60 288 86 416 Bonsly 50 80 95 10 45 10 290 85 417 Krabby 30 105 90 25 25 50 325 84 417 Corphish 43 80 65 50 35 35 308 84 419 Bagon 45 75 60 40 30 50 300 83 420 Horsea 30 40 70 70 25 60 295 82 421 Pineco 50 65 90 35 35 15 290 80 421 Chingling 45 30 50 65 50 45 285 80 421 Bronzor 57 24 86 24 86 23 300 80 424 Sandshrew 50 75 85 20 30 40 300 79 424 Poliwag 40 50 40 40 40 90 300 79 424 Mime Jr. 20 25 45 70 90 60 310 79 427 Ekans 35 60 44 40 54 55 288 77 427 Slakoth 60 60 60 35 35 30 280 77 427 Shuppet 44 75 35 63 33 45 295 77 430 Mareep 55 40 40 65 45 35 280 76 430 Trapinch 45 100 45 45 45 10 290 76 432 Paras 35 70 55 45 55 25 285 74 432 Riolu 40 70 40 35 40 60 285 74 434 Nidoran(f) 55 47 52 40 40 41 275 72 434 Geodude 40 80 100 30 30 20 300 72 436 Bellsprout 50 75 35 70 30 40 300 71 437 Chansey 250 5 5 35 105 50 450 70 438 Meowth 40 45 35 40 40 90 290 67 438 Meditite 30 40 55 40 55 60 280 67 440 Cherubi 45 35 45 62 53 35 275 66 441 Spearow 40 60 30 31 31 70 262 63 442 Budew 40 30 35 50 70 55 280 62 443 Nidoran(m) 46 57 40 40 40 50 273 59 443 Shellder 30 65 100 45 25 40 305 59 443 Kirlia 38 35 35 65 55 50 278 59 446 Diglett 10 55 25 35 45 95 265 58 447 Duskull 20 40 90 30 90 25 295 57 448 Taillow 40 55 30 30 30 85 270 56 448 Wingull 40 30 30 55 30 85 270 56 450 Wynaut 95 23 48 23 48 23 260 51 450 Bidoof 59 45 40 35 40 31 250 51 452 Shinx 45 65 34 40 34 45 263 50 453 Surskit 40 30 32 50 52 65 269 49 454 Skitty 50 45 45 35 35 50 260 48 455 Rattata 30 56 35 25 35 72 253 47 455 Jigglypuff 115 45 20 45 25 20 270 47 457 Hoothoot 60 30 30 36 56 50 262 43 458 Pidgey 40 45 40 35 35 56 251 42 459 Spinarak 40 60 40 40 40 30 250 41 460 Swinub 50 50 40 30 30 50 250 38 460 Nincada 31 45 90 30 30 40 266 38 462 Ledyba 40 20 30 40 80 55 265 37 462 Starly 40 55 30 30 30 60 245 37 464 Togepi 35 20 65 40 65 20 245 35 465 Hoppip 35 35 40 35 55 50 250 34 466 Marill 70 20 50 20 50 40 250 33 466 Slugma 40 40 40 70 40 20 250 33 466 Makuhita 72 60 30 20 30 25 237 33 469 Zubat 40 45 35 30 40 55 245 32 469 Whismur 64 51 23 51 23 28 240 32 471 Burmy 40 29 45 29 45 36 224 31 472 Combee 30 30 42 30 42 70 244 30 473 Smeargle 55 20 35 20 45 75 250 29 473 Zigzagoon 38 30 41 30 41 60 240 29 475 Poochyena 35 55 35 30 30 35 220 22 476 Seedot 40 40 50 30 30 30 220 21 477 Sentret 35 46 34 35 45 20 215 20 477 Lotad 40 30 30 40 50 30 220 20 479 Pichu 20 40 15 35 35 60 205 18 480 Cleffa 50 25 28 45 55 15 218 17 481 Tyrogue 35 35 35 35 35 35 210 16 482 Kakuna 45 25 50 25 25 35 205 15 482 Silcoon 50 35 55 25 25 15 205 15 482 Cascoon 50 35 55 25 25 15 205 15 482 Kricketot 37 25 41 25 41 25 194 15 486 Metapod 50 20 55 25 25 30 205 14 487 Wooper 55 45 45 25 25 15 210 13 487 Ralts 28 25 25 45 35 40 198 13 489 Caterpie 45 30 35 20 20 45 195 11 490 Wurmple 45 45 35 20 30 20 195 10 491 Weedle 40 35 30 20 20 50 195 8 491 Igglybuff 90 30 15 40 20 15 210 8 493 Azurill 50 20 40 20 40 20 190 7 494 Sunkern 30 30 30 30 30 30 180 5 495 Feebas 20 15 20 10 55 80 200 2 495 Happiny 100 5 5 15 65 30 220 2 497 Magikarp 20 10 55 15 20 80 200 1 498 Shedinja 1 90 45 30 30 40 236 0 Arceus' rating is 497, meaning that it 'wins' against 497 of the 498 Pokemon (the only Pokemon it doesn't 'win' against is Arceus itself). At the other end of the list, Shedinja's rating is 0, meaning that it 'wins' against none of the 498 Pokemon. Note that the stats I used in the formulae above are those of the Pokemon at Level 100 with no EVs, to be fair for all Pokemon. So there you have it: all the Pokemon's base stats rated. From here, I'm going to use this as a basis to consider typing and movepools as well, to give a much better overall rating of a Pokemon. So that's the practical application of this, if you were wondering. Thanks for reading, and sorry for the length of this post.
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http://users.smogon.com/X-Act For all your Pokemon needs (and more!) including: the Defensive EVs applet, the Probabilities of Breeding IVs in Pokemon applet, and the Ratings of Pokemon Base Stats applet (now Version 2.0!). And also the IV to PID applet! Last edited by X-Act; Mar 20th, 2008 at 6:14:10 AM. |
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Feb 19th, 2008, 12:42:08 PM
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#2 |
Join Date: Jan 2005
Posts: 632
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Fuck badges, you deserve a frikkin halo
Edit: Lol, Sunflora > Deoxys-A
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Not cool enough for a signature Last edited by Grawl; Feb 19th, 2008 at 12:53:07 PM. |
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Feb 19th, 2008, 12:47:23 PM
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#3 |
Join Date: Nov 2007
Posts: 167
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poor regigigas :(
From a quick glance, garchomp at #12 may just further the garchomp for uber discussion! |
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Feb 19th, 2008, 1:00:15 PM
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#4 |
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Join Date: Aug 2007
Posts: 3
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Very interesting. Deoxys-S and Shinx aren't lined up, by the way.
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~ Iggy Koopa |
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Feb 19th, 2008, 1:01:15 PM
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#5 |
Join Date: Jul 2007
Posts: 935
Granada, Spain
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Great analysis, this one. As a raw measure of stats, I think this is the closer to an objective way of ranking pokémon there is.
Of course, as you mentioned, movepool, abilities, EV spreads and typing have to be taken into account, but I think that at least, typing and movepool can be implemented into this. Typing is obvious, but I don't think the movepool could be integrated in such a mathematically elegant way. Rather, a compilation of the different movesets, their frequency in the metagame, and the moves of each one would have to be gathered, and then integrated in the calculations basically by hand. While tedious, if someone could do that, the accuracy of this would be incredible (while still not being definite, of course).
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D/P FC: 2749 8421 3675 |
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Feb 19th, 2008, 1:07:31 PM
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#6 |
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Join Date: Sep 2007
Posts: 261
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I think abilities and typing would be easiest to implement...where STAB could function as an advantage using how effective it is against all possible type combinations, and typing provides a disadvantage depending on the strength of its weaknesses. Basically, the "better" a type is that you're weak against, the more it counts against you (like an Ice weak would be much worse than a Poison weak, for example).
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Feb 19th, 2008, 1:35:11 PM
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#7 |
Join Date: Nov 2007
Posts: 376
Portsmouth, UK
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Great guide X-act, youi must have put a lot of workinto that!
Typing shouldn't be too hard to implement, you would need to give a value to each type depending on how common it is though, because having super effective STAB on something common like normal or Flying, is much better than having super effective stab on something like Bug
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No hope, or love, or glory Happy endings gone forever more |
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Feb 19th, 2008, 1:43:43 PM
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#8 |
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pfbwowbfobwobwobfwowbf
     
Administrator
Join Date: Feb 2005
Posts: 13,835
Most of them are good
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A great start (or actually continuation, after your type rating system), I really like your "balancing Pokemon" project and the maths behind it, as far as I can understand it. Looking forward to the final result and the rest of the process.
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Feb 19th, 2008, 1:51:06 PM
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#9 | |
Join Date: Jun 2007
Posts: 1,762
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Quote:
I wouldn't put too much weight onto this list right away, but I do like the maths you've done to set up this list. Great job. I hope for the moveset project to work out.
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Defense Tiers and Attack Tiers -- SkarmCents and BlissCents --- Minor Works --- Enlarged Avatar |
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Feb 19th, 2008, 1:52:07 PM
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#10 |
Join Date: May 2006
Posts: 1,855
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I don't really understand the maths part.... but the chart is impressive. I really wanna see the final result of this.
Edit: I think the types and traits have to be inputted before it actually starts looking correct. I mean, Shedinja is obviously not below Magikarp. Edit: I'm surprised Happiny only beats Magikarp/Shedinja... i thought it would be better then that.
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<+Raikage> 'what the hell is a recoome' <+Raikage> 'and a burter' Last edited by Amelia; Feb 19th, 2008 at 1:54:19 PM. |
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Feb 19th, 2008, 1:55:58 PM
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#11 |
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Join Date: Jun 2007
Posts: 361
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Garchomp has the same Rating as Groudon, and better than Latios and every single OU (except Regigigas and Slaking for obvious reasons). I think that it must be revised Garchomp's tier...
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Feb 19th, 2008, 2:11:59 PM
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#12 |
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Join Date: Dec 2007
Posts: 1,498
where have i been
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For some reason I thought Seaking was right below Lugia.
Haha, anyway, yet another great guide, X-Act! |
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Feb 19th, 2008, 2:14:11 PM
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#13 |
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It's only after we've lost everything that we're free to do anything.
   
Super Moderator
Join Date: Jan 2008
Posts: 3,229
Home: Goshen Scout Reservation
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Where is the one that rates types? I would much like to read that one also
Edit: Found it: http://www.smogon.com/forums/showthread.php?t=35651
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Alder: N, even if we don't understand each other, that's not a reason to reject each other. There are two sides to an argument. Is there one point of view that has all the answers? Give it some thought. 
Last edited by RBG; Feb 19th, 2008 at 5:28:59 PM. Reason: Found it |
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Feb 19th, 2008, 2:19:33 PM
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#14 |
Join Date: Dec 2007
Posts: 64
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Blissey @ 300. :D
Good work, though some stats are underrated. There are some huge gaps in stats like HP/DA/SpD that don't get enough rating for their worth. Blissey's HP, Shuckle's DA/SpD to name obvious examples. You need some sort of a weighed list of this. |
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Feb 19th, 2008, 2:21:53 PM
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#15 |
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Join Date: Jun 2007
Posts: 1,762
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Yeah, upon closer inspection a lot of things don't make sense. I really like the method, but I feel I should point these out...
1. Scyther (92 ) > Scizor (93) on this list. 2. Charizard > Infernape 3. Garchomp == Groudon 4. Golbat > Alakazam 5. Stanler > Breloom 6. Lopunny > Deoxys-A 7. Pinsir > Heracross 8. Deoxys-S > Deoxys-A etc. etc. I understand what this chart is saying, but clearly there are a ton of errors here. Deoxys-A should not be ranked lower than Lopunny, Scyther is clearly worse than Scizor in OU, Alakazam is certainly better than Golbat, etc. etc.
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Defense Tiers and Attack Tiers -- SkarmCents and BlissCents --- Minor Works --- Enlarged Avatar |
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Feb 19th, 2008, 2:25:20 PM
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#16 |
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Join Date: Jul 2007
Posts: 935
Granada, Spain
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By the way, now that I remember it, I wouldn't weight equally both the Special Attack and the Attack for each pokémon. I know that, as a mathematician, you want a single, elegant formula to describe all, but I think that the fact that most pokémon attack primarily with either physical attacks or special attacks should be taken into account.
A simple weighting in the form of a multiplier equal to the base stat could work, to give more importance to one stat or the other. So, instead of using: Damage_i,j = (0.42 x MovePower / HP_j) x (Atk_i / Def_j + SpA_i / SpD_j) I propose using the following: Damage_i,j = (0.42 x MovePower / HP_j) x (Atk_i x B_Atk/ Def_j + SpA_i x B_SAtk/ SpD_j)/(B_Atk + B_SAtk) Where B_Atk and B_SAtk are the base Attack and Special Attack stats, respectively. Both stats are taken into account, but, for example, Weavile, Gyarados, Machamp or Heracross don't get dragged down by their abysmal SAtk stats, and Gengar, Alakhazam, Gardevoir & CO aren't rated lower because of their pitiful Atk.
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D/P FC: 2749 8421 3675 |
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Feb 19th, 2008, 2:45:31 PM
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#17 |
Join Date: Dec 2007
Posts: 176
Flatland
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Hello,
Good application of Mathematics. You'd get an "A" in my course. do you have a practical example of when Win_i,j=0 and Win_j,i=0? I'd imagine that you'd have to have HD_i,j=0 and Spe_i=Spe_j, right? |
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Feb 19th, 2008, 4:13:33 PM
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#18 | |
Join Date: May 2006
Posts: 923
Obey Henry
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I love where this idea is going, and loved the chart, until i realised, and then saw, this:
Quote:
But awesome work and application of mathematics.
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derp |
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Feb 19th, 2008, 4:27:33 PM
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#19 |
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Bum bum bum bum
Moderator
Join Date: May 2007
Posts: 2,125
#nuggetbridge
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Cresselia has a base stat speed of 85.
Edit: There are more stat errors. Last edited by sandman; Feb 19th, 2008 at 4:29:40 PM. |
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Feb 19th, 2008, 4:33:03 PM
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#20 |
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The pizza doesn't scream in the oven! LOL!
      
Join Date: Feb 2005
Posts: 8,336
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Since when did base stats totals ever mattered
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Feb 19th, 2008, 4:40:17 PM
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#21 |
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np: Biffy Clyro - Shock Shock
Join Date: Feb 2006
Posts: 4,679
Malta
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Okay, to answer a few questions.
This should not be compared to OU in any way. This is just a way to compare base stats together. The fact that Pinsir is higher up the list than Heracross does not mean that Pinsir is a better Pokemon than Heracross. It means that Pinsir's base stats are better than Heracross. Hell, Regigigas is #4 in the list but it's barely used! Being #4 just means that its base stats are the fourth best of anything. That's all. And yes, Scyther's stats are better than Scizor's. :) In the same way, the position of Garchomp, or any other Pokemon for that matter says only how that Pokemon's base stats compare with the others. Garchomp's base stats are as good as Groudon's, but does that make it as good as Groudon? I don't know, and this chart doesn't answer that question. Don't use this chart as proof that Pokemon X should be in tier Y. It wasn't constructed for that purpose, AND it doesn't suggest anything like that in the first place. To Dr.Traveler, yes there are instances when Win_i,j=0 and Win_j,i=0 and i is not equal to j. For example, if Pokemon #i is Snorlax and Pokemon #j is Slowbro, then Win_i,j=0 and Win_j,i=0. Snorlax doesn't beat Slowbro but Slowbro doesn't beat Snorlax either. This happens because Snorlax and Slowbro have the same base Speed. In fact, if Win_i,j=0 and Spe_i > Spe_j, then Win_j,i = 1. Oh, to conclude, maybe people took this wrongly because I used the words 'win', 'beat', 'hits', etc. These, I admit, are misleading terms, and maybe I shouldn't have used them. All I'm doing is comparing base stats, not actually battling out Pokemon against each other to see who wins! EDIT: sandman, I'd appreciate if you tell me of any other errors in the base stats that you encounter, so that I fix the list. EDIT2: Time Mage, I'll repeat again: I'm comparing base stats, and that means that using the same move power for Atk and SpA is the way to go. When I compare Pokemon with their typing and movepools, then of course that would change.
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http://users.smogon.com/X-Act For all your Pokemon needs (and more!) including: the Defensive EVs applet, the Probabilities of Breeding IVs in Pokemon applet, and the Ratings of Pokemon Base Stats applet (now Version 2.0!). And also the IV to PID applet! Last edited by X-Act; Feb 19th, 2008 at 4:47:13 PM. |
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Feb 19th, 2008, 4:42:14 PM
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#22 |
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The pizza doesn't scream in the oven! LOL!
Join Date: Feb 2005
Posts: 8,336
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Couldn't we already just look at the base stats to see who has the higher total without all this extra math?
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Feb 19th, 2008, 4:45:50 PM
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#23 | |
Join Date: Aug 2007
Posts: 1,971
My Soul, Your Beats!
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Quote:
(see Voltorb > Shuckle)
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Creator of the DPP Pokemon Resource, the one thing no Trainer should be without! (eventually... maybe) My YouTube Channel My Blog (VERY, VERY small, ATM) |
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Feb 19th, 2008, 4:48:46 PM
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#24 | |
Join Date: Oct 2007
Posts: 769
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So that would mean that Syther's high base Speed and Attack is more valuable than Scizor's Defense by letting it get in more hits, whereas Blissey's pathetic defense and attack totally drag Blissey down. Given that ev'ing close to doubles Blissey's defense, that makes a lot of sense, looking at only Base Stats. I imagine that Deoxys-A's low score comes from the fact that without EV's or natures Deoxys can't OHKO quite a few things that EV's and nature lets him.
That seem right?
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<Jackal> who is jenigmat429 <Jackal> i like him Suspect Free Warstory Context can be important: Quote:
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Feb 19th, 2008, 4:51:50 PM
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#25 | |
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The pizza doesn't scream in the oven! LOL!
Join Date: Feb 2005
Posts: 8,336
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Quote:
Sorry to be a downer about this whole thing. |
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