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# Analysis of Base Stats

Discussion in 'Pokémetrics' started by X-Act, Feb 19, 2008.

1. ### X-Actnp: Biffy Clyro - Shock Shock

Joined:
Feb 17, 2006
Messages:
4,675
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```
Besides obviously listing the stats of each Pokemon, the list above also contains the Base Stat Total (BST) before the rating, for comparison purposes.

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.
2. ### Grawl

Joined:
Jan 12, 2005
Messages:
631
Fuck badges, you deserve a frikkin halo

Edit: Lol, Sunflora > Deoxys-A
3. ### dirtybirdy

Joined:
Nov 21, 2007
Messages:
167
poor regigigas :(

From a quick glance, garchomp at #12 may just further the garchomp for uber discussion!
4. ### Iggy Koopa

Joined:
Aug 14, 2007
Messages:
3
Very interesting. Deoxys-S and Shinx aren't lined up, by the way.
5. ### Time Mage

Joined:
Jul 27, 2007
Messages:
1,006
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).
6. ### scorchedsky

Joined:
Sep 18, 2007
Messages:
261
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).
7. ### Captain Falcon

Joined:
Nov 12, 2007
Messages:
376
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
8. ### MekkahSuper Moderator

Joined:
Feb 8, 2005
Messages:
14,213
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.
9. ### Dragontamer

Joined:
Jun 9, 2007
Messages:
2,068
IMO, great job as well. This is clearly a better system than BST, although movesets and movepools need to be considered. Nonetheless, there are a few things that go against my intuition. Walrein is IMO good, but higher than PorygonZ and Gyarados?

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.
10. ### Amelia

Joined:
May 18, 2006
Messages:
1,848
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.
11. ### Trust

Joined:
Jun 24, 2007
Messages:
361
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...
12. ### Chronos

Joined:
Dec 5, 2007
Messages:
1,498
For some reason I thought Seaking was right below Lugia.
Haha, anyway, yet another great guide, X-Act!

Joined:
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3,399
14. ### Kindred

Joined:
Dec 26, 2007
Messages:
64
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.
15. ### Dragontamer

Joined:
Jun 9, 2007
Messages:
2,068
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.
16. ### Time Mage

Joined:
Jul 27, 2007
Messages:
1,006
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.

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.
17. ### Dr.Traveler

Joined:
Dec 4, 2007
Messages:
176
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?
18. ### Vampy34

Joined:
May 29, 2006
Messages:
923
I love where this idea is going, and loved the chart, until i realised, and then saw, this:

I swear to god, this made me angry.

But awesome work and application of mathematics.
19. ### sandmanBum bum bum bum

Joined:
May 11, 2007
Messages:
2,123
Cresselia has a base stat speed of 85.

Edit: There are more stat errors.
20. ### AeroblacktylThe pizza doesn't scream in the oven! LOL!

Joined:
Feb 19, 2005
Messages:
8,336
Since when did base stats totals ever mattered
21. ### X-Actnp: Biffy Clyro - Shock Shock

Joined:
Feb 17, 2006
Messages:
4,675
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.
22. ### AeroblacktylThe pizza doesn't scream in the oven! LOL!

Joined:
Feb 19, 2005
Messages:
8,336
Couldn't we already just look at the base stats to see who has the higher total without all this extra math?
23. ### CardsOfTheHeart

Joined:
Aug 21, 2007
Messages:
1,970
BSTs don't tell the whole story. Stat distribution matters, too.
(see Voltorb > Shuckle)
24. ### Jenigmat

Joined:
Oct 29, 2007
Messages:
769
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?
25. ### AeroblacktylThe pizza doesn't scream in the oven! LOL!

Joined:
Feb 19, 2005
Messages:
8,336
So how does this tell the story any differently?