Pokémon Go

I've been playing Pokémon Go since 2025-03-01, fairly enthusiastically. While there exist useful resources, I found "common wisdom" regarding the game to be lacking rigor. This page started with the question, "how is it that I reliably defeat Team Rocket Pokémon with double my CP, but barely play above 50% in GO Battle League where opposing CPs are roughly equal?" spoiler: CP is an ass metric

I know very little about other Pokémon games or media.

Regarding nomenclature, "PvP" in this document refers to "Trainer Battles", i.e. Team Rocket, friends, Team Leaders, and the GO Battle League, even though Team Rocket and Team Leaders are AI. "PvE" refers to raids and Max battles only.

Fucking with the APK

The APK can be downloaded from APKMirror and analyzed with e.g. Apktool.

Important content includes (in base/assets/):

• the plaintext, key-value text/i18n_en-us.json (salt for your language)
• the binary bin/Data/Managed/Metadata/global-metadata.dat

On-device

• Android/data/com.nianticlabs.pokemongo/files/il2cpp/Metadata/global-metadata.dat (salt for your OS)
  • il2cpp indicates Unity stuff fwiw

Essential constants

Distribution of ATK by species

Distribution of DEF by species

Distribution of STA by species

CPM

CP multipliers are defined at increments of 0.5 for all Levels 1 through 50 (plus a few more), constant across all species and stats. Powering up a Pokémon increases its Level by 0.5. The half-level is L * 2 - 1, i.e. Level 3 is half-level 5. This suggests 99 constants (but the bitch ain't one). A Trainer's Pokémon cannot exceed the Trainer's Level plus 10.

CPMs range from 0.094 to 0.8403. Non-integer Levels are always defined using the quadratic mean (root of mean of squares): CPM(L + 0.5) = √((CPM(L)² + CPM(L + 1)²) / 2), getting us down to 50 constants.

There are five regimes of growth: 1–9.5, 10–19.5, 20–29.5, 30–39.5, and 40+. Beginning at Level 40, CPM growth becomes linear: 0.7903 (40), 0.8103 (44), 0.8303 (48), 0.8403 (50). So CPM is perfectly fit for integral Levels 40+ by the function 0.01 * (L - 40) / 2 + 0.7903. We can define all 99 half-level CPMs recursively in O(n) time and O(1) space using seven floating-point and six integer constants:

float nextcpm(float cpm, float step){
  return sqrt(power(cpm, 2) + step);
}

// halflevel: positive integer (usually less than 100) equal to L * 2 - 1
float cpm(int halflevel){
  if(halflevel >= 79){ // Levels 40 and above are computed directly
    return 0.0025 * (halflevel - 39) + 0.7903;
  }else if(halflevel >= 59){ // Levels 30..39.5
    step = 0.00445946079;
  }else if(halflevel >= 39){ // Levels 20..29.5
    step = 0.008924905903;
  }else if(halflevel >= 19){ // Levels 10..19.5
    step = 0.008919025675;
  }else if(halflevel > 1){ // Levels 1.5..9.5
    step = 0.009426125469;
  }else{
    return 0.094; // Level 1 (or invalid low value)
  }
  return nextcpm(cpm(halflevel - 1), step);
}

Should we feel so motivated, we can fit a second degree polynomial to the lower levels with reasonable accuracy, underpredicting early and overpredicting late:

Increasing Level has a cost in Stardust and XL Candy. The XL Candy cost is 0 until Level 40.5, at which point it costs 10 to power up to 41, up to 20 to power up from 49.5 to 50. The total cost from Levels 40 to 50 is 250k Stardust and 296 XL Candy.

CPM constants (Data sourced from Gamepress 2025-05-11)

Level	CPM	Stardust requirement
1	0.094	200
1.5	0.1351374318	200
2	0.16639787	200
2.5	0.192650919	200
3	0.21573247	400
3.5	0.2365726613	400
4	0.25572005	400
4.5	0.2735303812	400
5	0.29024988	600
5.5	0.3060573775	600
6	0.3210876	600
6.5	0.3354450362	600
7	0.34921268	800
7.5	0.3624577511	800
8	0.3752356	800
8.5	0.387592416	800
9	0.39956728	1000
9.5	0.4111935514	1000
10	0.4225	1000
10.5	0.4329264091	1000
11	0.44310755	1300
11.5	0.4530599591	1300
12	0.4627984	1300
12.5	0.472336093	1300
13	0.48168495	1600
13.5	0.4908558003	1600
14	0.49985844	1600
14.5	0.508701765	1600
15	0.51739395	1900
15.5	0.5259425113	1900
16	0.5343543	1900
16.5	0.5426357375	1900
17	0.5507927	2200
17.5	0.5588305862	2200
18	0.5667545	2200
18.5	0.5745691333	2200
19	0.5822789	2500
19.5	0.5898879072	2500
20	0.5974	2500
20.5	0.6048236651	2500
21	0.6121573	3000
21.5	0.6194041216	3000
22	0.6265671	3000
22.5	0.6336491432	3000
23	0.64065295	3500
23.5	0.6475809666	3500
24	0.65443563	3500
24.5	0.6612192524	3500
25	0.667934	4000
25.5	0.6745818959	4000
26	0.6811649	4000
26.5	0.6876849038	4000
27	0.69414365	4500
27.5	0.70054287	4500
28	0.7068842	4500
28.5	0.7131691091	4500
29	0.7193991	5000
29.5	0.7255756136	5000
30	0.7317	5000
30.5	0.7347410093	5000
31	0.7377695	6000
31.5	0.7407855938	6000
32	0.74378943	6000
32.5	0.7467812109	6000
33	0.74976104	7000
33.5	0.7527290867	7000
34	0.7556855	7000
34.5	0.7586303683	7000
35	0.76156384	8000
35.5	0.7644860647	8000
36	0.76739717	8000
36.5	0.7702972656	8000
37	0.7731865	9000
37.5	0.7760649616	9000
38	0.77893275	9000
38.5	0.7817900548	9000
39	0.784637	10000
39.5	0.7874736075	10000
40	0.7903	10000
40.5	0.7928	10000
41	0.7953	11000
41.5	0.7978	11000
42	0.8003	11000
42.5	0.8028	11000
43	0.8053	12000
43.5	0.8078	12000
44	0.8103	12000
44.5	0.8128	12000
45	0.8153	13000
45.5	0.8178	13000
46	0.8203	13000
46.5	0.8228	13000
47	0.8253	14000
47.5	0.8278	14000
48	0.8303	14000
48.5	0.8328	14000
49	0.8353	15000
49.5	0.8378	15000
50	0.8403
50.5	0.8428
51	0.8453

Base stats

Additionally, each Pokémon species has three base stats:

• Attack (ATK): 17 (Shuckle) to 414 (Deoxys (Attack Forme))
• Defense (DEF): 32 (Igglybuff) to 396 (Shuckle again)
• Stamina (STA): 1 (Shedinja) to 496 (Blissey)

FIXME: add type and cost to evolve to this database

Species base stats

Pokédex entry	Species	STA	ATK	DEF
0001	Bulbasaur	128	118	111
0002	Ivysaur	155	151	143
0003	Venusaur	190	198	189
0003	Mega Venusaur	190	241	246
0004	Charmander	118	116	93
0005	Charmeleon	151	158	126
0006	Charizard	186	223	173
0006	Mega Charizard X	186	273	213
0006	Mega Charizard Y	186	319	212
0007	Squirtle	127	94	121
0008	Wartortle	153	126	155
0009	Blastoise	188	171	207
0009	Mega Blastoise	188	264	237
0010	Caterpie	128	55	55
0011	Metapod	137	45	80
0012	Butterfree	155	167	137
0013	Weedle	120	63	50
0014	Kakuna	128	46	75
0015	Beedrill	163	169	130
0015	Mega Beedrill	163	303	148
0016	Pidgey	120	85	73
0017	Pidgeotto	160	117	105
0018	Pidgeot	195	166	154
0018	Mega Pidgeot	195	280	175
0019	Rattata	102	103	70
0019	Rattata Alolan Form	102	103	70
0020	Raticate	146	161	139
0020	Raticate Alolan Form	181	135	154
0021	Spearow	120	112	60
0022	Fearow	163	182	133
0023	Ekans	111	110	97
0024	Arbok	155	167	153
0025	Pikachu	111	112	96
0026	Raichu	155	193	151
0026	Raichu Alolan Form	155	201	154
0027	Sandshrew	137	126	120
0027	Sandshrew Alolan Form	137	125	129
0028	Sandslash	181	182	175
0028	Sandslash Alolan Form	181	177	195
0029	Nidoran♀	146	86	89
0030	Nidorina	172	117	120
0031	Nidoqueen	207	180	173
0032	Nidoran♂	130	105	76
0033	Nidorino	156	137	111
0034	Nidoking	191	204	156
0035	Clefairy	172	107	108
0036	Clefable	216	178	162
0037	Vulpix	116	96	109
0037	Vulpix Alolan Form	116	96	109
0038	Ninetales	177	169	190
0038	Ninetales Alolan Form	177	170	193
0039	Jigglypuff	251	80	41
0040	Wigglytuff	295	156	90
0041	Zubat	120	83	73
0042	Golbat	181	161	150
0043	Oddish	128	131	112
0044	Gloom	155	153	136
0045	Vileplume	181	202	167
0046	Paras	111	121	99
0047	Parasect	155	165	146
0048	Venonat	155	100	100
0049	Venomoth	172	179	143
0050	Diglett	67	109	78
0050	Diglett Alolan Form	67	108	81
0051	Dugtrio	111	167	136
0051	Dugtrio Alolan Form	111	201	142
0052	Meowth	120	92	78
0052	Meowth Alolan Form	120	99	78
0052	Meowth Galarian Form	137	115	92
0053	Persian	163	150	136
0053	Persian Alolan Form	163	158	136
0054	Psyduck	137	122	95
0055	Golduck	190	191	162
0056	Mankey	120	148	82
0057	Primeape	163	207	138
0058	Growlithe	146	136	93
0058	Growlithe Hisuian From	155	142	92
0059	Arcanine	207	227	166
0059	Arcanine Hisuian Form	216	232	165
0060	Poliwag	120	101	82
0061	Poliwhirl	163	130	123
0062	Poliwrath	207	182	184
0063	Abra	93	195	82
0064	Kadabra	120	232	117
0065	Alakazam	146	271	167
0065	Mega Alakazam	146	367	207
0066	Machop	172	137	82
0067	Machoke	190	177	125
0068	Machamp	207	234	159
0069	Bellsprout	137	139	61
0070	Weepinbell	163	172	92
0071	Victreebel	190	207	135
0072	Tentacool	120	97	149
0073	Tentacruel	190	166	209
0074	Geodude	120	132	132
0074	Geodude Alolan Form	120	132	132
0075	Graveler	146	164	164
0075	Graveler Alolan Form	146	164	164
0076	Golem	190	211	198
0076	Golem Alolan Form	190	211	198
0077	Ponyta	137	170	127
0077	Ponyta Galarian Form	137	170	127
0078	Rapidash	163	207	162
0078	Rapidash Galarian Form	163	207	162
0079	Slowpoke	207	109	98
0079	Slowpoke Galarian Form	207	109	98
0080	Slowbro	216	177	180
0080	Mega Slowbro	216	224	259
0080	Slowbro Galarian Form	216	182	156
0081	Magnemite	93	165	121
0082	Magneton	137	223	169
0083	Farfetch'd	141	124	115
0083	Farfetch'd Galarian Form	141	174	114
0084	Doduo	111	158	83
0085	Dodrio	155	218	140
0086	Seel	163	85	121
0087	Dewgong	207	139	177
0088	Grimer	190	135	90
0088	Grimer Alolan Form	190	135	90
0089	Muk	233	190	172
0089	Muk Alolan Form	233	190	172
0090	Shellder	102	116	134
0091	Cloyster	137	186	256
0092	Gastly	102	186	67
0093	Haunter	128	223	107
0094	Gengar	155	261	149
0094	Mega Gengar	155	349	199
0095	Onix	111	85	232
0096	Drowzee	155	89	136
0097	Hypno	198	144	193
0098	Krabby	102	181	124
0099	Kingler	146	240	181
0100	Voltorb	120	109	111
0100	Voltorb Hisuian Form	120	109	111
0101	Electrode	155	173	173
0101	Electrode Hisuian Form	155	176	176
0102	Exeggcute	155	107	125
0103	Exeggutor	216	233	149
0103	Exeggutor Alolan Form	216	230	153
0104	Cubone	137	90	144
0105	Marowak	155	144	186
0105	Marowak Alolan Form	155	144	186
0106	Hitmonlee	137	224	181
0107	Hitmonchan	137	193	197
0108	Lickitung	207	108	137
0109	Koffing	120	119	141
0110	Weezing	163	174	197
0110	Weezing Galarian Form	163	174	197
0111	Rhyhorn	190	140	127
0112	Rhydon	233	222	171
0113	Chansey	487	60	128
0114	Tangela	163	183	169
0115	Kangaskhan	233	181	165
0115	Mega Kangaskhan	233	246	210
0116	Horsea	102	129	103
0117	Seadra	146	187	156
0118	Goldeen	128	123	110
0119	Seaking	190	175	147
0120	Staryu	102	137	112
0121	Starmie	155	210	184
0122	Mr. Mime	120	192	205
0122	Mr. Mime Galarian Form	137	183	169
0123	Scyther	172	218	170
0124	Jynx	163	223	151
0125	Electabuzz	163	198	158
0126	Magmar	163	206	154
0127	Pinsir	163	238	182
0127	Mega Pinsir	163	305	231
0128	Tauros	181	198	183
0128	Tauros Paldean Form; Combat Breed	181	210	193
0128	Tauros Paldean Form; Aqua Breed	181	210	193
0128	Tauros Paldean Form; Blaze Breed	181	210	193
0129	Magikarp	85	29	85
0130	Gyarados	216	237	186
0130	Mega Gyarados	216	292	247
0131	Lapras	277	165	174
0132	Ditto	134	91	91
0133	Eevee	146	104	114
0134	Vaporeon	277	205	161
0135	Jolteon	163	232	182
0136	Flareon	163	246	179
0137	Porygon	163	153	136
0138	Omanyte	111	155	153
0139	Omastar	172	207	201
0140	Kabuto	102	148	140
0141	Kabutops	155	220	186
0142	Aerodactyl	190	221	159
0142	Mega Aerodactyl	190	292	210
0143	Snorlax	330	190	169
0144	Articuno	207	192	236
0144	Articuno Galarian Form	207	250	197
0145	Zapdos	207	253	185
0145	Zapdos Galarian Form	207	252	189
0146	Moltres	207	251	181
0146	Moltres Galarian Form	207	202	231
0147	Dratini	121	119	91
0148	Dragonair	156	163	135
0149	Dragonite	209	263	198
0150	Mewtwo	214	300	182
0150	Mewtwo Armored Mewtwo	214	182	278
0151	Mew	225	210	210
0152	Chikorita	128	92	122
0153	Bayleef	155	122	155
0154	Meganium	190	168	202
0155	Cyndaquil	118	116	93
0156	Quilava	151	158	126
0157	Typhlosion	186	223	173
0157	Typhlosion Hisuian Form	177	238	172
0158	Totodile	137	117	109
0159	Croconaw	163	150	142
0160	Feraligatr	198	205	188
0161	Sentret	111	79	73
0162	Furret	198	148	125
0163	Hoothoot	155	67	88
0164	Noctowl	225	145	156
0165	Ledyba	120	72	118
0166	Ledian	146	107	179
0167	Spinarak	120	105	73
0168	Ariados	172	161	124
0169	Crobat	198	194	178
0170	Chinchou	181	106	97
0171	Lanturn	268	146	137
0172	Pichu	85	77	53
0173	Cleffa	137	75	79
0174	Igglybuff	207	69	32
0175	Togepi	111	67	116
0176	Togetic	146	139	181
0177	Natu	120	134	89
0178	Xatu	163	192	146
0179	Mareep	146	114	79
0180	Flaaffy	172	145	109
0181	Ampharos	207	211	169
0181	Mega Ampharos	207	294	203
0182	Bellossom	181	169	186
0183	Marill	172	37	93
0184	Azumarill	225	112	152
0185	Sudowoodo	172	167	176
0186	Politoed	207	174	179
0187	Hoppip	111	67	94
0188	Skiploom	146	91	120
0189	Jumpluff	181	118	183
0190	Aipom	146	136	112
0191	Sunkern	102	55	55
0192	Sunflora	181	185	135
0193	Yanma	163	154	94
0194	Wooper	146	75	66
0194	Wooper Paldean Form	146	75	66
0195	Quagsire	216	152	143
0196	Espeon	163	261	175
0197	Umbreon	216	126	240
0198	Murkrow	155	175	87
0199	Slowking	216	177	180
0199	Slowking Galarian Form	216	190	180
0200	Misdreavus	155	167	154
0201	Unown	134	136	91
0202	Wobbuffet	382	60	106
0203	Girafarig	172	182	133
0204	Pineco	137	108	122
0205	Forretress	181	161	205
0206	Dunsparce	225	131	128
0207	Gligar	163	143	184
0208	Steelix	181	148	272
0208	Mega Steelix	181	212	327
0209	Snubbull	155	137	85
0210	Granbull	207	212	131
0211	Qwilfish	163	184	138
0211	Qwilfish Hisuian Form	163	184	151
0212	Scizor	172	236	181
0212	Mega Scizor	172	279	250
0213	Shuckle	85	17	396
0214	Heracross	190	234	179
0214	Mega Heracross	190	334	223
0215	Sneasel	146	189	146
0215	Sneasel Hisuian Form	146	189	146
0216	Teddiursa	155	142	93
0217	Ursaring	207	236	144
0218	Slugma	120	118	71
0219	Magcargo	137	139	191
0220	Swinub	137	90	69
0221	Piloswine	225	181	138
0222	Corsola	146	118	156
0222	Corsola Galarian Form	155	116	182
0223	Remoraid	111	127	69
0224	Octillery	181	197	141
0225	Delibird	128	128	90
0226	Mantine	163	148	226
0227	Skarmory	163	148	226
0228	Houndour	128	152	83
0229	Houndoom	181	224	144
0229	Mega Houndoom	181	289	194
0230	Kingdra	181	194	194
0231	Phanpy	207	107	98
0232	Donphan	207	214	185
0233	Porygon2	198	198	180
0234	Stantler	177	192	131
0235	Smeargle	146	40	83
0236	Tyrogue	111	64	64
0237	Hitmontop	137	173	207
0238	Smoochum	128	153	91
0239	Elekid	128	135	101
0240	Magby	128	151	99
0241	Miltank	216	157	193
0242	Blissey	496	129	169
0243	Raikou	207	241	195
0244	Entei	251	235	171
0245	Suicune	225	180	235
0246	Larvitar	137	115	93
0247	Pupitar	172	155	133
0248	Tyranitar	225	251	207
0248	Mega Tyranitar	225	309	276
0249	Lugia	235	193	310
0250	Ho-Oh	214	239	244
0251	Celebi	225	210	210
0252	Treecko	120	124	94
0253	Grovyle	137	172	120
0254	Sceptile	172	223	169
0254	Mega Sceptile	172	320	186
0255	Torchic	128	130	87
0256	Combusken	155	163	115
0257	Blaziken	190	240	141
0257	Mega Blaziken	190	329	168
0258	Mudkip	137	126	93
0259	Marshtomp	172	156	133
0260	Swampert	225	208	175
0260	Mega Swampert	225	283	218
0261	Poochyena	111	96	61
0262	Mightyena	172	171	132
0263	Zigzagoon	116	58	80
0263	Zigzagoon Galarian Form	116	58	80
0264	Linoone	186	142	128
0264	Linoone Galarian Form	186	142	128
0265	Wurmple	128	75	59
0266	Silcoon	137	60	77
0267	Beautifly	155	189	98
0268	Cascoon	137	60	77
0269	Dustox	155	98	162
0270	Lotad	120	71	77
0271	Lombre	155	112	119
0272	Ludicolo	190	173	176
0273	Seedot	120	71	77
0274	Nuzleaf	172	134	78
0275	Shiftry	207	200	121
0276	Taillow	120	106	61
0277	Swellow	155	185	124
0278	Wingull	120	106	61
0279	Pelipper	155	175	174
0280	Ralts	99	79	59
0281	Kirlia	116	117	90
0282	Gardevoir	169	237	195
0282	Mega Gardevoir	169	326	229
0283	Surskit	120	93	87
0284	Masquerain	172	192	150
0285	Shroomish	155	74	110
0286	Breloom	155	241	144
0287	Slakoth	155	104	92
0288	Vigoroth	190	159	145
0289	Slaking	284	290	166
0290	Nincada	104	80	126
0291	Ninjask	156	199	112
0292	Shedinja	1	153	73
0293	Whismur	162	92	42
0294	Loudred	197	134	81
0295	Exploud	232	179	137
0296	Makuhita	176	99	54
0297	Hariyama	302	209	114
0298	Azurill	137	36	71
0299	Nosepass	102	82	215
0300	Skitty	137	84	79
0301	Delcatty	172	132	127
0302	Sableye	137	141	136
0302	Mega Sableye	137	151	216
0303	Mawile	137	155	141
0303	Mega Mawile	137	188	217
0304	Aron	137	121	141
0305	Lairon	155	158	198
0306	Aggron	172	198	257
0306	Mega Aggron	172	247	331
0307	Meditite	102	78	107
0308	Medicham	155	121	152
0308	Mega Medicham	155	205	179
0309	Electrike	120	123	78
0310	Manectric	172	215	127
0310	Mega Manectric	172	286	179
0311	Plusle	155	167	129
0312	Minun	155	147	150
0313	Volbeat	163	143	166
0314	Illumise	163	143	166
0315	Roselia	137	186	131
0316	Gulpin	172	80	99
0317	Swalot	225	140	159
0318	Carvanha	128	171	39
0319	Sharpedo	172	243	83
0320	Wailmer	277	136	68
0321	Wailord	347	175	87
0322	Numel	155	119	79
0323	Camerupt	172	194	136
0324	Torkoal	172	151	203
0325	Spoink	155	125	122
0326	Grumpig	190	171	188
0327	Spinda	155	116	116
0328	Trapinch	128	162	78
0329	Vibrava	137	134	99
0330	Flygon	190	205	168
0331	Cacnea	137	156	74
0332	Cacturne	172	221	115
0333	Swablu	128	76	132
0334	Altaria	181	141	201
0334	Mega Altaria	181	222	218
0335	Zangoose	177	222	124
0336	Seviper	177	196	118
0337	Lunatone	207	178	153
0338	Solrock	207	178	153
0339	Barboach	137	93	82
0340	Whiscash	242	151	141
0341	Corphish	125	141	99
0342	Crawdaunt	160	224	142
0343	Baltoy	120	77	124
0344	Claydol	155	140	229
0345	Lileep	165	105	150
0346	Cradily	200	152	194
0347	Anorith	128	176	100
0348	Armaldo	181	222	174
0349	Feebas	85	29	85
0350	Milotic	216	192	219
0351	Castform	172	139	139
0351	Castform Rainy Form	172	139	139
0351	Castform Snowy Form	172	139	139
0351	Castform Sunny Form	172	139	139
0352	Kecleon	155	161	189
0353	Shuppet	127	138	65
0354	Banette	162	218	126
0354	Mega Banette	162	312	160
0355	Duskull	85	70	162
0356	Dusclops	120	124	234
0357	Tropius	223	136	163
0358	Chimecho	181	175	170
0359	Absol	163	246	120
0359	Mega Absol	163	314	130
0360	Wynaut	216	41	86
0361	Snorunt	137	95	95
0362	Glalie	190	162	162
0362	Mega Glalie	190	252	168
0363	Spheal	172	95	90
0364	Sealeo	207	137	132
0365	Walrein	242	182	176
0366	Clamperl	111	133	135
0367	Huntail	146	197	179
0368	Gorebyss	146	211	179
0369	Relicanth	225	162	203
0370	Luvdisc	125	81	128
0371	Bagon	128	134	93
0372	Shelgon	163	172	155
0373	Salamence	216	277	168
0373	Mega Salamence	216	310	251
0374	Beldum	120	96	132
0375	Metang	155	138	176
0376	Metagross	190	257	228
0377	Regirock	190	179	309
0378	Regice	190	179	309
0379	Registeel	190	143	285
0380	Latias	190	228	246
0380	Mega Latias	190	289	297
0381	Latios	190	268	212
0381	Mega Latios	190	335	241
0382	Kyogre	205	270	228
0382	Kyogre Primal Kyogre	218	353	268
0383	Groudon	205	270	228
0383	Groudon Primal Groudon	218	353	268
0384	Rayquaza	213	284	170
0384	Mega Rayquaza	227	377	210
0385	Jirachi	225	210	210
0386	Deoxys Normal Forme	137	345	115
0386	Deoxys Attack Forme	137	414	46
0386	Deoxys Defense Forme	137	144	330
0386	Deoxys Speed Forme	137	230	218
0387	Turtwig	146	119	110
0388	Grotle	181	157	143
0389	Torterra	216	202	188
0390	Chimchar	127	113	86
0391	Monferno	162	158	105
0392	Infernape	183	222	151
0393	Piplup	142	112	102
0394	Prinplup	162	150	139
0395	Empoleon	197	210	186
0396	Starly	120	101	58
0397	Staravia	146	142	94
0398	Staraptor	198	234	140
0399	Bidoof	153	80	73
0400	Bibarel	188	162	119
0401	Kricketot	114	45	74
0402	Kricketune	184	160	100
0403	Shinx	128	117	64
0404	Luxio	155	159	95
0405	Luxray	190	232	156
0406	Budew	120	91	109
0407	Roserade	155	243	185
0408	Cranidos	167	218	71
0409	Rampardos	219	295	109
0410	Shieldon	102	76	195
0411	Bastiodon	155	94	286
0412	Burmy	120	53	83
0413	Wormadam Plant Cloak	155	141	180
0413	Wormadam Sandy Cloak	155	141	180
0413	Wormadam Trash Cloak	155	127	175
0414	Mothim	172	185	98
0415	Combee	102	59	83
0416	Vespiquen	172	149	190
0417	Pachirisu	155	94	172
0418	Buizel	146	132	67
0419	Floatzel	198	221	114
0420	Cherubi	128	108	92
0421	Cherrim Overcast Form	172	170	153
0421	Cherrim Sunshine Form	172	170	153
0422	Shellos West Sea	183	103	105
0422	Shellos East Sea	183	103	105
0423	Gastrodon West Sea	244	169	143
0423	Gastrodon East Sea	244	169	143
0424	Ambipom	181	205	143
0425	Drifloon	207	117	80
0426	Drifblim	312	180	102
0427	Buneary	146	130	105
0428	Lopunny	163	156	194
0428	Mega Lopunny	163	282	214
0429	Mismagius	155	211	187
0430	Honchkrow	225	243	103
0431	Glameow	135	109	82
0432	Purugly	174	172	133
0433	Chingling	128	114	94
0434	Stunky	160	121	90
0435	Skuntank	230	184	132
0436	Bronzor	149	43	154
0437	Bronzong	167	161	213
0438	Bonsly	137	124	133
0439	Mime Jr.	85	125	142
0440	Happiny	225	25	77
0441	Chatot	183	183	91
0442	Spiritomb	137	169	199
0443	Gible	151	124	84
0444	Gabite	169	172	125
0445	Garchomp	239	261	193
0445	Mega Garchomp	239	339	222
0446	Munchlax	286	137	117
0447	Riolu	120	127	78
0448	Lucario	172	236	144
0448	Mega Lucario	172	310	175
0449	Hippopotas	169	124	118
0450	Hippowdon	239	201	191
0451	Skorupi	120	93	151
0452	Drapion	172	180	202
0453	Croagunk	134	116	76
0454	Toxicroak	195	211	133
0455	Carnivine	179	187	136
0456	Finneon	135	96	116
0457	Lumineon	170	142	170
0458	Mantyke	128	105	179
0459	Snover	155	115	105
0460	Abomasnow	207	178	158
0460	Mega Abomasnow	207	240	191
0461	Weavile	172	243	171
0462	Magnezone	172	238	205
0463	Lickilicky	242	161	181
0464	Rhyperior	251	241	190
0465	Tangrowth	225	207	184
0466	Electivire	181	249	163
0467	Magmortar	181	247	172
0468	Togekiss	198	225	217
0469	Yanmega	200	231	156
0470	Leafeon	163	216	219
0471	Glaceon	163	238	205
0472	Gliscor	181	185	222
0473	Mamoswine	242	247	146
0474	Porygon-Z	198	264	150
0475	Gallade	169	237	195
0475	Mega Gallade	169	326	230
0476	Probopass	155	135	275
0477	Dusknoir	128	180	254
0478	Froslass	172	171	150
0479	Rotom	137	185	159
0479	Rotom Fan Rotom	137	204	219
0479	Rotom Frost Rotom	137	204	219
0479	Rotom Heat Rotom	137	204	219
0479	Rotom Mow Rotom	137	204	219
0479	Rotom Wash Rotom	137	204	219
0480	Uxie	181	156	270
0481	Mesprit	190	212	212
0482	Azelf	181	270	151
0483	Dialga	205	275	211
0483	Dialga Origin Forme	205	270	225
0484	Palkia	189	280	215
0484	Palkia Origin Forme	189	286	223
0485	Heatran	209	251	213
0486	Regigigas	221	287	210
0487	Giratina Altered Forme	284	187	225
0487	Giratina Origin Forme	284	225	187
0488	Cresselia	260	152	258
0489	Phione	190	162	162
0490	Manaphy	225	210	210
0491	Darkrai	172	285	198
0492	Shaymin Land Forme	225	210	210
0492	Shaymin Sky Forme	225	261	166
0493	Arceus	237	238	238
0494	Victini	225	210	210
0495	Snivy	128	88	107
0496	Servine	155	122	152
0497	Serperior	181	161	204
0498	Tepig	163	115	85
0499	Pignite	207	173	106
0500	Emboar	242	235	127
0501	Oshawott	146	117	85
0502	Dewott	181	159	116
0503	Samurott	216	212	157
0503	Samurott Hisuian Form	207	218	152
0504	Patrat	128	98	73
0505	Watchog	155	165	139
0506	Lillipup	128	107	86
0507	Herdier	163	145	126
0508	Stoutland	198	206	182
0509	Purrloin	121	98	73
0510	Liepard	162	187	106
0511	Pansage	137	104	94
0512	Simisage	181	206	133
0513	Pansear	137	104	94
0514	Simisear	181	206	133
0515	Panpour	137	104	94
0516	Simipour	181	206	133
0517	Munna	183	111	92
0518	Musharna	253	183	166
0519	Pidove	137	98	80
0520	Tranquill	158	144	107
0521	Unfezant	190	226	146
0522	Blitzle	128	118	64
0523	Zebstrika	181	211	136
0524	Roggenrola	146	121	110
0525	Boldore	172	174	143
0526	Gigalith	198	226	201
0527	Woobat	163	107	85
0528	Swoobat	167	161	119
0529	Drilbur	155	154	85
0530	Excadrill	242	255	129
0531	Audino	230	114	163
0531	Mega Audino	230	147	239
0532	Timburr	181	134	87
0533	Gurdurr	198	180	134
0534	Conkeldurr	233	243	158
0535	Tympole	137	98	78
0536	Palpitoad	181	128	109
0537	Seismitoad	233	188	150
0538	Throh	260	172	160
0539	Sawk	181	231	153
0540	Sewaddle	128	96	124
0541	Swadloon	146	115	162
0542	Leavanny	181	205	165
0543	Venipede	102	83	99
0544	Whirlipede	120	100	173
0545	Scolipede	155	203	175
0546	Cottonee	120	71	111
0547	Whimsicott	155	164	176
0548	Petilil	128	119	91
0549	Lilligant	172	214	155
0550	Basculin Red-Striped Form	172	189	129
0550	Basculin Blue-Striped Form	172	189	129
0550	Basculin White-Striped Form	172	189	129
0551	Sandile	137	132	69
0552	Krokorok	155	155	90
0553	Krookodile	216	229	158
0554	Darumaka	172	153	86
0554	Darumaka Galarian Form	172	153	86
0555	Darmanitan Standard Mode	233	263	114
0555	Darmanitan Zen Mode	233	243	202
0555	Darmanitan Galarian Form, Standard Mode	233	263	114
0555	Darmanitan Galarian Form, Zen Mode	233	323	123
0556	Maractus	181	201	130
0557	Dwebble	137	118	128
0558	Crustle	172	188	200
0559	Scraggy	137	132	132
0560	Scrafty	163	163	222
0561	Sigilyph	176	204	167
0562	Yamask	116	95	141
0562	Yamask Galarian From	116	95	141
0563	Cofagrigus	151	163	237
0564	Tirtouga	144	134	146
0565	Carracosta	179	192	197
0566	Archen	146	213	89
0567	Archeops	181	292	139
0568	Trubbish	137	96	122
0569	Garbodor	190	181	164
0570	Zorua	120	153	78
0571	Zoroark	155	250	127
0572	Minccino	146	98	80
0573	Cinccino	181	198	130
0574	Gothita	128	98	112
0575	Gothorita	155	137	153
0576	Gothitelle	172	176	205
0577	Solosis	128	170	83
0578	Duosion	163	208	103
0579	Reuniclus	242	214	148
0580	Ducklett	158	84	96
0581	Swanna	181	182	132
0582	Vanillite	113	118	106
0583	Vanillish	139	151	138
0584	Vanilluxe	174	218	184
0585	Deerling	155	115	100
0586	Sawsbuck	190	198	146
0587	Emolga	146	158	127
0588	Karrablast	137	137	87
0589	Escavalier	172	223	187
0590	Foongus	170	97	91
0591	Amoonguss	249	155	139
0592	Frillish	146	115	134
0593	Jellicent	225	159	178
0594	Alomomola	338	138	131
0595	Joltik	137	110	98
0596	Galvantula	172	201	128
0597	Ferroseed	127	82	155
0598	Ferrothorn	179	158	223
0599	Klink	120	98	121
0600	Klang	155	150	174
0601	Klinklang	155	199	214
0602	Tynamo	111	105	78
0603	Eelektrik	163	156	130
0604	Eelektross	198	217	152
0605	Elgyem	146	148	100
0606	Beheeyem	181	221	163
0607	Litwick	137	108	98
0608	Lampent	155	169	115
0609	Chandelure	155	271	182
0610	Axew	130	154	101
0611	Fraxure	165	212	123
0612	Haxorus	183	284	172
0613	Cubchoo	146	128	74
0614	Beartic	216	233	152
0615	Cryogonal	190	190	218
0616	Shelmet	137	72	140
0617	Accelgor	190	220	120
0618	Stunfisk	240	144	171
0618	Stunfisk Galarian Form	240	144	171
0619	Mienfoo	128	160	98
0620	Mienshao	163	258	127
0621	Druddigon	184	213	170
0622	Golett	153	127	92
0623	Golurk	205	222	154
0624	Pawniard	128	154	114
0625	Bisharp	163	232	176
0626	Bouffalant	216	195	182
0627	Rufflet	172	150	97
0628	Braviary	225	232	152
0628	Braviary Hisuian From	242	213	137
0629	Vullaby	172	105	139
0630	Mandibuzz	242	129	205
0631	Heatmor	198	204	129
0632	Durant	151	217	188
0633	Deino	141	116	93
0634	Zweilous	176	159	135
0635	Hydreigon	211	256	188
0636	Larvesta	146	156	107
0637	Volcarona	198	264	189
0638	Cobalion	209	192	229
0639	Terrakion	209	260	192
0640	Virizion	209	192	229
0641	Tornadus Incarnate Forme	188	266	164
0641	Tornadus Therian Forme	188	238	189
0642	Thundurus Incarnate Forme	188	266	164
0642	Thundurus Therian Forme	188	295	161
0643	Reshiram	205	275	211
0644	Zekrom	205	275	211
0645	Landorus Incarnate Forme	205	261	182
0645	Landorus Therian Forme	205	289	179
0646	Kyurem	245	246	170
0646	Kyurem Black Kyurem	245	310	183
0646	Kyurem White Kyurem	245	310	183
0647	Keldeo Ordinary Form	209	260	192
0647	Keldeo Resolute Form	209	260	192
0648	Meloetta Aria Forme	225	250	225
0648	Meloetta Pirouette Forme	225	269	188
0649	Genesect	174	252	199
0650	Chespin	148	110	106
0651	Quilladin	156	146	156
0652	Chesnaught	204	201	204
0653	Fennekin	120	116	102
0654	Braixen	153	171	130
0655	Delphox	181	230	189
0656	Froakie	121	122	84
0657	Frogadier	144	168	114
0658	Greninja	176	223	152
0659	Bunnelby	116	68	72
0660	Diggersby	198	112	155
0661	Fletchling	128	95	80
0662	Fletchinder	158	145	110
0663	Talonflame	186	176	155
0664	Scatterbug	116	63	63
0665	Spewpa	128	48	89
0666	Vivillon	190	176	103
0667	Litleo	158	139	112
0668	Pyroar	200	221	149
0669	Flabébé	127	108	120
0670	Floette	144	136	151
0671	Florges	186	212	244
0672	Skiddo	165	123	102
0673	Gogoat	265	196	146
0674	Pancham	167	145	107
0675	Pangoro	216	226	146
0676	Furfrou	181	164	167
0677	Espurr	158	120	114
0678	Meowstic Male	179	166	167
0678	Meowstic Female	179	166	167
0679	Honedge	128	135	139
0680	Doublade	153	188	206
0681	Aegislash Shield Forme	155	97	291
0681	Aegislash Blade Forme	155	291	97
0682	Spritzee	186	110	113
0683	Aromatisse	226	173	150
0684	Swirlix	158	109	119
0685	Slurpuff	193	168	163
0686	Inkay	142	98	95
0687	Malamar	200	177	165
0688	Binacle	123	96	120
0689	Barbaracle	176	194	205
0690	Skrelp	137	109	109
0691	Dragalge	163	177	207
0692	Clauncher	137	108	117
0693	Clawitzer	174	221	171
0694	Helioptile	127	115	78
0695	Heliolisk	158	219	168
0696	Tyrunt	151	158	123
0697	Tyrantrum	193	227	191
0698	Amaura	184	124	109
0699	Aurorus	265	186	163
0700	Sylveon	216	203	205
0701	Hawlucha	186	195	153
0702	Dedenne	167	164	134
0703	Carbink	137	95	285
0704	Goomy	128	101	112
0705	Sliggoo	169	159	176
0706	Goodra	207	220	242
0707	Klefki	149	160	179
0708	Phantump	125	125	103
0709	Trevenant	198	201	154
0710	Pumpkaboo Small Size	127	122	124
0710	Pumpkaboo Average Size	135	121	123
0710	Pumpkaboo Large Size	144	120	122
0710	Pumpkaboo Super Size	153	118	120
0711	Gourgeist Small Size	146	171	219
0711	Gourgeist Average Size	163	175	213
0711	Gourgeist Large Size	181	179	206
0711	Gourgeist Super Size	198	182	200
0712	Bergmite	146	117	120
0713	Avalugg	216	196	240
0713	Avalugg Hisuian Form	216	214	238
0714	Noibat	120	83	73
0715	Noivern	198	205	175
0716	Xerneas	246	250	185
0717	Yveltal	246	250	185
0718	Zygarde 50% Forme	239	203	232
0718	Zygarde 10% Forme	144	205	173
0718	Zygarde Complete Forme	389	184	207
0719	Diancie	137	190	285
0719	Mega Diancie	137	342	235
0720	Hoopa Hoopa Confined	173	261	187
0720	Hoopa Hoopa Unbound	173	311	191
0721	Volcanion	190	252	216
0722	Rowlet	169	102	99
0723	Dartrix	186	142	139
0724	Decidueye	186	210	179
0724	Decidueye Hisuian Form	204	213	174
0725	Litten	128	128	79
0726	Torracat	163	174	103
0727	Incineroar	216	214	175
0728	Popplio	137	120	103
0729	Brionne	155	168	145
0730	Primarina	190	232	195
0731	Pikipek	111	136	59
0732	Trumbeak	146	159	100
0733	Toucannon	190	222	146
0734	Yungoos	134	122	56
0735	Gumshoos	204	194	113
0736	Grubbin	132	115	85
0737	Charjabug	149	145	161
0738	Vikavolt	184	254	158
0739	Crabrawler	132	150	104
0740	Crabominable	219	231	138
0741	Oricorio	181	196	145
0742	Cutiefly	120	110	81
0743	Ribombee	155	198	146
0744	Rockruff	128	117	78
0745	Lycanroc Midday Form	181	231	140
0745	Lycanroc Midnight Form	198	218	152
0745	Lycanroc Dusk Form	181	234	139
0746	Wishiwashi Solo Form	128	46	43
0746	Wishiwashi School Form	128	255	242
0747	Mareanie	137	98	110
0748	Toxapex	137	114	273
0749	Mudbray	172	175	121
0750	Mudsdale	225	215	174
0751	Dewpider	116	72	117
0752	Araquanid	169	126	219
0753	Fomantis	120	100	64
0754	Lurantis	172	192	169
0755	Morelull	120	108	119
0756	Shiinotic	155	154	168
0757	Salandit	134	136	80
0758	Salazzle	169	228	130
0759	Stufful	172	136	95
0760	Bewear	260	226	141
0761	Bounsweet	123	55	69
0762	Steenee	141	78	94
0763	Tsareena	176	222	195
0764	Comfey	139	165	215
0765	Oranguru	207	168	192
0766	Passimian	225	222	160
0767	Wimpod	93	67	74
0768	Golisopod	181	218	226
0769	Sandygast	146	120	118
0770	Palossand	198	178	178
0771	Pyukumuku	146	97	224
0775	Komala	163	216	165
0776	Turtonator	155	165	215
0777	Togedemaru	163	190	145
0779	Bruxish	169	208	145
0780	Drampa	186	231	164
0781	Dhelmise	172	233	179
0782	Jangmo-o	128	102	108
0783	Hakamo-o	146	145	162
0784	Kommo-o	181	222	240
0785	Tapu Koko	172	250	181
0786	Tapu Lele	172	259	208
0787	Tapu Bulu	172	249	215
0788	Tapu Fini	172	189	254
0789	Cosmog	125	54	57
0790	Cosmoem	125	54	242
0791	Solgaleo	264	255	191
0792	Lunala	264	255	191
0793	Nihilego	240	249	210
0794	Buzzwole	216	236	196
0795	Pheromosa	174	316	85
0796	Xurkitree	195	330	144
0797	Celesteela	219	207	199
0798	Kartana	139	323	182
0799	Guzzlord	440	188	99
0800	Necrozma	219	251	195
0800	Dusk Mane Necrozma	200	277	220
0800	Dawn Wings Necrozma	200	277	220
0802	Marshadow	207	265	190
0803	Poipole	167	145	133
0804	Naganadel	177	263	159
0805	Stakataka	156	213	298
0806	Blacephalon	142	315	148
0808	Meltan	130	118	99
0809	Melmetal	264	226	190
0810	Grookey	137	122	91
0811	Thwackey	172	165	134
0812	Rillaboom	225	239	168
0813	Scorbunny	137	132	79
0814	Raboot	163	170	125
0815	Cinderace	190	238	163
0816	Sobble	137	132	79
0817	Drizzile	163	186	113
0818	Inteleon	172	262	142
0819	Skwovet	172	95	86
0820	Greedent	260	160	156
0821	Rookidee	116	88	67
0822	Corvisquire	169	129	110
0823	Corviknight	221	163	192
0827	Nickit	120	85	82
0828	Thievul	172	172	164
0829	Gossifleur	120	70	104
0830	Eldegoss	155	148	211
0831	Wooloo	123	76	97
0832	Dubwool	176	159	198
0840	Applin	120	71	116
0841	Flapple	172	214	144
0842	Appletun	242	178	146
0848	Toxel	120	97	65
0849	Toxtricity Amped Form	181	224	140
0849	Toxtricity Low Key Form	181	224	140
0850	Sizzlipede	137	118	90
0851	Centiskorch	225	220	158
0854	Sinistea	120	134	96
0855	Polteageist	155	248	189
0856	Hatenna	123	98	93
0857	Hattrem	149	153	133
0858	Hatterene	149	237	182
0862	Obstagoon	212	180	194
0863	Perrserker	172	195	162
0864	Cursola	155	253	182
0865	Sirfetch'd	158	248	176
0866	Mr. Rime	190	212	179
0867	Runerigus	151	163	237
0870	Falinks	163	193	170
0874	Stonjourner	225	222	182
0877	Morpeko Full Belly	151	192	121
0877	Morpeko Hangry	151	192	121
0885	Dreepy	99	117	61
0886	Drakloak	169	163	105
0887	Dragapult	204	266	170
0888	Zacian Hero of Many Battles	192	254	236
0888	Zacian Crowned Sword	192	332	240
0889	Zamazenta Hero of Many Battles	192	254	236
0889	Zamazenta Crowned Shield	192	250	292
0890	Eternatus	268	278	197
0891	Kubfu	155	170	112
0892	Urshifu Single Strike Style	225	254	177
0892	Urshifu Rapid Strike Style	225	254	177
0893	Zarude	233	242	215
0894	Regieleki	190	250	125
0895	Regidrago	400	202	101
0899	Wyrdeer	230	206	145
0900	Kleavor	172	253	174
0901	Ursaluna	277	243	181
0903	Sneasler	190	259	158
0904	Overqwil	198	222	171
0905	Enamorus Incarnate Forme	179	281	162
0905	Enamorus Therian Forme	179	250	201
0906	Sprigatito	120	116	99
0907	Floragato	156	157	128
0908	Meowscarada	183	233	153
0909	Fuecoco	167	112	96
0910	Crocalor	191	162	134
0911	Skeledirge	232	207	178
0912	Quaxly	146	120	86
0913	Quaxwell	172	162	123
0914	Quaquaval	198	236	159
0915	Lechonk	144	81	79
0916	Oinkologne Male	242	186	153
0916	Oinkologne Female	251	169	162
0919	Nymble	107	81	65
0920	Lokix	174	199	144
0921	Pawmi	128	95	45
0922	Pawmo	155	147	82
0923	Pawmot	172	232	141
0924	Tandemaus	137	98	90
0925	Maushold Family of Four	179	159	157
0925	Maushold Family of Three	179	159	157
0926	Fidough	114	102	126
0927	Dachsbun	149	159	212
0928	Smoliv	121	100	89
0929	Dolliv	141	137	131
0930	Arboliva	186	219	189
0935	Charcadet	120	92	74
0936	Armarouge	198	234	185
0937	Ceruledge	181	239	189
0938	Tadbulb	156	104	73
0939	Bellibolt	240	184	165
0944	Shroodle	120	124	70
0945	Grafaiai	160	199	149
0957	Tinkatink	137	85	110
0958	Tinkatuff	163	109	145
0959	Tinkaton	198	155	196
0960	Wiglett	67	109	52
0961	Wugtrio	111	205	136
0962	Bombirdier	172	198	172
0965	Varoom	128	123	107
0966	Revavroom	190	229	168
0971	Greavard	137	105	106
0972	Houndstone	176	186	195
0974	Cetoddle	239	119	80
0975	Cetitan	347	208	123
0979	Annihilape	242	220	178
0980	Clodsire	277	127	151
0983	Kingambit	238	203	225
0996	Frigibax	163	134	86
0997	Arctibax	207	173	128
0998	Baxcalibur	229	254	168
0999	Gimmighoul Roaming Form	128	140	76
1000	Gholdengo	202	252	190
1001	Wo-Chien	198	186	242
1002	Chien-Pao	190	261	167
1003	Ting-Lu	321	194	203
1004	Chi-Yu	146	269	221
1005	Roaring Moon	233	280	196
1006	Iron Valiant	179	279	171
1007	Koraidon	205	263	223
1008	Miraidon	205	263	223
1009	Walking Wake		?	?
1010	Iron Leaves	?	?	?
1011	Dipplin	?	?	?
1012	Poltchageist	?	?	?
1013	Sinistcha	?	?	?
1014	Okidogi	?	?	?
1015	Munkidori	?	?	?
1016	Fezandipiti	?	?	?
1017	Ogerpon	?	?	?
1018	Archaludon	?	?	?
1019	Hydrapple	?	?	?
1020	Gouging Fire	?	?	?
1021	Raging Bolt	?	?	?
1022	Iron Boulder	?	?	?
1023	Iron Crown	?	?	?
1024	Terapagos	?	?	?
1025	Pecharunt	?	?	?

Effective stats

Each individual Pokémon augments its base species stats with three individual values (IVs), each ranging from 0 to 15.

• A Pokémon with all 15s is colloquially known as a "hundo", and enters the 100% Pokédex.
• A Pokémon with all 0s is somewhat less colloquially known as a "nundo", and enters nothing.
• Evolution and Level changes do not affect IVs.
• Purification raises each IV by 2, not to exceed 15.
• Trading regenerates the IVs.

Adding the base species stats to the IVs and scaling by the appropriate CPM generates an effective attack Eff_A, effective defense Eff_D, and maximum HP MHP (Eff_S) for that Pokémon, all positive rationals.

• Eff_x = (Base_x + IV_x) * CPM(Level) = Base_x * CPM(Level) + IV_x * CPM(Level)

Shadow Pokémon have their A divided by ⅚, and their D multiplied by ⅚.

For instance, a hundo Altaria at level 26 has:

• base ATK 141
• base DEF 201
• base STA 181
• IV_A = IV_D = IV_S = 15
• CPM = 0.6811649
• Eff_A = (141 + 15) * CPM = 156 * 0.6811649 = 106.2617244
• Eff_D = (201 + 15) * CPM = 216 * 0.6811649 = 147.1316184
• Eff_S = (181 + 15) * CPM = 196 * 0.6811649 = 133.5083204

Taking the floor of Eff_S tells you maximum HP.

• MHP = ⌊Eff_S⌋ = 133

nb: i've seen other formulas claimed for maximum HP, but they don't seem to match reality. everywhere i've checked, maximum HP = ⌊Eff_S⌋

Battle mechanics

Each named Attack (both Fast and Charged) has a base power P, a non-negative integer. This P can (and usually is) different depending on whether it's PvE or PvP.

For Fast Attacks, PvE Power ranges from 0 to 32, while PvP Power ranges from 0 to 20. If Attack A is stronger than Attack B in PvE mode, it will not be weaker than B in PvP mode, and vice versa (i.e. partial ordering is maintained). Furthermore, no Fast Attack's PvE Power is less than its PvP Power. Incinerate is thus the most powerful Fast Attack in both modes.

Fast Attacks

Attack	Power	Energy	Cooldown	DPS	EPS	Power	Energy	Turns	DPT	EPT
Acid	11	10	1	11	10	6	5	2	3	2.5
Air Slash	12	8	1	12	8	9	9	3	3	3
Astonish	7	13	1	7	13	12	10	3	4	3.33
Bite	6	4	0.5	12	8	4	2	1	4	2
Bubble	10	12	1	10	12	8	11	3	2.67	3.67
Bug Bite	5	6	0.5	10	12	3	3	1	3	3
Bullet Punch	10	11	1	10	11	6	7	2	3	3.5
Bullet Seed	7	13	1	7	13	5	13	3	1.67	4.33
Charge Beam	7	14	1	7	14	5	11	3	1.67	3.67
Charm	20	11	1.5	13.33	7.33	15	6	3	5	2
Confusion	19	14	1.5	12.67	9.33	16	12	4	4	3
Counter	13	9	1	13	9	8	6	2	4	3
Cut	5	5	0.5	10	10	3	2	1	3	2
Double Kick	10	13	1	10	13	8	12	3	2.67	4
Dragon Breath	6	4	0.5	12	8	4	3	1	4	3
Dragon Tail	14	8	1	14	8	13	9	3	4.33	3
Ember	10	10	1	10	10	7	6	2	3.5	3
Extrasensory	11	11	1	11	11	8	10	3	2.67	3.33
Fairy Wind	9	13	1	9	13	4	9	2	2	4.5
Feint Attack	11	10	1	11	10	6	6	2	3	3
Fire Fang	13	9	1	13	9	8	6	2	4	3
Fire Spin	13	9	1	13	9	11	10	3	3.67	3.33
Force Palm	10	16	1	10	16	13	10	3	4.33	3.33
Frost Breath	11	9	1	11	9	7	5	2	3.5	2.5
Fury Cutter	4	8	0.5	8	16	2	4	1	2	4
Geomancy	20	14	1.5	13.33	9.33	4	13	3	1.33	4.33
Gust	25	20	2	12.5	10	16	12	4	4	3
Hex	8	13	1	8	13	7	13	3	2.33	4.33
Hidden Power	15	15	1.5	10	10	9	8	3	3	2.67
Ice Fang	12	20	1.5	8	13.33	8	6	2	4	3
Ice Shard	10	10	1	10	10	9	10	3	3	3.33
Incinerate	32	22	2.5	12.8	8.8	20	20	5	4	4
Infestation	9	13	1	9	13	6	12	3	2	4
Iron Tail	14	6	1	14	6	10	7	3	3.33	2.33
Karate Chop	10	13	1	10	13	5	9	2	2.5	4.5
Leafage	6	4	0.5	12	8	6	7	2	3	3.5
Lick	5	6	0.5	10	12	3	3	1	3	3
Lock-On	2	10	0.5	4	20	1	5	1	1	5
Low Kick	5	5	0.5	10	10	4	5	2	2	2.5
Magical Leaf	17	17	1.5	11.33	11.33	10	10	3	3.33	3.33
Metal Claw	6	5	0.5	12	10	5	7	2	2.5	3.5
Metal Sound	4	6	0.5	8	12	3	8	2	1.5	4
Mud Shot	4	6	0.5	8	12	4	8	2	2	4
Mud-Slap	19	13	1.5	12.67	8.67	12	10	3	4	3.33
Peck	10	10	1	10	10	6	5	2	3	2.5
Poison Jab	13	9	1	13	9	7	7	2	3.5	3.5
Poison Sting	4	6	0.5	8	12	4	9	2	2	4.5
Pound	6	5	0.5	12	10	4	4	2	2	2
Powder Snow	6	15	1	6	15	5	8	2	2.5	4
Present	6	23	1.5	4	15.33	3	12	3	1	4
Psycho Cut	4	7	0.5	8	14	3	9	2	1.5	4.5
Psywave	4	7	0.5	8	14	3	4	1	3	4
Quick Attack	10	13	1	10	13	5	8	2	2.5	4
Razor Leaf	13	7	1	13	7	9	4	2	4.5	2
Rock Smash	17	12	1.5	11.33	8	9	7	3	3	2.33
Rock Throw	13	8	1	13	8	8	5	2	4	2.5
Rollout	15	19	1.5	10	12.67	7	13	3	2.33	4.33
Sand Attack	4	7	0.5	8	14	2	4	1	2	4
Scratch	6	4	0.5	12	8	4	2	1	4	2
Shadow Claw	6	4	0.5	12	8	6	8	2	3	4
Smack Down	13	7	1	13	7	11	8	3	3.67	2.67
Snarl	11	13	1	11	13	5	13	3	1.67	4.33
Spark	4	6	0.5	8	12	5	7	2	2.5	3.5
Splash	0	17	1.5	0	11.33	0	12	4	0	3
Steel Wing	14	8	1	14	8	7	6	2	3.5	3
Struggle Bug	15	15	1.5	10	10	9	8	3	3	2.67
Sucker Punch	5	6	0.5	10	12	8	7	2	4	3.5
Tackle	5	5	0.5	10	10	3	3	1	3	3
Take Down	7	8	1	7	8	5	8	3	1.67	2.67
Thunder Fang	10	13	1	10	13	8	6	2	4	3
Thunder Shock	4	7	0.5	8	14	4	9	2	2	4.5
Transform	0	0	2	0	0	0	0	3	0	0
Vine Whip	6	5	0.5	12	10	5	8	2	2.5	4
Volt Switch	13	20	1.5	8.67	13.33	12	16	4	3	4
Water Gun	5	5	0.5	10	10	3	3	1	3	3
Water Shuriken	9	14	1	9	14	6	14	3	2	4.67
Waterfall	13	7	1	13	7	12	8	3	4	2.67
Wing Attack	10	11	1	10	11	5	7	2	2.5	3.5
Yawn	0	13	1.5	0	8.67	0	12	4	0	3
Zen Headbutt	11	9	1	11	9	8	6	3	2.67	2

Charged Attacks have a much greater range of PvE Power, from 10 (Frustration) to 230 (Sunsteel Strike). They do not illustrate the same ordering properties as Fast Attacks: Aeroblast is the most Powerful in PvP at 170.

Charged Attacks

Attack	Power	Cooldown	DPS	Power	Energy	DPE
Acid Spray	20	3	6.67	20	-45	0.44
Acrobatics	100	2	50	110	-55	2
Aerial Ace	55	2.5	22	55	-40	1.38
Aeroblast	180	3.5	51.43	170	-75	2.27
Aeroblast+	200	3.5	57.14	170	-75	2.27
Aeroblast++	225	3.5	64.29	170	-75	2.27
Air Cutter	55	2.5	22	45	-35	1.29
Ancient Power	70	3.5	20	60	-45	1.33
Aqua Jet	45	2.5	18	70	-40	1.75
Aqua Tail	50	2	25	55	-35	1.57
Aura Sphere	100	2	50	100	-55	1.82
Aura Wheel	100	2.7	37.04	100	-45	2.22
Aurora Beam	80	3.5	22.86	80	-60	1.33
Avalanche	85	2.5	34	90	-45	2
Behemoth Bash	125	1.5	83.33	80	-45	1.78
Behemoth Blade	200	3.5	57.14	100	-55	1.82
Blast Burn	120	3.5	34.29	110	-50	2.2
Blaze Kick	40	1	40	60	-40	1.5
Bleakwind Storm	150	2.5	60	60	-45	1.33
Blizzard	130	3	43.33	140	-75	1.87
Body Slam	50	2	25	50	-35	1.43
Bone Club	40	1.5	26.67	55	-35	1.57
Boomburst	150	2.5	60	150	-70	2.14
Brave Bird	130	2	65	130	-55	2.36
Breaking Swipe	45	1	45	50	-35	1.43
Brick Break	40	1.5	26.67	40	-40	1
Brine	65	2.5	26	60	-50	1.2
Brutal Swing	65	2	32.5	55	-35	1.57
Bubble Beam	45	2	22.5	25	-40	0.63
Bug Buzz	95	3.5	27.14	100	-60	1.67
Bulldoze	80	3.5	22.86	45	-45	1
Close Combat	105	2.5	42	100	-45	2.22
Crabhammer	85	2	42.5	85	-50	1.7
Cross Chop	50	1.5	33.33	55	-35	1.57
Cross Poison	40	1.5	26.67	50	-35	1.43
Crunch	65	3	21.67	70	-45	1.56
Dark Pulse	80	3	26.67	80	-50	1.6
Darkest Lariat	80	2	40	120	-60	2
Dazzling Gleam	100	3.5	28.57	90	-55	1.64
Dig	100	4.5	22.22	70	-50	1.4
Disarming Voice	70	4	17.5	70	-45	1.56
Discharge	65	2.5	26	55	-40	1.38
Doom Desire	65	1.5	43.33	75	-40	1.88
Double Iron Bash	70	2	35	50	-35	1.43
Draco Meteor	150	3.5	42.86	150	-65	2.31
Dragon Ascent	140	3.5	40	150	-70	2.14
Dragon Claw	45	1.5	30	50	-35	1.43
Dragon Pulse	90	3.5	25.71	90	-60	1.5
Drain Punch	50	2.5	20	20	-40	0.5
Draining Kiss	60	2.5	24	60	-55	1.09
Drill Peck	70	2.5	28	65	-40	1.63
Drill Run	85	3	28.33	80	-45	1.78
Dynamic Punch	85	2.5	34	90	-45	2
Earth Power	100	3.5	28.57	90	-55	1.64
Earthquake	140	3.5	40	110	-65	1.69
Energy Ball	90	4	22.5	90	-55	1.64
Feather Dance	35	3	11.67	35	-50	0.7
Fell Stinger	45	2	22.5	20	-35	0.57
Fire Blast	140	4	35	140	-80	1.75
Fire Punch	50	2	25	60	-40	1.5
Flame Burst	70	2.5	28	70	-55	1.27
Flame Charge	70	4	17.5	65	-50	1.3
Flame Wheel	55	2.5	22	60	-55	1.09
Flamethrower	65	2	32.5	90	-55	1.64
Flash Cannon	100	2.5	40	110	-70	1.57
Flower Trick	75	2.7	27.78	30	-35	0.86
Fly	90	2	45	80	-45	1.78
Flying Press	115	2.5	46	90	-40	2.25
Focus Blast	140	3.5	40	150	-75	2
Foul Play	70	2	35	60	-40	1.5
Freeze Shock	160	1.5	106.67	120	-60	2
Frenzy Plant	100	2.5	40	100	-45	2.22
Frustration	10	2.0	5	10	-70	0.14
Fusion Bolt	140	2	70	90	-45	2
Fusion Flare	140	2	70	90	-45	2
Future Sight	115	2.5	46	110	-65	1.69
Giga Impact	200	4.5	44.44	150	-80	1.88
Glaciate	160	2.5	64	60	-40	1.5
Grass Knot	90	2.5	36	90	-50	1.8
Gunk Shot	130	3	43.33	130	-75	1.73
Gyro Ball	85	3.5	24.29	80	-60	1.33
Heat Wave	95	3	31.67	95	-75	1.27
Heavy Slam	70	2	35	70	-50	1.4
High Horsepower	105	1.5	70	100	-60	1.67
High Jump Kick	90	1.5	60	110	-55	2
Horn Attack	45	2	22.5	40	-35	1.14
Hurricane	105	2.5	42	110	-65	1.69
Hydro Cannon	90	2	45	80	-40	2
Hydro Pump	135	3.5	38.57	130	-75	1.73
Hyper Beam	150	4	37.5	150	-80	1.88
Hyper Fang	80	2.5	32	80	-50	1.6
Ice Beam	95	3.5	27.14	90	-55	1.64
Ice Burn	90	2	45	120	-60	2
Ice Punch	50	2	25	60	-40	1.5
Icicle Spear	55	2	27.5	65	-40	1.63
Icy Wind	65	3.5	18.57	60	-45	1.33
Iron Head	60	2	30	70	-50	1.4
Last Resort	90	3	30	90	-55	1.64
Leaf Blade	70	2.5	28	70	-35	2
Leaf Storm	130	2.5	52	130	-55	2.36
Leaf Tornado	45	3	15	45	-40	1.13
Liquidation	70	3.0	23.33	70	-45	1.56
Low Sweep	40	2	20	40	-40	1
Lunge	55	3	18.33	60	-45	1.33
Luster Purge	100	1.5	66.67	120	-60	2
Magma Storm	75	2.5	30	65	-40	1.63
Magnet Bomb	75	3	25	70	-45	1.56
Megahorn	105	2	52.5	110	-55	2
Meteor Beam	140	2	70	120	-60	2
Meteor Mash	100	2.5	40	100	-50	2
Mirror Coat	60	2.5	24	60	-55	1.09
Mirror Shot	50	2.5	20	35	-35	1
Mist Ball	105	2	52.5	120	-60	2
Moonblast	130	4	32.5	110	-60	1.83
Moongeist Beam	230	3	76.67	135	-65	2.08
Mud Bomb	60	2.5	24	60	-40	1.5
Muddy Water	45	2	22.5	35	-35	1
Mystical Fire	60	2	30	60	-45	1.33
Nature's Madness	90	2	45	80	-50	1.6
Night Shade	60	2.5	24	70	-45	1.56
Night Slash	45	2	22.5	50	-35	1.43
Oblivion Wing	85	2	42.5	85	-50	1.7
Obstruct	20	1.5	13.33	15	-40	0.38
Octazooka	55	2.5	22	50	-50	1
Ominous Wind	55	2.5	22	45	-45	1
Origin Pulse	120	1.5	80	130	-60	2.17
Outrage	110	4	27.5	110	-60	1.83
Overheat	160	4	40	130	-55	2.36
Parabolic Charge	70	3	23.33	70	-50	1.4
Payback	95	2	47.5	110	-60	1.83
Petal Blizzard	110	2.5	44	110	-65	1.69
Play Rough	90	3	30	90	-60	1.5
Poison Fang	30	1.5	20	45	-40	1.13
Poltergeist	140	3.5	40	150	-75	2
Power Gem	80	3	26.67	85	-50	1.7
Power Whip	90	2.5	36	90	-50	1.8
Power-Up Punch	50	2	25	20	-35	0.57
Precipice Blades	120	1.5	80	130	-60	2.17
Psybeam	65	3	21.67	70	-60	1.17
Psychic	95	3	31.67	75	-55	1.36
Psychic Fangs	25	1	25	40	-35	1.14
Psycho Boost	70	4	17.5	70	-35	2
Psyshock	60	2.5	24	70	-40	1.75
Psystrike	95	2.5	38	90	-45	2
Rage Fist	100	3	33.33	50	-35	1.43
Razor Shell	55	1.5	36.67	35	-35	1
Return	25	0.5	50	130	-70	1.86
Roar of Time	160	2	80	150	-65	2.31
Rock Blast	50	2	25	50	-40	1.25
Rock Slide	75	2.5	30	65	-45	1.44
Rock Tomb	65	3	21.67	80	-50	1.6
Rock Wrecker	110	3.5	31.43	110	-50	2.2
Sacred Fire	120	2.5	48	130	-65	2
Sacred Fire+	135	2.5	54	130	-65	2
Sacred Fire++	155	2.5	62	130	-65	2
Sacred Sword	50	1	50	60	-35	1.71
Sand Tomb	60	4	15	25	-40	0.63
Sandsear Storm	150	2.5	60	60	-45	1.33
Scald	75	3.5	21.43	85	-50	1.7
Scorching Sands	90	3	30	80	-50	1.6
Seed Bomb	55	2	27.5	65	-45	1.44
Seed Flare	115	2.5	46	130	-75	1.73
Shadow Ball	100	3	33.33	100	-55	1.82
Shadow Bone	85	3	28.33	80	-45	1.78
Shadow Force	140	2	70	120	-90	1.33
Shadow Punch	35	1.5	23.33	55	-35	1.57
Shadow Sneak	50	3	16.67	50	-45	1.11
Signal Beam	75	3	25	75	-55	1.36
Silver Wind	65	3.5	18.57	60	-45	1.33
Skull Bash	130	3	43.33	130	-75	1.73
Sky Attack	80	2	40	85	-55	1.55
Sludge	50	2	25	70	-40	1.75
Sludge Bomb	85	2.5	34	80	-50	1.6
Sludge Wave	105	3	35	110	-65	1.69
Solar Beam	180	5	36	150	-80	1.88
Spacial Rend	160	2.5	64	95	-50	1.9
Sparkling Aria	85	3	28.33	80	-45	1.78
Spirit Shackle	70	2.5	28	50	-40	1.25
Stomp	50	1.5	33.33	55	-40	1.38
Stone Edge	105	2.5	42	100	-55	1.82
Struggle	35	2	17.5	35	-100	0.35
Submission	55	2	27.5	60	-50	1.2
Sunsteel Strike	230	3	76.67	135	-65	2.08
Superpower	85	3	28.33	85	-40	2.13
Surf	60	1.5	40	75	-45	1.67
Swift	65	3	21.67	55	-35	1.57
Synchronoise	80	2.5	32	80	-50	1.6
Techno Blast	120	2	60	120	-55	2.18
Thunder	100	2.5	40	100	-60	1.67
Thunder Punch	50	2	25	60	-40	1.5
Thunderbolt	80	2.5	32	90	-55	1.64
Torch Song	100	3.5	28.57	70	-45	1.56
Trailblaze	65	2.0	32.5	65	-45	1.44
Tri Attack	75	2.5	30	65	-50	1.3
Triple Axel	60	2.0	30	60	-45	1.33
Twister	50	3	16.67	45	-45	1
Upper Hand	50	2	25	70	-40	1.75
V-create	105	3	35	95	-40	2.38
Vise Grip	35	2	17.5	40	-40	1
Volt Tackle	90	3.5	25.71	90	-50	1.8
Water Pulse	65	3	21.67	80	-55	1.45
Weather Ball	55	1.5	36.67	55	-35	1.57
Wild Charge	90	2.5	36	100	-45	2.22
Wildbolt Storm	150	2.5	60	60	-45	1.33
Wrap	60	3	20	60	-45	1.33
X-Scissor	45	1.5	30	65	-40	1.63
Zap Cannon	140	3.5	40	150	-80	1.88

Calculating an Attack's damage requires the attacker's Eff_A, the defender's Eff_D, two multipliers M and M_M, and the Attack's P. The result is subtracted from the defender's HP. We will see that damage is always a positive integer, and thus HP is always an integer.

Multiplier M is defined as the product of:

• the Attack's type effectiveness relative to the defender (see below)
• the Attack's type effectiveness relative to the attacker
  • 1.2 if the attacker shares type with the Attack, 1 otherwise (Same Type Attack Bonus, STAB)

A subsequent multiplier M_M is different depending on whether the battle is PvE or PvP.

PvE mode

Multiplier M_M is defined as the product over

• 0.5
• 0.25 if the Attack is dodged, 1 otherwise
  • it is possible that this ranges from 0.25 to 1 Dank (talk) 07:36, 9 May 2025 (UTC)
• 1.2 if the Attack is weather-boosted, 1 otherwise
• A friendship bonus: 1 unless
  • 1.03 if battling with at least one Good Friend, unless
  • 1.05 if battling with at least one Great Friend, unless
  • 1.07 if battling with at least one Ultra Friend, unless
  • 1.1 if battling with at least one Best Friend
• A Mega bonus: 1 unless
  • 1.1 if battling with at least one Mega Pokémon, unless
  • 1.3 if battling with at least one Mega Pokémon of the Attack's type
• A Max bonus at Power Stops: 1 unless
  • 1.1 for level 1 support (1 placed Pokémon), unless
  • 1.15 for level 2 support (2–3 placed Pokémon), unless
  • 1.188 for level 3 support (4–14 placed Pokémon), unless
  • 1.2 for level 4 support (15+ placed Pokémon)

PvP mode

Multiplier M_M is defined as the product over

• 0.65
• Minigame score for Charged Attacks, ranging from 0.25 to 1
  • "Excellent!" is necessary and sufficient for a 1
  • "Great!" maps to [0.75, 1)
  • "Nice!" maps to [0.5, 0.75)
  • otherwise [0.25, 0.5)

Damage calculation

At this point, P is a non-negative integer, while Eff_A, Eff_D, M, and M_M are positive rationals.

Damage = ⌊P * Eff_A / Eff_D * M * M_M⌋ + 1

Some notes:

• A / D yields a positive rational
  • The floor function yields an integer, but A / D is calculated with reasonable precision
• Damage is always a positive integer
• P is the dominant term outside of pathological mismatches
• Maximum A / D is 414/32 = 12.9375, worst A / D is 17/396 = 0.0429
  • Maximum (Base+IV)_A / (Base+IV)_D is 429/32 = 13.40625, a ~3.6% gain
  • Minimum (Base+IV)_D / (Base+IV)_D is 17/411 = 0.0413625, a ~3.4% loss
  • Now make both sides 15: for A, 429 / 47 = 9.12765, a ~29.5% loss
  • Now make both sides 15: for D,
• All CPMs are less than 1, shrinking the effective values
  • We can factor out the CPM ratio and define a constant 100x100 symmetric matrix
  • Minimum value: 0.094 / 0.8403 ~= 0.11186
  • Maximum value: 0.8403 / 0.094 ~= 8.939
• Doubling Attack Power is equivalent to doubling Eff_A, or reducing Eff_D by half.
  • An Attack IV cannot double a base ATK greater than 15
  • A Defense IV cannot count for half of Eff_D with base DEF greater than 15
  • The overwhelming majority of base ATKs and DEFs exceed 15

Type effectiveness

If a Pokémon is dual-typed, each is considered relative to the Attack. Remember, type effectiveness is based on the type of the Attack, not the attacker. The types of the attacker are only relevant for the STAB multiplier.

This table defines exponents. Find the row corresponding to the Attack type. Find each cell corresponding to a defender species type (there will be at least one). Add these exponents. The type effectiveness multiplier is 1.6 raised to the appropriate power. An exponent of 0 is neutral (multiplier of 1.6⁰ = 1). 1 corresponds to "super effective", -1 to "resisted", and -2 to "immune". For a dual-type species, the total exponent can range from -4 to 2, yielding a multiplier ranging from 0.15259 to 2.56. There is thus no true "immunity" (a multiplier of 0), and the Damage calculation always guarantees at least one point anyway. A -1 is a 37.5% reduction in multiplier, and -2 is almost a 61% reduction. A +1 is a 60% increase. Given that STAB is a 20% increase, we see that Attack type effectiveness is better than STAB, and that Attack type ineffectiveness negates STAB (and then some).

An interesting observation is that Attack effectiveness is 1.6x as potent as Attack resistance (60% increase vs 37.5% decrease), but Attack effectiveness is completely negated by Attack resistance (-1 + 1 == 0). For instance, an Electric Attack on a Dragon-Flying Pokémon like Dragonite is neutral, because Dragon is resistant to Electric, and Flying is vulnerable.

Attack type (rows) vs defender species type(s) (columns). Smaller numbers favor defense.

Attack	Normal	Fighting	Flying	Poison	Ground	Rock	Bug	Ghost	Steel	Fire	Water	Grass	Electric	Psychic	Ice	Dragon	Dark	Fairy	Total (Attack)
Normal	0	0	0	0	0	-1	0	-2	-1	0	0	0	0	0	0	0	0	0	-4
Fighting	1	0	-1	-1	0	1	-1	-2	1	0	0	0	0	-1	1	-1	1	-1	-3
Flying	0	1	0	0	0	0	1	0	-1	0	0	1	-1	0	0	0	0	0	1
Poison	0	0	0	-1	-1	-1	0	-1	-2	0	0	1	0	0	0	0	0	1	-4
Ground	0	0	-2	1	0	1	-1	0	1	1	0	-1	1	0	0	0	0	0	1
Rock	0	-1	1	0	-1	0	1	0	-1	1	0	0	0	0	1	0	0	0	1
Bug	0	-1	-1	-1	0	0	0	-1	-1	-1	0	1	0	1	0	0	1	-1	-4
Ghost	-2	0	0	0	0	0	0	1	0	0	0	0	0	1	0	0	-1	0	-1
Steel	0	0	0	0	0	1	0	0	-1	-1	-1	0	-1	0	1	0	0	1	-1
Fire	0	0	0	0	0	-1	1	0	1	-1	-1	1	0	0	1	-1	0	0	0
Water	0	0	0	0	1	1	0	0	0	1	-1	-1	0	0	0	-1	0	0	0
Grass	0	0	-1	-1	1	1	-1	0	-1	-1	1	-1	0	0	0	-1	0	0	-4
Electric	0	0	1	0	-2	0	0	0	0	0	1	-1	-1	0	0	-1	0	0	-3
Psychic	0	1	0	1	0	0	0	0	-1	0	0	0	0	-1	0	0	-2	0	-2
Ice	0	0	1	0	1	0	0	0	-1	-1	-1	1	0	0	-1	1	0	0	0
Dragon	0	0	0	0	0	0	0	0	-1	0	0	0	0	0	0	1	0	-2	-1
Dark	0	-1	0	0	0	0	0	1	0	0	0	0	0	1	0	0	-1	-1	-1
Fairy	0	1	0	-1	0	0	0	0	-1	-1	0	0	0	0	0	1	1	0	0
Total (Defense)	-1	0	-1	-3	-1	2	0	-4	-9	-3	-2	1	-2	1	3	-2	-1	-3	-25

The rightmost column is the sum over given Attack types (larger is better). The bottommost row is the sum over given base types (smaller is better). The rightmost, bottommost cell is the sum over all relationships; equally, it is the sum over the rightmost column; equally, it is the sum over the bottommost row. Its value of -25 indicates that type effectiveness favors the defender overall, though the most common relationship is neutrality: there are 324 total interactions, and 208 of them (~64.2%) are neutral. Note that this completely ignores e.g. type population and strength of type population.

It is interesting (surprising?) to note that different Attack types have different total strengths. Only two Attack types are strong against their own type: Ghost and Dragon. Nine are weak against their own type: Fire, Water, Grass, Electric, Ice, Poison, Psychic, Dark, and Steel. Only three Attack types have overall net effectiveness: Flying, Ground, and Rock, each with a net 1. Four types sum to -4: Grass, Bug, Normal, and Poison. Electric and Fighting have -3. Psychic has -2.

Likewise, different species types provide different total defense. Rock, Grass, Psychic, and Ice all have net weakness, especially Ice (3) and Rock (2). Fighting and Bug are neutral; each have three weaknesses balanced out by three strengths. Water, Electric, and Dragon at -2 have nothing to be embarrassed about. Fire and Poison both enjoy -3. Ghost is less generally robust than its -4 suggests, due to -2 against Normal and Fighting. Steel is pretty insane at -9, with resistance to 10 different types, weakness against three, and strong resistance to Poison. As Josef Stalin said, it's good to be Steel.

Grass eats the shit sandwich of type effectiveness as the only type both net-susceptible (1) and net-weak (-4). Subtracting the defense total from the attack total for a type yields a net core effectiveness, ranging from -5 (Grass) to a stunning 8 (Steel).

Attack type	TotalA	TotalD	Net
Normal	-4	-1	-3
Fighting	-3	0	-3
Flying	1	-1	2
Poison	-4	-3	-1
Ground	1	-1	0
Rock	1	2	-1
Bug	-4	0	-4
Ghost	-1	-4	3
Steel	-1	-9	8
Fire	0	-3	3
Water	0	-2	2
Grass	-4	1	-5
Electric	-3	-2	-1
Psychic	-2	1	-3
Ice	0	3	-3
Dragon	-1	-2	1
Dark	-1	-1	0
Fairy	0	-3	3

Dual typing

Assuming random Attack type, being a dual-type Pokémon is a benefit more often than a liability. Most types enjoy a net resistance (a negative column total), so having two of them means means greater total resistance (plus more Attack types with a STAB bonus) more often than it does less. Given that every species has exactly one or two (distinct) types, there are 18 choose 2 = 18!/2!*16! = 153 total type pairs possible plus the base 18, for a total of 171 possible species typings (not all of them are actually populated in the game). You will sometimes see 324 = 18², from 18*17 dual types plus 18 base types, but this counts e.g. Ghost-Dark and Dark-Ghost as two distinct typings. For the purpose of Attack type efficiency, order doesn't matter, so the 18*17 (the 2-permutations of 18) is irrelevant.

Of course, if your opponent can choose Attack based on your Pokémon, dual types gives them more opportunity to select an effective attack.

Against a given typing, an Attack could theoretically have an exponent as low as -4 and as high as 2. No Attack type is very ineffective against two different types, though, so the effective minimum is -3.

Define BN2 as the number of types against which an Attack is very ineffective, BN1 for ineffective, and BP1 for effective (-2, -1, and 1 from the table above). B0 = 18 - BN2 - BN1 - BP1.

• -3: very ineffective against one type, and ineffective against the other: BN2*BN1
  • Since BN2 is always 0 or 1, this reduces to 0 or BN1
• -2: very ineffective against the single type, or very ineffective against one type and neutral against the other, or ineffective against both types: BN2*(B0+1) + C(BN1, 2)
• -1: ineffective against the one type, or ineffective against one type and neutral against the other, or very ineffective against one type and effective against the other: BN1*(B0+1) + BN2*BP1
• 0: neutrality against all types, or effectiveness against one combined with ineffectiveness against the other: B0 + C(B0, 2) + BP1*BN1
• 1: effective against the single type, or effective against one of two types while neutral against the other: BP1*(B0 + 1)
• 2: effective against both types (2 cannot be accomplished against a singly-typed species): C(BP1, 2)

The sum over these five values will always be 171.

As an example, Normal is BN2 against one type, BN1 against two types, and BP1 against zero:

• B0 is 15
• -3 against Ghost-Steel and Ghost-Rock (2)
• -2 against Ghost, Steel-Rock, and Ghost-{anything but Steel or Rock} (17)
• -1 against Steel, Rock, Steel-{anything but Rock or Ghost}, and Rock-{anything but Steel or Ghost} (34)
• 0 against all other typings (118)

The scaled total sums over the products of typing count and net exponent.

Attack type	BN2	BN1	B0	BP1	-3	-2	-1	0	1	2	Total (scaled)
Normal	1	2	15	0	2	17	34	118	0	0	-74
Fighting	1	6	6	5	6	22	41	51	42	10	-41
Flying	0	2	13	3	0	1	28	97	42	3	18
Poison	1	4	11	2	4	18	50	74	24	1	-72
Ground	1	2	10	5	2	12	27	65	55	10	18
Rock	0	3	11	4	0	3	36	78	48	6	18
Bug	0	7	8	3	0	21	63	57	27	3	-72
Ghost	1	1	14	2	1	15	17	107	30	1	-18
Steel	0	4	11	3	0	6	48	78	36	3	-18
Fire	0	4	10	4	0	6	44	71	44	6	0
Water	0	3	12	3	0	3	39	87	39	3	0
Grass	0	7	8	3	0	21	63	57	27	3	-72
Electric	1	3	12	2	3	11	41	89	26	1	-44
Psychic	1	2	13	2	2	15	30	95	28	1	-36
Ice	0	4	10	4	0	6	44	71	44	6	0
Dragon	1	1	15	1	1	16	17	121	16	0	-42
Dark	0	3	13	2	0	3	43	96	28	1	-19
Fairy	0	3	12	3	0	3	39	87	39	3	0

FIXME: analyze population of typings

The actual multipliers end up being:

Type effectiveness	Multiplier	With STAB
-3	0.244	0.2928
-2	0.390625	0.46875
-1	0.625	0.75
0	1	1.2
1	1.6	1.92
2	2.56	3.072

Minimal spanning sets

It is useful to know the sets of types which can provide efficiency against all types, and the sets of types which can provide resistance to all types. It is particularly useful to know the smallest such sets.

For attack, first we determine independent requirements. To do so, add types which could not have been covered yet:

• Normal can only be covered by Fighting, so start there.
  • Fighting adds Rock, Steel, Ice, and Dark (5 total)
• Water requires Grass or Electric
  • Grass adds Ground (7 total)
  • Electric adds Flying (7 total)
    • We now have N, R, S, I, D, Water, (Ground or Flying)
• Fairy requires Poison or Steel
  • Poison adds Grass (9 total)
  • Steel adds nothing (8 total)
    • We now have N, R, S, I, D, W, (Gnd or Fly), Fairy, Grass
• Ghost requires Ghost or Dark
  • Ghost adds Psychic (11 total)
  • Dark adds Psychic (11 total)
    • We now have N, R, S, I, D, W, (Gnd or Fly), Fairy, Grass, Ghost, Psychic
• Fire requires Ground, Rock, or Water
  • Water adds Ground if we don't have it (12-13 total)
  • Ground adds Electric and Poison (14 total)
• Dragon requires Ice, Dragon, or Fairy
  • Dragon adds nothing (15 total)
  • Fairy adds Fighting (16 total)
  • Ice adds Ground if we don't have it (16 total, locks in Electric)
• Fighting requires Flying or Psychic
  • Psychic adds nothing (17)
  • Flying adds Bug (18, done)

So, we can cover all target types with 7 attack types: Fighting, Electric, Poison, (Ghost or Dark), Ground, Ice, and Flying. There are probably other small sets.

FIXME: Now, we know the target type for Raids and Max battles, so this is only really relevant for PvP. We can only bring 3 Pokémon to a PvP battle, but each can have a different type of Fast Attack and (technically two different) Charged Attacks. So it would be nice to know three sets of two (or three) where one of the Attacks is efficient against a type, and the other class of Attacks is not inefficient against that same type.

XP rewards

Many events in Pokémon Go result in XP. Lucky Eggs double XP rewards while active (only one can be used at a time). Certain events double XP as well (this stacks with a Lucky Egg). Research can award various amounts of XP; a Research Breakthrough always awards 3000 XP.

Things which typically do not reward XP include:

• opening the game or leaving it running (whether moving or stationary)
• accepting or sending a Friend request
• interactions with Team Rocket
• PvP battles
• buddy hearts and buddy level progression
• trading Pokémon
• use of berries in an encounter
• creation of a Route or Pokéstop
• any non-capturing throws in an encounter
• opening gifts (from Friends or Mateo)
• receiving items (from gifts, Pokéstops, route completion, or battles)
• using items
• and transferring Pokémon to the Professor for soul harvesting.

Of course, XP can result when these are part of Research tasks.

Encounters

An "encounter" includes all interactions with a distinct Pokémon, including those following wins against Team Rocket and those following wins in Raids and Max Battles. Leaving the encounter screen and returning to the same Pokémon, even multiple times, is all one encounter. An encounter does not end until the Pokémon is captured or flees.

• If the Pokémon flees, the reward is 25 XP.
• If the Pokémon is captured, the reward is 100 XP, plus zero or more bonuses:
  • A possible bonus for capture with a high-quality throw:
    • 1000 XP for Excellent, or
    • 100 XP for Great, or
    • 20 XP for Nice.
  • 20 XP for capture with a curveball.
  • 50 XP for capture with the first throw of the encounter.
  • 100 XP for 100th collection of each species (all subtypes count as one species) ("Collector")
  • 300 XP for using AR Plus ("Expert Handler")
  • A possible bonus for first capture of the day:
    • 6000 XP for a 7 day streak of at least one capture (the streak resets), or
    • 1500 XP otherwise.
  • 1000 XP for capture with a Master Ball.

Hatching eggs

Hatching an Egg yields XP corresponding to the class of the Egg as expressed in kilometers.

Km	XP
2	500
5	1000
7	1000
10	2000
12	4000

Battles

No XP is awarded for battling Team Rocket, nor PvP games.

Event	XP
Giving a berry to a Pokémon in a gym	50

Friendship

200 XP is awarded whenever one sends a Gift (this is awarded when the Gift is sent, not when it is opened).

XP is awarded whenever a friendship reaches a new level.

Level	XP	Cumulative days	Max XP per Friend-day
Good Friend	3000	1	3000
Great Friend	10000	7	1857
Ultra Friend	50000	30	2100
Best Friend	100000	60	1811

Routes

Completing a Route always awards XP. The first Route completed on a given day yields 4000 XP. Subsequent Routes award 2000 XP each. Route awards are limited only by time.

A streak of seven days with completed Routes awards 12000 XP, and resets the streak counter.

Oddities and irregularities

Adventure Effects

Pokémon taught certain Attacks can use them outside of battle for a cost in Stardust and that Pokémon's Candy. These are called Adventure Effects, and only one can be active at a time per Trainer.

Attack	Cost	Time per use	Effects
Roar of Time	5k + 5 Dialga Candy	6 min
Spacial Rend	5k + 5 Palkia Candy	10 min
Ice Burn	5k + 5 Kyurem Candy	10 min
Freeze Shock	5k + 5 Kyurem Candy	10 min
Sunsteel Strike	3k + 5 Necrozma Candy	10 min
Moongeist Beam	3k + 5 Necrozma Candy	10 min

Evolution

Evolution does not preserve Attacks, though it does preserve IVs. Evolution preserves Max Move levels. Evolution generates 1 Candy of the Pokémon's Candy type. Evolution counts as capturing the target Pokémon. Shiny Pokémon stay Shiny through Evolution, and Evolution cannot Shiny up a non-Shiny Pokémon. A Pokémon can be Evolved even at 0 HP. A freshly-Evolved Pokémon has full HP. Evolution does not change Level. Evolution typically raises CP, but not always (and it might even lower it). Evolution preserves traded status.

Evolving some Pokémon has requirements beyond (or in place of) Candy. This list is not exhaustive. The special requirements generally must be fulfilled while the lower Pokémon is your active buddy, though they needn't be "active" (i.e. on the map screen). An exception is when the Pokémon must be walked a certain distance (it must be on the map for the walking to count). Evolution which requires items consumes those items.

Target species	Requirements
Kingdra	Seadra + 100 Horsea Candy + Dragon Scale
Porygon2	Porygon + 25 Porygon Candy + Upgrade
Porygon-Z	Porygon2 + 100 Porygon Candy + Sinnoh Stone
Scizor	Scyther + 50 Scyther Candy + Metal Coat
Steelix	Onix + 50 Onix Candy + Metal Coat
Politoed	Poliwhirl + 100 Poliwag Candy + King's Rock
Slowking	Slowpoke + 50 Slowpoke Candy + King's Rock
Flapple	Applin + 200 Applin Candy + 20x Tart Apples
Appletun	Applin + 200 Applin Candy + 20x Sweet Apples
Kingambit	Bisharp + 100 Pawniard Candy + defeat 15 Dark- or Steel-type in raids
Annihilape	Primeape + 100 Mankey Candy + defeat 30 Psychic- or Ghost-type in battles
Florges	Floette + 100 Flabébé Candy + earn 20 hearts
Armarouge	Charcadet + 50 Charcadet Candy + defeat 30 Psychic-type in battles
Ceruledge	Charcadet + 50 Charcadet Candy + defeat 30 Ghost-type in battles
Overqwil	Hisuian Qwilfish + 50 Qwilfish Candy + win 10 raids
Rapid Strike Style Urshifu	Kubfu + 200 Kubfu Candy + defeat 30 Water-type in raids or Max battles
Single Strike Style Urshifu	Kubfu + 200 Kubfu Candy + defeat 30 Dark-type in raids or Max battles
Malamar	Inkay + 50 Inkay Candy + turning the mobile device upside-down
Trevenant	Phantump + 200 Phantump Candy OR the Phantump was traded
Haunter	Gengar + 100 Gastly Candy OR the Gengar was traded
Graveler	Golem + 100 Geodude Candy OR the Golem was traded
Alakazam	Kadabra + 100 Abra Candy OR the Kadabra was traded
Machamp	Machoke + 100 Machop Candy OR the Machoke was traded

Eevolution

Eevee's evolution is complex, terminating in one of eight different Pokémon. Alternatively, one time per target per Trainer, the evolution type can be specified by naming the Eevee prior to evolving it. All evolutions require 25 Eevee Candy.

Target	Type	Name	Requirements
Espeon	Psychic	Sakura	Walk a Buddy Eevee 10km, have that Eevee as your Buddy at the time of evolution, and evolve at day
Umbreon	Dark	Tamao	Walk a Buddy Eevee 10km, have that Eevee as your Buddy at the time of evolution, and evolve at night
Leafeon	Grass	Linnea	Evolve near an active Mossy Lure
Glaceon	Ice	Rea	Evolve near an active Glacial Lure
Sylveon	Fairy	Kira	Earn 70 Hearts with the Eevee as your Buddy
Flareon	Fire	Pyro	No requirements
Vaporeon	Water	Rainer	No requirements
Jolteon	Electricity	Sparky	No requirements

I am unsure of the precedence among the first five options. If none of them are met, the target is selected randomly among Flareon, Vaporeon, and Jolteon.

Note that Level 42 requires evolving one of each Eevee type (while at Level 41).

Strategy

Some parts of this assume you're in an urban area or otherwise have access to many spawns and Pokéstops per hour, but much applies to all players.

Leveling up

Leveling up (through Level 40) is strictly a matter of accumulating XP. Level 2 requires only one thousand XP. Level 40 requires five million beyond Level 39, for twenty million total. Levels 41 through 50 have additional, formidable Research requirements beyond their already brutal XP demands.

The mathematics of Friendship

State increases upon the first interaction of any kind between two Friends on a given day (how does this work with different time zones? Dank (talk) 09:15, 9 May 2025 (UTC)). It can only be advanced once per day. There is a single level for each pair of Friends. Removing a friend does not reset the friendship level until 120 days (of Sodom?) have passed. Adding the friend back during this period will reset the counter. An interaction for purposes of Friend state is:

• Opening (not sending) a Gift
• Participating together in a raid or Max battle
• A PvP battle
• A trade

Since the XP bonuses of Friend transitions are large, Lucky Eggs can be effectively employed before a Level change. This can be more effective if several Levels change within the Lucky Egg's lifespan, which can be accomplished by a burst of Gift opening for synchronized Friends, i.e. a set of Friends all at the same state.

Friends are essentially unlimited resources thanks to online bazaars. Up to 115 new Gifts are available each day via Pokéstops and a Buddy. You can open up to 20 Gifts per day, and carry 20 at a time (they do not count against your Bag). There is no limit on sending Gifts. Gift XP is maximized by adding 135 friends each day, sending 115 Gifts (assuming all are opened), and opening 20 Gifts (assuming at least this many are received). All 135 friends will become Good Friends, providing 405,000 XP per day before being immediately harvested. This is of course all rather tedious, and leaves no room for actual long-term friends (with benefits beyond XP). I tend to add a dozen people or so every few days, interact through the Ultra Friend level (requiring thirty days), and remove them afterwards. This yields 63,000 XP per harvested friend, ideally 2100 XP per Friend-day, 70% of the optimal 3k with less than 4% of the work. Furthermore, a Lucky Egg applied to the large 50k XP bonus yields XP that would require synchronizing 17 transitions to Good Friends, which I'd rather drink the bathroom cleaner.

For purposes of battle bonuses and reduced Stardust costs to trade, you want to make and keep some Best Friends.

For purposes of prioritizing your limited Gift openings, if a Friend has a blue ring around their headshot, you have interacted with them today, and opening their Gift will not advance the state. If there is a grey arrow pointing right, that Friend has an unopened Gift from you.

It's all about the level

Appraisal shows only CP, and IVs. The former is actively misleading, while the latter are largely inconsequential. Oh, it also shows HP, which is quite useful, and kinda shows level in the shittiest way possible.

CP is a great big lie

CP = ⌊max(10, Eff_A * √Eff_D * √Eff_S * CPM² / 10)⌋

CP is a terrible stat for overall fighting quality (it's not so bad for raids, see below). For PvP, it ought only be regarded as a cost function, not a measure of quality. CP uses the square of the CPM...but CPMs are always less than 1, thus squaring them reduces them. CP thus undervalues level (which is linear when calculating effective stats), while overvaluing Eff_A (which gets divided by Eff_D when calculating damage). It overvalues Eff_A a lot. Some authors refer to Eff_A counting "double", but this is a non-linear difference. The max Eff_A would be 414+15=429; its square root is ~21, a reduction of over 95%! The lowest Eff_A is 10; its square root is ~3.2, a reduction of about 68%. Eff_A isn't being counted twice as much as other stats, but many times more.

This is why you can beat Team Rocket Pokémon with 3x and 4x your CP. It's almost all in ATK, which is getting divided by DEF. They can hit you hard, but they're stupid, and your Charged Attacks and type counters beat them down.

Defense and HP aren't "more important" in PvP. Rather, ATK contributes linearly to this cost function, whereas they contribute their square roots. You can thus get more levels for the same CP cost, and levels affect all three effective stats. The perfect IVs for PvP are *not* 0-15-15 as so often claimed, but actually I-J-K, where I, J, and K are the largest values that don't push you above the target CP threshold, with precedence given to maximizing K, and then J. What is much more important is species selection. Avoid high ATK. Prefer high Stamina. Attack isn't simply "more important" in PvE; rather, stats have no cost (as there are no CP ceilings, aside from some very specific endgame). You thus want all the stats you can get. Since raids allow you to absorb effectively infinite damage, but have a time component, strong ATK is indeed critical (justifying to a degree its overvaluation in CP)--but IVs won't get you there, as raid bosses typically have DEF >> 15!

IVs ain't shit

IVs are largely inconsequential for ATK and DEF, due to usually being a small percentage of the effective stat's total range. Their impact is further reduced (and possibly eliminated) by the floor function used to compute damage. Read that again: the use of the floor function when calculating damage means a 15 IV might have absolutely no impact vis-à-vis a 0. One more time: no, there is not always "some small advantage" to a higher IV. If you insist that there always is, either you or I do not understand math. spoiler: it is you

The most beneficial IV, by far, is STA.

FIXME Demonstrate that IV changes usually result in zero change to damage for powerful Pokémon (i.e. those with large ATK/DEF)

Similarly, the most important stat overall is STA, as it is the only one which is not freely scaled. Note, however, that the CPM combined with the floor function imply hit points only actually growing by 1 for every 1/CPM points added to Eff_S. Read that again: An IV_S of n + 1 might have absolutely no improvement over n.

Especially for powerful Pokémon, Attack Power, STAB, and type effectiveness have much greater impact than any difference in IVs.

Type effectiveness isn't everything

Type effectiveness, STAB, and weather bonuses are powerful (the former two in PvP especially), but they don't necessarily beat out a truly large base stat or level difference. If there's a Weather Bonus, that's a multiple of 1.2. If you have an ATK difference greater than 20% of the opponent's DEF, that's a higher damage (and remember that Weather Bonus doesn't apply to most PvP).

Towards a better CP

I've argued that CP is irredeemably busted as a single summary of power. Some people like the stat product, the product of ATK, DEF, and STA (or, for an individual Pokémon, the product of Eff_A, Eff_D, and Eff_S). I disagree.

The usefulness of ATK and DEF fall off as they grow. Assume you're attacking an opponent with 100 DEF. The ATK/DEF ratio (ignoring IVs and CPM) for an ATK of 1, 50, 100, 150, 200, and 250 are 0.01, 0.5, 1, 1.5, 2, and 2.5 (the likely effect of CPM scaling is to reduce this ratio). This ratio is then used in the product determining Damage, which (as noted before) is dominated by the particular Attack's Power. Against a DEF of 100, 20 more points of ATK are equivalent to a weather bonus. Against a DEF of 100, if the rest of the product (P * M * M_M) is 5, each additional point of Damage (equivalent to a hit point) requires an extra 20 ATK. It's not exactly a 20:1 mapping due to CPM scaling of STA, but for this instance, each STA point of the defender is probably more useful than each ATK point of the attacker.

This does break down if ATK >> DEF. The ATK/DEF ratio can grow quite large (if DEF >> ATK, you're inflicting only a few points of Damage per Attack, but never zero). An Eff_A of 200 against an Eff_D of 20 yields a ratio of 10, a very serious multiplier (it's important to remember that CPM is generally going to drive wildly unbalanced ratios towards 1). But a DEF of at least 140 means an attacker of equal level requires 280 ATK to get a 2x multiplier. More than half of all species have a base DEF of 140, while only a few have an ATK of 280+. Adding a few ATK is likely to get lost in the floor function when calculating actual Damage, whereas a few more STA can mean surviving another attack. When DEF >> ATK, the effect is most pronounced on Charged Attacks, as the guaranteed point of Damage represents a lesser return on the Power. In such a case, it might behoove an attacker in PvE mode to dispense with Charged Attacks entirely. In any case, it is rare that such extreme deltas in base stats exist.

IVs are more important for low ATK/DEF than high. If using a species with an absurdly low base ATK or DEF, a strong IV can be a major assistance.

It would probably be best to define a Win Expectation for each pair of species. Better yet, for each pair of species-levels. Still better, for each pair of species-levels-IVs. Oh shit, also for Attacks. Ideally, for any two sets of individual Pokémon, in any configuration of bonus multipliers (weather, allies, etc.).

But this requires knowing individual opponents. Assuming we must speak of Pokémon in an opponent-independent way, we have two serious problems:

• PvE and PvP reward two completely different things, and
• How do we include type effectiveness?

Regarding the first, I think a single stat simply loses too much information (this is why CP is garbage for PvP, and a silly gate for leagues). CP is more or less fine for PvE, I guess. So I'm going to introduce a new stat, Dankness (DvP).

Digression: stat product is also bad

For PvP, when you're working against a CP ceiling, the reduced cost of DEF and STA should be reflected. Stat product has the advantage of being simple, but when working under a CP ceiling, I think it ought be more like √A*D*S. If you think they're equally useful (I disagree, but I'll allow it), then consider this: a Pokémon with A = 10, D = 2500, S = 2500 has CP growth of 110 (10 + 50 + 50) but a stat product of 62.5M. A Pokémon with A = 100, D = 25, S = 25 has the same CP growth (100 + 5 + 5) but a product of 62.5k, one thousand times less the stat product of the first Pokémon. Think this unrealistic? OK, A = 50, D = 64, S = 64. CP growth is 66. The same CP growth is seen from A = 60, D = 9, S = 9. The stat products are 204800 vs 4860, more than a 42x multiple. The point is, DEF and STA are very cheap compared to ATK in terms of CP.

Dankness vP

We are defeated when the integral of suffered Damage over time meets or exceeds our hit points. We win when the integral of inflicted Damage over time exceeds our opponent's hit points. The smaller time decides the battle.

Our stat will ideally be dominated by two things, equally:

• How long it takes to kill us (DEF and STA), and
• Our ability to inflict Damage per unit time (ATK and Attacks)

As these are the two things which ultimately decide each PvP battle (assuming perfect play). The difference between two calculations ought reflect the expected change in these things.

Our ability to inflict Damage is a function of Eff_A, opponent Eff_D, our Attacks (Power, Time, Energy, and Cost), and the multipliers (especially type effectiveness). We don't know anything about our opponent, though. We could assume universal probability of opponent, and average over them, but that's a ridiculous assumption. Even something like "fewer weaknesses are better than more weaknesses" is hard to justify, because fewer weaknesses are not necessarily better for a given set of opponents (it could be argued that fewer weaknesses impacts opponent selection). So we're going to leave that out for now. We will, however, consider STAB, and furthermore factor resistance into Power expectations.

FIXME yes, and...?

Can Pokémon Go PvP be solved?

Define a 3PC as a collection of three individual Pokémon. Given the rule that only one Pokémon at a time may be Mega per Trainer, only one member of a 3PC can be in Mega mode (the Mega multiplier doesn't apply in PvP anyway). This set can be ordered six different ways. We call a 3PC with an order a 3POC (not a 3PoC, which would be three Pokémon of color, aka "shinies").

I would like to know whether there exists a 3POC that

• assuming perfect play on the part of both Trainers,
• for every opposing 3POC,

does not lose. I think that this is unlikely, but possession of such a trio would "solve" PvP.

Should none exist, I would like to know whether there exists a 3PC that

• assuming perfect play on the part of both Trainers,
• for every opposing 3POC,

has some 3POC which does not lose.

Should none exist, I would like to know the smallest collection from which, for each opposing 3POC, a 3POC can be selected which does not lose.

External links

• Pokémon GO Spawn Mechanics by Zeroghan on GOHUB
• CP Multiplier on Gamepress
• Type Effectiveness in Battle from the Pokémon GO Help Center
• Mastering the Turn System in Pokémon GO PvP by avrip on GOHUB
• Pokebattler is legit