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Pokémon Go

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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.

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)

Essential constants

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. CPMs range from 0.094 to 0.8403. For non-integer levels, CPM(L + 0.5) = √((CPM(L) + CPM(L + 1)) / 2).

Pokémon levels and CPMs
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 0.792803968 10000
41 0.79530001 11000
41.5 0.797800015 11000
42 0.8003 11000
42.5 0.802799995 11000
43 0.8053 12000
43.5 0.8078 12000
44 0.81029999 12000
44.5 0.812799985 12000
45 0.81529999 13000
45.5 0.81779999 13000
46 0.82029999 13000
46.5 0.82279999 13000
47 0.82529999 14000
47.5 0.82779999 14000
48 0.83029999 14000
48.5 0.83279999 14000
49 0.83529999 15000
49.5 0.83779999 15000
50 0.84029999
50.5 0.84279999
51 0.84529999

Additionally, each Pokémon species has three base stats defined at each level:

FIXME add full species table

Effective stats

Each individual Pokémon augments its base species stats with three individual values (IVs) ranging from 0 to 15. Adding the former to the latter and scaling by the appropriate CPM generates an effective attack EffA, effective defense EffD, and maximum HP MHP for that Pokémon, all positive rationals.

  • Effx = (Basex + IVx) * CPM(Level) = Basex * CPM(Level) + IVx * CPM(Level)

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

FIXME need hitpoint calculation

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 a PvE (raids, gyms, Max) or PvP battle (including scraps with Team Rocket).

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 EffA, the defender's EffD, two multipliers M and MM, 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 MM is different depending on whether the battle is PvE or PvP.

PvE mode

Multiplier MM is defined as the product of

  • 0.5
  • 0.25 if the Attack is dodged, 1 otherwise
  • 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 MM is defined as the product of

  • 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 EffA, EffD, M, and MM are positive rationals.

Damage = ⌊P * EffA / EffD * M * MM⌋ + 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 EffA, or reducing EffD by half.
    • An Attack IV cannot double a base ATK greater than 15
    • A Defense IV cannot count for half of EffD with base DEF greater than 15
    • The overwhelming majority of base ATKs and DEFs exceed 15

Type effectiveness

Attacker Normal
Normal
Fire
Water
Grass
Electric
Ice
Fighting
Poison
Ground
Flying
Psychic

Catch rate

Stardust rewards

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). You can open up to 30 and send up to 200 Gifts per day.

XP is awarded whenever a friendship reaches a new level.

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

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.

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.

Strategy

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

Friends and Gifts are essentially unlimited resources, the former thanks to online bazaars, the latter due to their ready availability from Pokéstops. Friend system XP is maximized by adding 220 friends each day, sending 200 Gifts (assuming all are opened), and opening 20 Gifts (assuming at least this many are received). All 220 friends will become Good Friends, providing 660,000 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.

It's all about the level

Appraisal shows only CP and IVs. The former is actively misleading, while the latter are largely inconsequential.

CP is a great big lie

CP = ⌊max(10, EffA * √EffD * √MHP * 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 EffA (which gets divided by EffD when calculating damage). It overvalues EffA a lot. Some authors refer to EffA counting "double", but this is a non-linear difference:

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 important 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 scaled.

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

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