User:333-blue/sandbox/Pokémon GO formulas

In-game main formulas:

Capture Rate formula

$RealCaptureRate=1-[1-min(1,{\frac {BCR}{2*CPM}})]^{Multipliers}$ $Multipliers=BallTypeFactor*Curve*Berry*Throw*Medal$

$Pok{\acute {e}}BallFactor=1$ $GreatBallFactor=1.5$ $UltraBallFactor=2$

$NoCurve=1$ $Curve=1.7$

$NoBerry=1$ $RazzBerry=1.5$ $GoldenBerry=2.5$

$Nice\thickapprox 1.15$ $Great\thickapprox 1.5$ $Excellent\thickapprox 1.85$

$SingleTypePok{\acute {e}}mon=1+Medal$ $DoubleTypePok{\acute {e}}mon=1+{\frac {Medal}{2}}$

$Bronze=0.1$ $Silver=0.2$ $Gold=0.3$

Ball Catch Rate

$BallCarchRate=1-[1-min(1,{\frac {BCR}{2*CPM}})]^{BallTypeFactor}$

CP Multiplier Table

Power Up Level	Next Power Up		CPM
Power Up Level	Stardust	Candy	CPM
1	200	1	0.094
2	200	1	0.1351374318
3	200	1	0.16639787
4	200	1	0.192650919
5	400	1	0.21573247
6	400	1	0.2365726613
7	400	1	0.25572005
8	400	1	0.2735303812
9	600	1	0.29024988
10	600	1	0.3060573775
11	600	1	0.3210876
12	600	1	0.3354450362
13	800	1	0.34921268
14	800	1	0.3624577511
15	800	1	0.37523559
16	800	1	0.3875924064
17	1000	1	0.39956728
18	1000	1	0.4111935514
19	1000	1	0.42250001
20	1000	1	0.4335116883
21	1300	2	0.44310755
22	1300	2	0.4530599591
23	1300	2	0.46279839
24	1300	2	0.4723360832
25	1600	2	0.48168495
26	1600	2	0.4908558003
27	1600	2	0.49985844
28	1600	2	0.508701765
29	1900	2	0.51739395
30	1900	2	0.5259425113
31	1900	2	0.53435433
32	1900	2	0.542635767
33	2200	2	0.55079269
34	2200	2	0.5588305763
35	2200	2	0.56675452
36	2200	2	0.574569153
37	2500	2	0.58227891
38	2500	2	0.5898879171
39	2500	2	0.59740001
40	2500	2	0.6048188139
40.75 (raid boss tier 1)	—		0.61
41	3000	3	0.61215729
42	3000	3	0.6194041117
43	3000	3	0.62656713
44	3000	3	0.6336491729
45	3500	3	0.64065295
46	3500	3	0.6475809666
47	3500	3	0.65443563
48	3500	3	0.6612192524
49	4000	3	0.667934
49.35 (raid boss tier 2)	—		0.67
50	4000	3	0.6745818959
51	4000	4	0.68116492
52	4000	4	0.6876849236
53	4500	4	0.69414365
54	4500	4	0.70054287
55	4500	4	0.70688421
56	4500	4	0.713169119
57	5000	4	0.71939909
58	5000	4	0.7255756036
58.7 (raid boss tier 3)	—		0.73
59	5000	4	0.7317
60	5000	4	0.734741036
61	6000	6	0.73776948
62	6000	6	0.7407855738
63	6000	6	0.74378943
64	6000	6	0.7467812109
65	7000	8	0.74976104
66	7000	8	0.7527290867
67	7000	8	0.75568551
68	7000	8	0.7586303783
69	8000	10	0.76156384
70	8000	10	0.7644860647
71	8000	10	0.76739717
72	8000	10	0.7702972656
73	9000	12	0.7731865
74	9000	12	0.7760649616
75	9000	12	0.77893275
76	9000	12	0.7817900548
77	10000	15	0.78463697
78	10000	15	0.7874735776
78.9 (raid boss tier 4)	—		0.79
79	10000	15	0.79030001
80	10000	15	0.7931163638
81	—		0.79592275
Italic text shows that this can only be gotten through bugs/hacks/tips.
Bold text shows that this is the maximum level you can get normally.

Updated

Level CPM Stardust
1	0.0939999967813492	200
1.5	0.1351374320893390	200
2	0.1663978695869450	200
2.5	0.1926509131553250	200
3	0.2157324701547620	400
3.5	0.2365726514248220	400
4	0.2557200491428380	400
4.5	0.2735303721065720	400
5	0.2902498841285710	600
5.5	0.3060573813898630	600
6	0.3210875988006590	600
6.5	0.3354450319964510	600
7	0.3492126762866970	800
7.5	0.3624577366099390	800
8	0.3752355873584750	800
8.5	0.3875924077138780	800
9	0.3995672762393950	1000
9.5	0.4111935532161000	1000
10	0.4225000143051150	1000
10.5	0.4329264205125090	1000
11	0.4431075453758240	1300
11.5	0.4530599481650490	1300
12	0.4627983868122100	1300
12.5	0.4723360853112780	1300
13	0.4816849529743190	1600
13.5	0.4908558071795490	1600
14	0.4998584389686580	1600
14.5	0.5087017489616000	1600
15	0.5173939466476440	1900
15.5	0.5259425161103220	1900
16	0.5343543291091920	1900
16.5	0.5426357538035990	1900
17	0.5507926940917970	2200
17.5	0.5588305844903850	2200
18	0.5667545199394230	2200
18.5	0.5745691281453700	2200
19	0.5822789072990420	2500
19.5	0.5898879078889450	2500
20	0.5974000096321110	2500
20.5	0.6048236486651710	2500
21	0.6121572852134700	3000
21.5	0.6194041079582340	3000
22	0.6265671253204350	3000
22.5	0.6336491787485760	3000
23	0.6406529545784000	3500
23.5	0.6475809713865540	3500
24	0.6544356346130370	3500
24.5	0.6612192658058590	3500
25	0.6679340004920950	4000
25.5	0.6745818856474920	4000
26	0.6811649203300480	4000
26.5	0.6876849012553730	4000
27	0.6941436529159550	4500
27.5	0.7005429010330630	4500
28	0.7068842053413390	4500
28.5	0.7131690748738230	4500
29	0.7193990945816040	5000
29.5	0.7255755869151540	5000
30	0.7317000031471250	5000
30.5	0.7347410385504290	5000
31	0.7377694845199580	6000
31.5	0.7407855797371360	6000
32	0.7437894344329830	6000
32.5	0.7467811972477650	6000
33	0.7497610449790950	7000
33.5	0.7527290997322810	7000
34	0.7556855082511900	7000
34.5	0.7586303702098510	7000
35	0.7615638375282290	8000
35.5	0.7644860495921800	8000
36	0.7673971652984620	8000
36.5	0.7702972936773620	8000
37	0.7731865048408510	9000
37.5	0.7760649470649920	9000
38	0.7789327502250670	9000
38.5	0.7817900507676660	9000
39	0.7846369743347170	10000
39.5	0.7874736085132750	10000
40	0.7903000116348270	10000
40.5 
CPMS = 0.00283151865

Power Up Level

$Pok{\acute {e}}monCurrentLevel=(1+PowerUpLevel)\div 2$ $PowerUpLevel=Pok{\acute {e}}monCurrentLevel\times 2-1$

$Minimum=1$ $Maximum=TrainerCurrentLevel\times 2+2$

Gym Damage Formula

$Damage=[Floor({\frac {1}{2}}\cdot Power\cdot {\frac {ATK}{DEF}}\cdot STAB\cdot Effective)]+1$ $ATK=(BaseAttack+AttackIV)\cdot CPMulti$ $DEF=(BaseDefend+DefendIV)\cdot CPMulti$ $HP=(BaseStamina+StaminaIV)\cdot CPMulti$ $Gym=(BaseStamina+StaminaIV)\cdot CPMulti\cdot 2$

Example between a 15/15/15 IV Level 39 Vaporeon with WG/HP and a 0/0/0 IV Level 1 Dragonite with DB/DP

Water Gun's DPS and DPU:
$WGDPS={\frac {[Floor({\frac {1}{2}}\cdot 6\cdot {\frac {(205+15)\cdot 0.78463697}{(201+0)\cdot 0.094}}\cdot 1.25\cdot 0.8)]+1}{0.5}}={\frac {27+1}{0.5}}=56$
$WGDPU=[Floor({\frac {1}{2}}\cdot 6\cdot {\frac {(205+15)\cdot 0.78463697}{(201+0)\cdot 0.094}}\cdot 1.25\cdot 0.8)]+1=27+1=28$
The Dragonite's HP and at a Gym:
$HP=Floor(182\cdot 0.094)=17$
$Gym=[Floor(182\cdot 0.094)]\cdot 2=34$
Uses:
$Uses=Ceil({\frac {34}{28}})=2$
Seconds:
$Seconds=0.5\cdot 2=1$
So it will take 1 second (or to say 2 uses) before the Dragonite faints.

In this situation, the Vaporeon wins the match easily.