User:333-blue/sandbox/Pokémon GO formulas

In-game main formulas:

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

$$Pok\acute{e} Ball Factor = 1$$ $$Great Ball Factor = 1.5$$ $$Ultra Ball Factor = 2$$

$$NoCurve = 1$$ $$Curve = 1.7$$

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

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

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

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

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

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
$$Pok\acute{e}monCurrentLevel=(1+PowerUpLevel)\div2$$ $$PowerUpLevel=Pok\acute{e}monCurrentLevel\times2-1$$

$$Minimum=1$$ $$Maximum=TrainerCurrentLevel\times2+2$$

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 G ym : $$HP=Floor(182 \cdot 0.094)=17$$ $$Gym=[Floor(182 \cdot 0.094)] \cdot 2=34$$ 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 V aporeon wins the match easily.