Klik's PokeGo Leveling Math
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Hey Folks! If you haven't heard yet, the datamining is in. If the datamining is correct, the level cap is 40, with the cumu exp at 40 being 20M. My projection showed lvl 40 cumu being 20.2M, and it also showed that any level much beyond 40 would take FAR too long to reach, so I have to conclude that the datamining is accurate. I'll leave the rest of this sheet untouched, but that data is in!!
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Level
Next Level
Exp Requirement
Exp Req % Delta
Cumulative XP
Cumu XP % Delta
10
12 1,000 NA 1,000 NA
11
23 2,000 100% 3,000 200%
12
34 3,000 50% 6,000 100%
13
45 4,000 33% 10,000 67%
14
56 5,000 25% 15,000 50%
15
67 6,000 20% 21,000 40%
16
78 7,000 17% 28,000 33%
17
89 8,000 14% 36,000 29%
18
910 9,000 13% 45,000 25%
19
1011 10,000 11% 55,000 22%
20
1112 10,000 0% 65,000 18%
21
1213 10,000 0% 75,000 15%
22
1314 10,000 0% 85,000 13%
23
1415 15,000 50% 100,000 18%
24
1516 20,000 33% 120,000 20%
25
1617 20,000 0% 140,000 17%
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1718 20,000 0% 160,000 14%
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1819 25,000 25% 185,000 16%
28
1920 25,000 0% 210,000 14%
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2021 50,000 100% 260,000 24%
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2122 75,000 50% 335,000 29%
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2223 100,000 33% 435,000 30%
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2324 125,000 25% 560,000 29%
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2425 150,000 20% 710,000 27%
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2526 190,000 27% 900,000 27%
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2627 200,000 5% 1,100,000 22%
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2728 250,000 25% 1,350,000 23%
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2829 300,000 20% 1,650,000 22%
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2930 350,000 17% 2,000,000 21%
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3031 500,000 43% 2,500,000 25%
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3132 500,000 0% 3,000,000 20%
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Projected Levels
Projected Level XP Req
Projected Cumulative XP
YEAR lvl is reached at 100k XP/Day
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31 380,000 3,100,000 0.08
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32 460,000 3,800,000 0.10
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33 560,000 4,700,000 0.13
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34 670,000 5,800,000 0.16
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35 810,000 7,100,000 0.19
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36 980,000 8,800,000 0.24
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37 1,180,000 10,800,000 0.30
50
38 1,420,000 13,300,000 0.36
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39 1,720,000 16,400,000 0.45
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40 2,070,000 20,200,000 0.55
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41 2,500,000 24,900,000 0.7
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42 3,020,000 30,600,000 0.8
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43 3,640,000 37,700,000 1.0
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44 4,400,000 46,400,000 1.3
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45 5,300,000 57,100,000 1.6
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46 6,400,000 70,300,000 1.9
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47 7,730,000 86,600,000 2.4
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48 9,320,000 106,600,000 2.9
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49 11,250,000 131,200,000 3.6
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50 13,580,000 161,600,000 4.4
63
51 16,390,000 198,900,000 5.4
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52 19,780,000 244,900,000 6.7
65
53 23,870,000 301,600,000 8.3
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54 28,800,000 371,300,000 10
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55 34,760,000 457,100,000 13
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56 41,950,000 562,800,000 15
69
57 50,630,000 692,900,000 19
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58 61,100,000 853,200,000 23I wasn't planning on adding any commentary to the model, but a particular tweet pissed me off. Let's be clear about the implication of this curve: regardless of what datamining says about a level cap of 100, exactly one of a these 3 statements MUST be true: (1) no one will ever reach 100, or any level close to it; (2) the level exp curve changes from exponential beyond 30 so this nasty curve doesn't reflect reality, or (3) someone will reach 100 once a future change is made to exp , either through generation, the requirement curve, or both.
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59 73,730,000 1,050,400,000 29
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60 88,990,000 1,293,300,000 35
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61 107,390,000 1,592,300,000 44
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62 129,600,000 1,960,500,000 54
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63 156,410,000 2,413,800,000 66
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64 188,760,000 2,971,900,000 81To explain the math, d/dx of a function ae^x IS ae^x, which in less-mathy terms means an exponential curve looks like this regardless of whether the level 1 exp requirement is 1 or 1 billion and regardless of whether there are 20 levels or 20 million levels (it's a descreate approximation of the continuous function for any number of points). You can intuitively think about it like this: the slope of the curve is ae^x at all points, regardless of scale, so you know the graph will look like this no matter how far you scale out. Here's a link to a wolfram alpha explanation: https://www.wolframalpha.com/input/?i=d%2Fdx+ae%5Ex
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65 227,800,000 3,659,000,000 100
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66 274,920,000 4,505,000,000 123
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67 331,780,000 5,546,600,000 152
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68 400,400,000 6,829,100,000 187
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69 483,220,000 8,408,000,000 230
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70 583,170,000 10,352,100,000 284
Wolfram Alpha d/dx ae^x
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71 703,790,000 12,745,600,000 349
Or, in a more enjoyable format: (link: http://img-9gag-fun.9cache.com/photo/aqmGw5Y_700b_v2.jpg)
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72 849,350,000 15,692,600,000 430
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73 1,025,030,000 19,320,900,000 529
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74 1,237,040,000 23,788,200,000 652
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75 1,492,900,000 29,288,300,000 802
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76 1,801,680,000 36,060,100,000 988
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77 2,174,330,000 44,397,700,000 1,216
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78 2,624,050,000 54,663,100,000 1,498
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79 3,166,790,000 67,301,900,000 1,844
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80 3,821,790,000 82,862,900,000 2,270
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81 4,612,260,000 102,022,000,000 2,795
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82 5,566,230,000 125,610,800,000 3,441
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83 6,717,520,000 154,653,600,000 4,237
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84 8,106,930,000 190,411,600,000 5,217
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85 9,783,710,000 234,437,300,000 6,423
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86 11,807,310,000 288,642,200,000 7,908
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87 14,249,460,000 355,380,100,000 9,736
100
88 17,196,720,000 437,548,700,000 11,988
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Pokemon Go Leveling
Expected Time to reach datamined levels