Difference between revisions of "Experience Table"
From Melvor Idle
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(Amend experience difference formula & formatting) |
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− | The experience difference between level <math display='inline'>L-1</math> and level <math display='inline'>L</math> is <math display='inline'>\left\lfloor \frac{1}{4} \left( L-1+300 \ | + | The experience difference between level <math display='inline'>L-1</math> and level <math display='inline'>L</math> is approximately <math display='inline'>\left\lfloor \frac{1}{4} \left( L-1+300\times 2^{\frac{L-1}{7}} \right) \right\rfloor</math>. The table below show this experience difference for each level and also the cumulative experience from level 1 to level <math display='inline'>L</math>. |
! Level !! XP !! Difference | ! Level !! XP !! Difference | ||
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The formula needed to calculate the amount of experience needed to reach level L is: | The formula needed to calculate the amount of experience needed to reach level L is: | ||
− | :<math>\ | + | :<math>\text{Experience} = \left \lfloor{\frac{1}{4}\sum_{\ell=1}^{L-1}}\left\lfloor{\ell + 300\cdot2^{\ell/7}}\right\rfloor\right\rfloor</math> |
If the floor functions are ignored, the resulting summation can be found in closed form to be: | If the floor functions are ignored, the resulting summation can be found in closed form to be: | ||
− | :<math>\ | + | :<math>\text{Experience} \approx \frac{1}{8} \left( {L}^{2} - L + 600 \, \frac{{2}^{L/7}-2^{1/7}} {{2}^{1/7}-1} \right)</math> |
The approximation is very accurate, always within 100 experience but usually less than around 10 experience. | The approximation is very accurate, always within 100 experience but usually less than around 10 experience. | ||
{{Menu}} | {{Menu}} |
Revision as of 13:32, 22 February 2021
Note: Enabling "Virtual Levels" in the Settings will show the player if they would be on a level higher than 99, even though this gives no benefits.
The experience difference between level [math]L-1[/math] and level [math]L[/math] is approximately [math]\left\lfloor \frac{1}{4} \left( L-1+300\times 2^{\frac{L-1}{7}} \right) \right\rfloor[/math]. The table below show this experience difference for each level and also the cumulative experience from level 1 to level [math]L[/math].
Level | XP | Difference | Level | XP | Difference | Level | XP | Difference | Level | XP | Difference | |||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
1 | 0 | 0 | 26 | 8,740 | 898 | 51 | 111,945 | 10,612 | 76 | 1,336,443 | 126,022 | |||
2 | 83 | 83 | 27 | 9,730 | 990 | 52 | 123,660 | 11,715 | 77 | 1,475,581 | 139,138 | |||
3 | 174 | 91 | 28 | 10,824 | 1,094 | 53 | 136,594 | 12,934 | 78 | 1,629,200 | 153,619 | |||
4 | 276 | 102 | 29 | 12,031 | 1,207 | 54 | 150,872 | 14,278 | 79 | 1,798,808 | 169,608 | |||
5 | 388 | 112 | 30 | 13,363 | 1,332 | 55 | 166,636 | 15,764 | 80 | 1,986,068 | 187,260 | |||
6 | 512 | 124 | 31 | 14,833 | 1,470 | 56 | 184,040 | 17,404 | 81 | 2,192,818 | 206,750 | |||
7 | 650 | 138 | 32 | 16,456 | 1,623 | 57 | 203,254 | 19,214 | 82 | 2,421,087 | 228,269 | |||
8 | 801 | 151 | 33 | 18,247 | 1,791 | 58 | 224,466 | 21,212 | 83 | 2,673,114 | 252,027 | |||
9 | 969 | 168 | 34 | 20,224 | 1,977 | 59 | 247,886 | 23,420 | 84 | 2,951,373 | 278,259 | |||
10 | 1,154 | 185 | 35 | 22,406 | 2,182 | 60 | 273,742 | 25,856 | 85 | 3,258,594 | 307,221 | |||
11 | 1,358 | 204 | 36 | 24,815 | 2,409 | 61 | 302,288 | 28,546 | 86 | 3,597,792 | 339,198 | |||
12 | 1,584 | 226 | 37 | 27,473 | 2,658 | 62 | 333,804 | 31,516 | 87 | 3,972,294 | 374,502 | |||
13 | 1,833 | 249 | 38 | 30,408 | 2,935 | 63 | 368,599 | 34,795 | 88 | 4,385,776 | 413,482 | |||
14 | 2,107 | 274 | 39 | 33,648 | 3,240 | 64 | 407,015 | 38,416 | 89 | 4,842,295 | 456,519 | |||
15 | 2,411 | 304 | 40 | 37,224 | 3,576 | 65 | 449,428 | 42,413 | 90 | 5,346,332 | 504,037 | |||
16 | 2,746 | 335 | 41 | 41,171 | 3,947 | 66 | 496,254 | 46,826 | 91 | 5,902,831 | 556,499 | |||
17 | 3,115 | 369 | 42 | 45,529 | 4,358 | 67 | 547,953 | 51,699 | 92 | 6,517,253 | 614,422 | |||
18 | 3,523 | 408 | 43 | 50,339 | 4,810 | 68 | 605,032 | 57,079 | 93 | 7,195,629 | 678,376 | |||
19 | 3,973 | 450 | 44 | 55,649 | 5,310 | 69 | 668,051 | 63,019 | 94 | 7,944,614 | 748,985 | |||
20 | 4,470 | 497 | 45 | 61,512 | 5,863 | 70 | 737,627 | 69,576 | 95 | 8,771,558 | 826,944 | |||
21 | 5,018 | 548 | 46 | 67,983 | 6,471 | 71 | 814,445 | 76,818 | 96 | 9,684,577 | 913,019 | |||
22 | 5,624 | 606 | 47 | 75,127 | 7,144 | 72 | 899,257 | 84,812 | 97 | 10,692,629 | 1,008,052 | |||
23 | 6,291 | 667 | 48 | 83,014 | 7,887 | 73 | 992,895 | 93,638 | 98 | 11,805,606 | 1,112,977 | |||
24 | 7,028 | 737 | 49 | 91,721 | 8,707 | 74 | 1,096,278 | 103,383 | 99 | 13,034,431 | 1,228,825 | |||
25 | 7,842 | 814 | 50 | 101,333 | 9,612 | 75 | 1,210,421 | 114,143 |
The formula needed to calculate the amount of experience needed to reach level L is:
- [math]\text{Experience} = \left \lfloor{\frac{1}{4}\sum_{\ell=1}^{L-1}}\left\lfloor{\ell + 300\cdot2^{\ell/7}}\right\rfloor\right\rfloor[/math]
If the floor functions are ignored, the resulting summation can be found in closed form to be:
- [math]\text{Experience} \approx \frac{1}{8} \left( {L}^{2} - L + 600 \, \frac{{2}^{L/7}-2^{1/7}} {{2}^{1/7}-1} \right)[/math]
The approximation is very accurate, always within 100 experience but usually less than around 10 experience.
Melvor Idle version v0.19.2 (Released: 1st April 2021) | ||||||||||||||
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