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Experience Table: Difference between revisions
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(Added that Virtual Levels can show the player if they would have reached higher levels than 99.) |
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'''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 almost no benefits. [[Pets|Pet]] drop rate calculations are based on your Virtual Level, however that calculation will use your Virtual Level regardless of the setting. | |||
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. | |||
<onlyinclude>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 shows this experience difference for each level and also the cumulative experience from level 1 to level <math display='inline'>L</math>. Note that experience levels are nonlinear and so the amount of experience between 1 and 92 is the same as the amount of experience between 92 and 99. Experience also doubles about every 7 levels. For example, the experience between 7 and 8 is 138 and the experience between 14 and 15 is 274, which is roughly double. | |||
{| class="wikitable alternating-rows sticky-header" style="text-align:right;" id="xp_table" <!-- this ID is an anchor for incoming links --> | |||
! Level !! XP !! Difference | ! Level !! XP !! Difference | ||
! rowspan="26" | | ! rowspan="26" | | ||
| Line 133: | Line 136: | ||
| 75 || 1,210,421 || 114,143 | | 75 || 1,210,421 || 114,143 | ||
| colspan="3" | | | colspan="3" | | ||
|}</onlyinclude> | |||
Levels beyond 99 are currently virtual and only contribute to pet chance. A level 120 expansion is currently planned but has not been released, so this table is here for reference only. | |||
{| class="wikitable alternating-rows mw-collapsible mw-collapsed" style="text-align:right;margin:auto; width:100%;" | |||
|+ style='white-space:nowrap;border:solid 1px #465160; padding: 3px;'|Levels 100-120 | |||
! Level !! XP !! Difference | |||
! rowspan="8" | | |||
! Level !! XP !! Difference | |||
! rowspan="8" | | |||
! Level !! XP !! Difference | |||
|- | |||
| 100 || 14,391,160 || 1,356,729 | |||
| 107 || 28,782,069 || 2,713,437 | |||
| 114 || 57,563,718 || 5,426,849 | |||
|- | |||
| 101 || 15,889,109 || 1,497,949 | |||
| 108 || 31,777,943 || 2,995,874 | |||
| 115 || 63,555,443 || 5,991,725 | |||
|- | |||
| 102 || 17,542,976 || 1,653,867 | |||
| 109 || 35,085,654 || 3,307,711 | |||
| 116 || 70,170,840 || 6,615,397 | |||
|- | |||
| 103 || 19,368,992 || 1,826,016 | |||
| 110 || 38,737,661 || 3,652,007 | |||
| 117 || 77,474,828 || 7,303,988 | |||
|- | |||
| 104 || 21,385,073 || 2,016,081 | |||
| 111 || 42,769,801 || 4,032,140 | |||
| 118 || 85,539,082 || 8,064,254 | |||
|- | |||
| 105 || 23,611,006 || 2,225,933 | |||
| 112 || 47,221,641 || 4,451,840 | |||
| 119 || 94,442,737 || 8,903,655 | |||
|- | |||
| 106 || 26,068,632 || 2,457,626 | |||
| 113 || 52,136,869 || 4,915,228 | |||
| 120 || 104,273,167 || 9,830,430 | |||
|} | |} | ||
The formula to calculate the amount of experience needed to reach level <math display='inline'>L</math> 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. | |||
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