

Line 1: 
Line 1: 
 '''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. [[PetsPet]] 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 almost no benefits. [[PetsPet]] drop rate calculations are based on your Virtual Level, however that calculation will use your Virtual Level regardless of the setting. 

 

 <onlyinclude>The experience difference between level <math display='inline'>L1</math> and level <math display='inline'>L</math> is approximately <math display='inline'>\left\lfloor \frac{1}{4} \left( L1+300\times 2^{\frac{L1}{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 6 and 7 is 138 and the experience between 14 and 15 is 274, which is roughly double.   <onlyinclude>The experience difference between level <math display='inline'>L1</math> and level <math display='inline'>L</math> is approximately <math display='inline'>\left\lfloor \frac{1}{4} \left( L1+300\times 2^{\frac{L1}{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 alternatingrows stickyheader" style="textalign:right;" id="xp_table" <! this ID is an anchor for incoming links >   { class="wikitable alternatingrows stickyheader" style="textalign:right;" id="xp_table" <! this ID is an anchor for incoming links > 
Revision as of 22:08, 24 January 2022
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. Pet drop rate calculations are based on your Virtual Level, however that calculation will use your Virtual Level regardless of the setting.
The experience difference between level [math]\displaystyle{ L1 }[/math] and level [math]\displaystyle{ L }[/math] is approximately [math]\displaystyle{ \left\lfloor \frac{1}{4} \left( L1+300\times 2^{\frac{L1}{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]\displaystyle{ 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.
Levels 100120
Level 
XP 
Difference


Level 
XP 
Difference


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]\displaystyle{ L }[/math] is:
 [math]\displaystyle{ \text{Experience} = \left \lfloor{\frac{1}{4}\sum_{\ell=1}^{L1}}\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]\displaystyle{ \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.