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What happens after my bear hits max level?

As you probably know, a bear levels up when you receive a duplicate of it.

After a particular bear reaches its maximum level (for most types of bears this occurs at Level 100), further duplicates of the same bear will not make it more powerful. Rather, these duplicates will reduce the nap time of the bear. These nap time reductions have diminishing returns. I.e., the first few times it happens, the nap time will decrease by a lot. However, later on the nap time will decrease by very little.

  • To be more exact, nap times approach 40% of their original value as you get more and more duplicates of a particular bear beyond the maximum level. The approach is quick at first, but gets extremely slow toward the end.

An Example

Skinny Bear in version 01.03.00 has a max level of 100 and a base naptime of 60 minutes.

Number of Bears Excess Bears Fraction by which naptime is reduced from the base Fraction of base naptime remaining Skinny Bear's actual naptime (in minutes) Skinny Bear's displayed naptime (in minutes except where noted)
1-100 0 0 1 60 1 hour
101 1 0.15 0.85 51 51
102 2 0.24 0.76 45.6 45
103 3 0.3 0.7 42 42
104 4 0.342857 0.657143 39.4386 39
105 5 0.375 0.625 37.5 37
106 6 0.4 0.6 36 36
107 7 0.42 0.58 34.8 34
108 8 0.436364 0.563636 33.8181 33
109 9 0.45 0.55 33 33
110 10 0.461538 0.538462 32.3070 32
111 11 0.471429 0.528571 31.7143 31
112 12 0.48 0.52 31.2 31
113 13 0.4875 0.5125 30.75 30
114 14 0.494118 0.505882 30.3529 30
115 15 0.5 0.5 30 30
116 16 0.505263 0.494737 29.6842 29
117 17 0.51 0.49 29.4 29
118 18 0.514286 0.485714 29.1429 29
119 19 0.518182 0.481818 28.9091 28
120 20 0.521739 0.478261 28.6957 28
121 21 0.525 0.475 28.5 28
122 22 0.528 0.472 28.32 28
123 23 0.530769 0.469231 28.1538 28
124 24 0.533333 0.466667 28 28
125 25 0.535714 0.464286 27.8571 27
126 26 0.537931 0.462069 27.7241 27
127 27 0.54 0.46 27.6 27
128 28 0.541935 0.458065 27.4839 27
129 29 0.54375 0.45625 27.375 27
130 30 0.545454 0.454546 27.2727 27
. . .          
Infinity Infinity 0.6 0.4 24 24

Note the following:

  • Going from your 100th Skinny Bear to your 101st Skinny Bear reduces the nap time by 9 minutes.
  • Going from your 101st Skinny Bear to your 102nd Skinny Bear reduces the nap time by 5.4 minutes. (I.e., the returns are diminishing.)
  • At your 115th bear, the nap time is 50% of its base value.
  • A bear can never go below 40% of its base nap time value.

The Math-y Details

The fraction by which naptime is reduced is given by this formula:

Nap Time Reduction Fraction = 0.6 * (Excess Bears) / (Excess Bears + 3)

where Excess Bears is the number of bears you've earned beyond the Max Level. E.g., if you have acquired 103 Skinny Bears, then Excess Bears is 3 because Skinny Bear's Max Level is 100.

This gives the following exact points of reference:

  • Nap time is reduced by 30% if you have 3 Excess Bears.
  • Nap time is reduced by 40% if you have 6 Excess Bears.
  • Nap time is reduced by 50% if you have 15 Excess Bears.
  • Nap time is reduced by 60% if you have infinite Excess Bears.

Or, written another way:

  • Naptime is 70% of normal if you have 3 Excess Bears.
  • Naptime is 60% of normal if you have 6 Excess Bears.
  • Naptime is 50% of normal if you have 15 Excess Bears.
  • Naptime is 40% of normal if you have infinite Excess Bears.

If you're in between those exact points, you'll have to do the math to figure out exactly what the naptime should be.

When you click a bear on the bear selection screen, we display the nap time in the largest sensible unit of measure and don't display fractional parts. E.g., 3.89 hours is displayed as "3 hours". This is just what gets displayed; the actual nap time is still 3.89 hours.

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