What happens after my bear hits max level? – Spry Fox Support

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.
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.

An Example

Skinny Bear in version 01.03.00 has a max level of 100 and a base nap time 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.
When the nap time isn't an exact number of minutes, we don't display fractional part but the actual nap time still includes the fractional part. (This is more of an issue when the nap time is displayed in hours because we won't display the minutes even though there may be so many minutes that it's almost closer to an additional hour.)

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 infinity 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 infinity Excess Bears.

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

An Example

The Math-y Details

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