I did not find any good graphics that visualize the chances of finding cosmetic boxes. So I created some myself. The chances stay the same after level 16.

Image 1: Chances for levels 1 to 10.

Image 2: Chances for levels 11 to 16+.

Image 3: Average number of cosmetic boxes per level.

Interesting insights

If you only play level 16+, you still need to beat on average 17 levels to get one ultra-rare cosmetic box.

If you beat the first 20 levels, you get 10 common, 8.5 uncommon, 4.2 rare and 0.6 ultra rare cosmetic boxes on average.

Average boxes per level

The following table shows the average number of boxes you get per level.

Level	total	common	uncommon	rare	ultra-rare
1	0,2	0,1398	0,0564	0,0038	0
2	0,28	0,186032	0,083776	0,010136	0,000056
3	0,36	0,223236	0,114084	0,021996	0,000684
4	0,44	0,247764	0,147268	0,042064	0,002904
5	0,52	0,253916	0,1833	0,07436	0,008424
6	0,8	0,37302	0,27858	0,12878	0,01962
7	0,88	0,419252	0,305956	0,135116	0,019676
8	0,96	0,456456	0,336264	0,146976	0,020304
9	1,04	0,480984	0,369448	0,167044	0,022524
10	1,12	0,487136	0,40548	0,19934	0,028044
11	1,4	0,60624	0,50076	0,25376	0,03924
12	1,48	0,652472	0,528136	0,260096	0,039296
13	1,56	0,689676	0,558444	0,271956	0,039924
14	1,64	0,714204	0,591628	0,292024	0,042144
15	1,72	0,720356	0,62766	0,32432	0,047664
16+	1,8	0,69966	0,66654	0,37494	0,05886

Thank you to the REPO wiki, which contains the base chances and goes into more detail on how cosmetic box spawning works.

If you use any of these graphics, please credit me or reach out to me first.