BrianFreud
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Now that I've finally managed to get 95% of my 2013 and 2014 gift boxes home and sorted out, I figured I'd finally try to answer "how rare is it" for these boxes. 
The number of boxes I collected in each year should be sufficient enough to eliminate just bad luck. Also, it's probably worth noting that these boxes aren't dyable, so whatever color you got, that's what it still is.
I've run the numbers separately and both years combined. Based on these counts, it looks like the RNG was far less streaky in 2013 than in 2014. In any case, this does show that those boxes we assumed were the rare ones really are the rarest, followed by hues 76, 15, 36, 37, 43, and 92.
I've hidden most of the data with spoiler tags, since each table has 109 lines.
2013 gift boxes
Sorted by hue
=================================================
2014 gift boxes
Sorted by hue
=================================================
Combined 2013 and 2014 gift boxes
Sorted by hue
=================================================
2013 gift boxes
Sorted by percentage of total
=================================================
2014 gift boxes
Sorted by percentage of total
=================================================
Combined 2013 and 2014 gift boxes
Sorted by percentage of total
The number of boxes I collected in each year should be sufficient enough to eliminate just bad luck. Also, it's probably worth noting that these boxes aren't dyable, so whatever color you got, that's what it still is.
I've run the numbers separately and both years combined. Based on these counts, it looks like the RNG was far less streaky in 2013 than in 2014. In any case, this does show that those boxes we assumed were the rare ones really are the rarest, followed by hues 76, 15, 36, 37, 43, and 92.
I've hidden most of the data with spoiler tags, since each table has 109 lines.
2013 gift boxes
Sorted by hue
Code:
Hue Count Percentage of total
0 46 3.35%
2 11 0.80%
3 12 0.87%
4 15 1.09%
5 8 0.58%
6 8 0.58%
7 17 1.24%
8 14 1.02%
9 16 1.17%
10 12 0.87%
11 12 0.87%
12 13 0.95%
13 10 0.73%
14 10 0.73%
15 8 0.58%
16 15 1.09%
17 15 1.09%
18 11 0.80%
19 14 1.02%
20 12 0.87%
21 11 0.80%
22 11 0.80%
23 12 0.87%
24 13 0.95%
25 14 1.02%
26 11 0.80%
27 17 1.24%
28 13 0.95%
29 17 1.24%
30 15 1.09%
31 22 1.60%
32 13 0.95%
33 11 0.80%
34 13 0.95%
35 11 0.80%
36 9 0.66%
37 6 0.44%
38 15 1.09%
39 14 1.02%
40 15 1.09%
41 15 1.09%
42 14 1.02%
43 10 0.73%
44 21 1.53%
45 13 0.95%
46 15 1.09%
47 15 1.09%
48 12 0.87%
49 12 0.87%
50 9 0.66%
51 16 1.17%
52 10 0.73%
53 18 1.31%
54 16 1.17%
55 23 1.68%
56 13 0.95%
57 8 0.58%
58 18 1.31%
59 18 1.31%
60 15 1.09%
61 18 1.31%
62 7 0.51%
63 9 0.66%
64 8 0.58%
65 10 0.73%
66 12 0.87%
67 9 0.66%
68 18 1.31%
69 15 1.09%
70 10 0.73%
71 15 1.09%
72 13 0.95%
73 7 0.51%
74 22 1.60%
75 11 0.80%
76 6 0.44%
77 12 0.87%
78 21 1.53%
79 14 1.02%
80 18 1.31%
81 6 0.44%
82 12 0.87%
83 18 1.31%
83 12 0.87%
85 13 0.95%
86 15 1.09%
87 18 1.31%
88 7 0.51%
89 11 0.80%
90 16 1.17%
91 12 0.87%
92 11 0.80%
93 21 1.53%
94 9 0.66%
95 13 0.95%
96 15 1.09%
97 9 0.66%
98 9 0.66%
99 9 0.66%
100 9 0.66%
101 14 1.02%
1918 4 0.29%
2075 6 0.44%
2640 1 0.07%
2707 2 0.15%
2715 1 0.07%
2722 3 0.22%
2726 5 0.36%
2728 3 0.22%
Total 1372=================================================
2014 gift boxes
Sorted by hue
Code:
Hue Count Percentage of total
0 11 1.27%
2 4 0.46%
3 4 0.46%
4 4 0.46%
5 7 0.81%
6 9 1.04%
7 8 0.93%
8 7 0.81%
9 12 1.39%
10 8 0.93%
11 8 0.93%
12 16 1.85%
13 9 1.04%
14 11 1.27%
15 5 0.58%
16 11 1.27%
17 10 1.16%
18 4 0.46%
19 5 0.58%
20 7 0.81%
21 5 0.58%
22 4 0.46%
23 5 0.58%
24 8 0.93%
25 6 0.70%
26 8 0.93%
27 6 0.70%
28 14 1.62%
29 12 1.39%
30 8 0.93%
31 15 1.74%
32 4 0.46%
33 7 0.81%
34 7 0.81%
35 7 0.81%
36 4 0.46%
37 7 0.81%
38 8 0.93%
39 8 0.93%
40 8 0.93%
41 10 1.16%
42 14 1.62%
43 4 0.46%
44 9 1.04%
45 7 0.81%
46 12 1.39%
47 8 0.93%
48 9 1.04%
49 4 0.46%
50 6 0.70%
51 10 1.16%
52 10 1.16%
53 7 0.81%
54 5 0.58%
55 13 1.51%
56 5 0.58%
57 12 1.39%
58 7 0.81%
59 6 0.70%
60 10 1.16%
61 8 0.93%
62 13 1.51%
63 7 0.81%
64 8 0.93%
65 10 1.16%
66 9 1.04%
67 7 0.81%
68 9 1.04%
69 10 1.16%
70 9 1.04%
71 9 1.04%
72 6 0.70%
73 13 1.51%
74 14 1.62%
75 13 1.51%
76 5 0.58%
77 6 0.70%
78 4 0.46%
79 8 0.93%
80 8 0.93%
81 9 1.04%
82 14 1.62%
83 9 1.04%
84 8 0.93%
85 11 1.27%
86 10 1.16%
87 8 0.93%
88 9 1.04%
89 10 1.16%
90 6 0.70%
91 4 0.46%
92 3 0.35%
93 10 1.16%
94 10 1.16%
95 8 0.93%
96 9 1.04%
97 10 1.16%
98 8 0.93%
99 10 1.16%
100 10 1.16%
101 6 0.70%
1918 4 0.46%
2075 3 0.35%
2640 2 0.23%
2707 2 0.23%
2715 1 0.12%
2722 3 0.35%
2726 4 0.46%
2728 7 0.81%
Total 863=================================================
Combined 2013 and 2014 gift boxes
Sorted by hue
Code:
Hue Count Percentage of total
0 57 2.55%
2 15 0.67%
3 16 0.72%
4 19 0.85%
5 15 0.67%
6 17 0.76%
7 25 1.12%
8 21 0.94%
9 28 1.25%
10 20 0.89%
11 20 0.89%
12 29 1.30%
13 19 0.85%
14 21 0.94%
15 13 0.58%
16 26 1.16%
17 25 1.12%
18 15 0.67%
19 19 0.85%
20 19 0.85%
21 16 0.72%
22 15 0.67%
23 17 0.76%
24 21 0.94%
25 20 0.89%
26 19 0.85%
27 23 1.03%
28 27 1.21%
29 29 1.30%
30 23 1.03%
31 37 1.66%
32 17 0.76%
33 18 0.81%
34 20 0.89%
35 18 0.81%
36 13 0.58%
37 13 0.58%
38 23 1.03%
39 22 0.98%
40 23 1.03%
41 25 1.12%
42 28 1.25%
43 14 0.63%
44 30 1.34%
45 20 0.89%
46 27 1.21%
47 23 1.03%
48 21 0.94%
49 16 0.72%
50 15 0.67%
51 26 1.16%
52 20 0.89%
53 25 1.12%
54 21 0.94%
55 36 1.61%
56 18 0.81%
57 20 0.89%
58 25 1.12%
59 24 1.07%
60 25 1.12%
61 26 1.16%
62 20 0.89%
63 16 0.72%
64 16 0.72%
65 20 0.89%
66 21 0.94%
67 16 0.72%
68 27 1.21%
69 25 1.12%
70 19 0.85%
71 24 1.07%
72 19 0.85%
73 20 0.89%
74 36 1.61%
75 24 1.07%
76 11 0.49%
77 18 0.81%
78 25 1.12%
79 22 0.98%
80 26 1.16%
81 15 0.67%
82 26 1.16%
83 27 1.21%
84 20 0.89%
85 24 1.07%
86 25 1.12%
87 26 1.16%
88 16 0.72%
89 21 0.94%
90 22 0.98%
91 16 0.72%
92 14 0.63%
93 31 1.39%
94 19 0.85%
95 21 0.94%
96 24 1.07%
97 19 0.85%
98 17 0.76%
99 19 0.85%
100 19 0.85%
101 20 0.89%
1918 8 0.36%
2075 9 0.40%
2640 3 0.13%
2707 4 0.18%
2715 2 0.09%
2722 6 0.27%
2726 9 0.40%
2728 10 0.45%
Total 2235=================================================
2013 gift boxes
Sorted by percentage of total
Code:
Hue Count Percentage of total
2640 1 0.07%
2715 1 0.07%
2707 2 0.15%
2722 3 0.22%
2728 3 0.22%
1918 4 0.29%
2726 5 0.36%
37 6 0.44%
76 6 0.44%
81 6 0.44%
2075 6 0.44%
62 7 0.51%
73 7 0.51%
88 7 0.51%
5 8 0.58%
6 8 0.58%
15 8 0.58%
57 8 0.58%
64 8 0.58%
36 9 0.66%
50 9 0.66%
63 9 0.66%
67 9 0.66%
94 9 0.66%
97 9 0.66%
98 9 0.66%
99 9 0.66%
100 9 0.66%
13 10 0.73%
14 10 0.73%
43 10 0.73%
52 10 0.73%
65 10 0.73%
70 10 0.73%
2 11 0.80%
18 11 0.80%
21 11 0.80%
22 11 0.80%
26 11 0.80%
33 11 0.80%
35 11 0.80%
75 11 0.80%
89 11 0.80%
92 11 0.80%
3 12 0.87%
10 12 0.87%
11 12 0.87%
20 12 0.87%
23 12 0.87%
48 12 0.87%
49 12 0.87%
66 12 0.87%
77 12 0.87%
82 12 0.87%
83 12 0.87%
91 12 0.87%
12 13 0.95%
24 13 0.95%
28 13 0.95%
32 13 0.95%
34 13 0.95%
45 13 0.95%
56 13 0.95%
72 13 0.95%
85 13 0.95%
95 13 0.95%
8 14 1.02%
19 14 1.02%
25 14 1.02%
39 14 1.02%
42 14 1.02%
79 14 1.02%
101 14 1.02%
4 15 1.09%
16 15 1.09%
17 15 1.09%
30 15 1.09%
38 15 1.09%
40 15 1.09%
41 15 1.09%
46 15 1.09%
47 15 1.09%
60 15 1.09%
69 15 1.09%
71 15 1.09%
86 15 1.09%
96 15 1.09%
9 16 1.17%
51 16 1.17%
54 16 1.17%
90 16 1.17%
7 17 1.24%
27 17 1.24%
29 17 1.24%
53 18 1.31%
58 18 1.31%
59 18 1.31%
61 18 1.31%
68 18 1.31%
80 18 1.31%
83 18 1.31%
87 18 1.31%
44 21 1.53%
78 21 1.53%
93 21 1.53%
31 22 1.60%
74 22 1.60%
55 23 1.68%
0 46 3.35%
Total 1372=================================================
2014 gift boxes
Sorted by percentage of total
Code:
Hue Count Percentage of total
2715 1 0.12%
2640 2 0.23%
2707 2 0.23%
92 3 0.35%
2075 3 0.35%
2722 3 0.35%
2 4 0.46%
3 4 0.46%
4 4 0.46%
18 4 0.46%
22 4 0.46%
32 4 0.46%
36 4 0.46%
43 4 0.46%
49 4 0.46%
78 4 0.46%
91 4 0.46%
1918 4 0.46%
2726 4 0.46%
15 5 0.58%
19 5 0.58%
21 5 0.58%
23 5 0.58%
54 5 0.58%
56 5 0.58%
76 5 0.58%
25 6 0.70%
27 6 0.70%
50 6 0.70%
59 6 0.70%
72 6 0.70%
77 6 0.70%
90 6 0.70%
101 6 0.70%
5 7 0.81%
8 7 0.81%
20 7 0.81%
33 7 0.81%
34 7 0.81%
35 7 0.81%
37 7 0.81%
45 7 0.81%
53 7 0.81%
58 7 0.81%
63 7 0.81%
67 7 0.81%
2728 7 0.81%
7 8 0.93%
10 8 0.93%
11 8 0.93%
24 8 0.93%
26 8 0.93%
30 8 0.93%
38 8 0.93%
39 8 0.93%
40 8 0.93%
47 8 0.93%
61 8 0.93%
64 8 0.93%
79 8 0.93%
80 8 0.93%
84 8 0.93%
87 8 0.93%
95 8 0.93%
98 8 0.93%
6 9 1.04%
13 9 1.04%
44 9 1.04%
48 9 1.04%
66 9 1.04%
68 9 1.04%
70 9 1.04%
71 9 1.04%
81 9 1.04%
83 9 1.04%
88 9 1.04%
96 9 1.04%
17 10 1.16%
41 10 1.16%
51 10 1.16%
52 10 1.16%
60 10 1.16%
65 10 1.16%
69 10 1.16%
86 10 1.16%
89 10 1.16%
93 10 1.16%
94 10 1.16%
97 10 1.16%
99 10 1.16%
100 10 1.16%
0 11 1.27%
14 11 1.27%
16 11 1.27%
85 11 1.27%
9 12 1.39%
29 12 1.39%
46 12 1.39%
57 12 1.39%
55 13 1.51%
62 13 1.51%
73 13 1.51%
75 13 1.51%
28 14 1.62%
42 14 1.62%
74 14 1.62%
82 14 1.62%
31 15 1.74%
12 16 1.85%
Total 863=================================================
Combined 2013 and 2014 gift boxes
Sorted by percentage of total
Code:
Hue Count Percentage of total
2715 2 0.09%
2640 3 0.13%
2707 4 0.18%
2722 6 0.27%
1918 8 0.36%
2075 9 0.40%
2726 9 0.40%
2728 10 0.45%
76 11 0.49%
15 13 0.58%
36 13 0.58%
37 13 0.58%
43 14 0.63%
92 14 0.63%
2 15 0.67%
5 15 0.67%
18 15 0.67%
22 15 0.67%
50 15 0.67%
81 15 0.67%
3 16 0.72%
21 16 0.72%
49 16 0.72%
63 16 0.72%
64 16 0.72%
67 16 0.72%
88 16 0.72%
91 16 0.72%
6 17 0.76%
23 17 0.76%
32 17 0.76%
98 17 0.76%
33 18 0.81%
35 18 0.81%
56 18 0.81%
77 18 0.81%
4 19 0.85%
13 19 0.85%
19 19 0.85%
20 19 0.85%
26 19 0.85%
70 19 0.85%
72 19 0.85%
94 19 0.85%
97 19 0.85%
99 19 0.85%
100 19 0.85%
10 20 0.89%
11 20 0.89%
25 20 0.89%
34 20 0.89%
45 20 0.89%
52 20 0.89%
57 20 0.89%
62 20 0.89%
65 20 0.89%
73 20 0.89%
84 20 0.89%
101 20 0.89%
8 21 0.94%
14 21 0.94%
24 21 0.94%
48 21 0.94%
54 21 0.94%
66 21 0.94%
89 21 0.94%
95 21 0.94%
39 22 0.98%
79 22 0.98%
90 22 0.98%
27 23 1.03%
30 23 1.03%
38 23 1.03%
40 23 1.03%
47 23 1.03%
59 24 1.07%
71 24 1.07%
75 24 1.07%
85 24 1.07%
96 24 1.07%
7 25 1.12%
17 25 1.12%
41 25 1.12%
53 25 1.12%
58 25 1.12%
60 25 1.12%
69 25 1.12%
78 25 1.12%
86 25 1.12%
16 26 1.16%
51 26 1.16%
61 26 1.16%
80 26 1.16%
82 26 1.16%
87 26 1.16%
28 27 1.21%
46 27 1.21%
68 27 1.21%
83 27 1.21%
9 28 1.25%
42 28 1.25%
12 29 1.30%
29 29 1.30%
44 30 1.34%
93 31 1.39%
55 36 1.61%
74 36 1.61%
31 37 1.66%
0 57 2.55%
Total 2235