What's the effect of having more than one scrap recovery arm?
How much scrap do I get with two Scrap Recovery Arm augments installed? 110%, 120%, 121%, or some number that doesn't make any sense?
Solution 1:
After reading Hackworth's table, I decided to test a bit. I got 2 scrap recovery arms, and started writing down every time I received some scrap. I wrote down both the amount I was promised and the actual amount I received. Then I put it in Excel, and compared it to 3 lists corresponding to Hackworth's A, B and C (additive, multiplicative and independently rounded, respectively). It turns out the formula (at least for 2 arms, I assume it's the same for 3) is: Scrap received = floor(Scrap promised * (1 + 10% / (number of arms) ) or: Sr = floor(Sp*(1+0,1*n))
Documentation: Excel sheet with data (I also have screenshots from 3 different amounts, but as a new user I'm not allowed to post more than 2 links in one post)
tl;dr: The arms stack additively rounded down
Solution 2:
I can't answer the question definitely, but I know that the scrap recovery arms do stack, and I have set up a table that lets anyone with 2 or 3 scrap recovery arms quickly decide which stacking method is being used.
There are 3 possible ways to calculate the bonus scrap:
A. The 10% bonus stacks additively, giving a total of 120% (130%), rounded down.
B. The 10% bonus stacks multiplicatively, giving a total of 121% (133.1%), rounded down.
C. The 10% bonus is calculated and rounded independently for each arm, and added up after rounding each bonus scrap amount individually.
Putting it into a spreadsheet for base scrap 1-100 gives the following results for total scrap. If you ever get to play with 2 or 3 arms, you can compare your actual results against this table, and if you get e.g. 58 or 59 base scrap at 2 arms, you can definitely tell which calculation method is being used in the game. Either way, as already pointed out in the comments, the difference is quite small in practice and should probably not be a deciding factor on the question whether or not to get a second or even third scrap recovery arm over a different kind of augmentation.
Scrap 2 arms 3 arms
A B C A B C
1 1 1 1 1 1 1
2 2 2 2 2 2 2
3 3 3 3 3 3 3
4 4 4 4 5 5 4
5 6 6 5 6 6 5
6 7 7 6 7 7 6
7 8 8 7 9 9 7
8 9 9 8 10 10 8
9 10 10 9 11 11 9
10 12 12 12 13 13 13
11 13 13 13 14 14 14
12 14 14 14 15 15 15
13 15 15 15 16 17 16
14 16 16 16 18 18 17
15 18 18 17 19 19 18
16 19 19 18 20 21 19
17 20 20 19 22 22 20
18 21 21 20 23 23 21
19 22 22 21 24 25 22
20 24 24 24 26 26 26
21 25 25 25 27 27 27
22 26 26 26 28 29 28
23 27 27 27 29 30 29
24 28 29 28 31 31 30
25 30 30 29 32 33 31
26 31 31 30 33 34 32
27 32 32 31 35 35 33
28 33 33 32 36 37 34
29 34 35 33 37 38 35
30 36 36 36 39 39 39
31 37 37 37 40 41 40
32 38 38 38 41 42 41
33 39 39 39 42 43 42
34 40 41 40 44 45 43
35 42 42 41 45 46 44
36 43 43 42 46 47 45
37 44 44 43 48 49 46
38 45 45 44 49 50 47
39 46 47 45 50 51 48
40 48 48 48 52 53 52
41 49 49 49 53 54 53
42 50 50 50 54 55 54
43 51 52 51 55 57 55
44 52 53 52 57 58 56
45 54 54 53 58 59 57
46 55 55 54 59 61 58
47 56 56 55 61 62 59
48 57 58 56 62 63 60
49 58 59 57 63 65 61
50 60 60 60 65 66 65
51 61 61 61 66 67 66
52 62 62 62 67 69 67
53 63 64 63 68 70 68
54 64 65 64 70 71 69
55 66 66 65 71 73 70
56 67 67 66 72 74 71
57 68 68 67 74 75 72
58 69 70 68 75 77 73
59 70 71 69 76 78 74
60 72 72 72 78 79 78
61 73 73 73 79 81 79
62 74 75 74 80 82 80
63 75 76 75 81 83 81
64 76 77 76 83 85 82
65 78 78 77 84 86 83
66 79 79 78 85 87 84
67 80 81 79 87 89 85
68 81 82 80 88 90 86
69 82 83 81 89 91 87
70 84 84 84 91 93 91
71 85 85 85 92 94 92
72 86 87 86 93 95 93
73 87 88 87 94 97 94
74 88 89 88 96 98 95
75 90 90 89 97 99 96
76 91 91 90 98 101 97
77 92 93 91 100 102 98
78 93 94 92 101 103 99
79 94 95 93 102 105 100
80 96 96 96 104 106 104
81 97 98 97 105 107 105
82 98 99 98 106 109 106
83 99 100 99 107 110 107
84 100 101 100 109 111 108
85 102 102 101 110 113 109
86 103 104 102 111 114 110
87 104 105 103 113 115 111
88 105 106 104 114 117 112
89 106 107 105 115 118 113
90 108 108 108 117 119 117
91 109 110 109 118 121 118
92 110 111 110 119 122 119
93 111 112 111 120 123 120
94 112 113 112 122 125 121
95 114 114 113 123 126 122
96 115 116 114 124 127 123
97 116 117 115 126 129 124
98 117 118 116 127 130 125
99 118 119 117 128 131 126
100 120 121 120 130 133 130