Benford’s Law is about the distribution of initial digits in numbers from the real world. It plays a role in detecting, for example, financial fraud in tax returns because made-up numbers are quite easily distinguishable from actual ones.

There have been several attempts to explain Benford’s Law based on the processes that give rise to actual numbers. I’ve been analysing U.S. State of the Union speeches over the past 200+ years. The patterns agree with what Benford’s Law would predict, but it’s much less clear that the putative explanations make sense, given the time scale and varying authorship of these documents.

Here’s the list of the top 100 in decreasing order of frequency of occurrence, with increasing indents by magnitude:

000
one
two
1
2
3
three
30
million
5
4
billion
10
6
four
20
500
12
five
7
15
hundred
9
50
25
100
8
11
14
ten
six
40
13
16
18
00
22
thousand
seven
17
1947
300
200
24
eight
60
1890
27
21
35
28
26
23
19
90
400
80
1893
70
1946
1945
75
1899
600
31
twenty
33
700
45
1860
1891
1898
65
250
150
1892
fifty
1900
twelve
41
37
1894
nine
1897
1846
1861
36
1878
55
1911
1889
thirty
1909
29
32
1885
1858
54
34
63

Within each range, the larger the number the lower its frequency. But there are some interesting exceptions: numbers that are multiples of 5 or 10 tend to appear ‘earlier’ than they should. The references to years almost all cluster around the end of the 19th Century and the beginning of the 20th.

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