Pareto

Click here to find the frequency of occurrence for lotto numbers. I also copied the data at the end of this article.

🙂 Well, lotto numbers are definitely not Pareto:

The 20 % of numbers most frequently drawn are definitely not 80 % of all the numbers drawn.

Pareto would mean that 20 % of the most frequently drawn numbers equal 80 % of all numbers drawn. Using this classical example, this would, of course, be nonsense.

It cannot be done in the same way with lottery numbers. Except if you were to manipulate the lottery balls and drum. It makes total sense, too. Because Pareto is the 80/20 rule and it only applies for a few phenomena occurring in the “nature of society”. And even there, you never get exactly the mathematical result. Lottery numbers, however, are not a sociological thing.

And, indeed, there are a few examples for 80/20. Yet I am sure I could come up with an equally suitable example resulting in 60/40, 70/30, 90/10 or even 97/3 for every 80/20 instance. Or I might construct one. You want to bet?
It is very easy. Whenever people do or own the same thing and whenever it is possible to divide this individually at a considerably differing rate, there will be a number of persons whose part as a sum total is higher than that of the others.

Let us take riding bikes. It is an example I am very much in favour of, because I like going by bike and do it quite often. Let us, just for the fun of it, define people living in Germany who own a bike and use is once a year as “German Bikers“.

Now it is hardly difficult to postulate that some bikers go less than 100 kilometres by bike every year. And some manage to do more than 5,000 kilometres by bike. By using the number 100, I defined two sets totally at random. Those of the “seldom bikers” with an upper limit of 100 kilometres every year and the “often bikers” with more than 100 kilometres per year.

Now if I had a precise bookkeeping of all bikers and their kilometres per year, I could compute a “DĂŒrre“- probability (this is a little joke at an aside). It says how many kilometres (as part of the total covered by all bikes) the often-bikers (as part of the set of bikers) went by bike.

Of course, any number might suffice as an exemplary division criterion: 500, 1,000, 2,000, 3,000, 5,000 kilometres per year. It does not matter. If I changed this parameter (higher or lower), I can find many “DĂŒrre”- distributions with the set of data. And I am sure some of them would be very nice, and perhaps even surprising.
And if the data change (for instance due to climate changes if it rains less, or if the petrol prices rise, or if we develop new body awareness…) or if I take the data of a different cultural region or country, the distribution will, naturally, change again.

To be sure, this is not a way to prove Pareto wrong. Empiric (Empirie) is basically not a way to prove anything. All it provides is a plausible assumption. Yet the same is true for a possible (and useless) attempt at proving an alleged fact.

It is like insomnia and full moon. Insomnia is not influenced by the moon. You can measure it. Yet if we cannot sleep and there is a full moon, we take particular notice of the full moon. We notice that the night is totally different from a normal night. And we are quick to assume the constellation might have caused our insomnia. But poor Luna is not at all responsible.

Well, let us not annoy the game theory apostles too much. So the motto is:

All Pareto!

RMD
(Translated by EG)

P.S.
Frequency of lottery numbers:

The Wednesday lottery draws are included since the time when Saturday and Wednesday draws started having identical procedures.

This is how often the individual numbers were drawn so far – not considering the extra number (as of 13.11.2010).

1
415
2
422
3
423
4
423
5
419
6
441
7
418
8
384
9
434
10
415
11
426
12
402
13
359
14
399
15
391
16
394
17
429
18
407
19
413
20
402
21
404
22
433
23
398
24
412
25
436
26
439
27
427
28
386
29
397
30
400
31
433
32
457
33
436
34
405
35
409
36
422
37
415
38
439
39
419
40
421
41
422
42
426
43
437
44
405
45
384
46
396
47
406
48
423
49
461

Here is how often the individual numbers were drawn– including the extra number (as of: 13.11.2010)

1
490
2
495
3
489
4
492
5
484
6
502
7
509
8
459
9
493
10
504
11
491
12
457
13
430
14
467
15
462
16
480
17
504
18
477
19
483
20
456
21
465
22
496
23
469
24
474
25
508
26
501
27
486
28
445
29
471
30
474
31
506
32
523
33
507
34
469
35
485
36
484
37
476
38
515
39
473
40
496
41
494
42
496
43
493
44
483
45
453
46
469
47
470
48
488
49
529

Quelle: http://lotto.logicland.de/lottozahlen-statistik.ziehungshaeuf.php

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