18. January 2021

# Pareto

0Kommentare

đ 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 ânature of societyâ. 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 âGerman Bikersâ.

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 âseldom bikersâ with an upper limit of 100 kilometres every year and the âoften bikersâ 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 âDĂŒrreâ- 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 âDĂŒrreâ- 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 â 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 drawnâ 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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