Wahrscheinlichkeiten Achtelfinal-Auslosung (Spieltage)

Freyr, Mittwoch, 12.12.2018, 23:18 (vor 1962 Tagen) @ kelgrim
bearbeitet von Freyr, Mittwoch, 12.12.2018, 23:23

So funktioniert das aber wohl nicht. Habe das auch so zuerst gemacht, aber war falsch. (unterhaltung im reddit)

Man kannn nicht die 650 BVB-TOT Ereignisse durch 3694 teilen

Now that all possible draws are known it is easy to assume that each draw is equally likely, then calculate the fraction of all possible draws where each match exist and call that the probability of this match. But in fact this is not correct as was pointed out to me two years ago by Julien Guyon when I published a similar analysis. That is because there is another source of bias, which is due to the draw procedure of the UEFA.

Calculating UEFA Champions League Round of 16 Draw Probabilities

EDIT: hier noch deutlicher für 2017

"I make a quick PHP script to calculate all the possible permutations (8!=40320), then I eliminate the invalid options and find that only 4238 permutations are possible. I count all the possible team pairings as below:
I calculate the associated percentage for each pair (example for Liverpool-Real it’s 799 out of 4238=18.85%)
Then I start to realize that my approach was incorrect.
In fact, my numbers were only valid if the draw process consisted of a single step – somebody picking up a random number from 1 to 4238 and then showing up the 8 pairings behind that number.
But in fact, the draw process consist of 8 steps or 8 events, each one depending on the previous one. We speak in this case of conditional probabilities, which are represented using a probability tree. The probability tree for a subset of 6 teams looks like this:"

probabilities table before the draw