In this article, we put the simulation as a methodology into a human-like example.
By Wednesday evening, it became known which 16 teams will enter the next round of the most popular series of football club-level, the Champions League. From there, the competition continues in a straight-off system. On Monday, it will be a draw for which team to fight with.
In the basic case, the formula would be simple, anyone can get everyone with the same chance. However, there are various restrictions in the drawing system. So the really fanatical fans of course curious which team is expected to be their opponent after the draws.
The following limitations apply:
- group winners (8) can only play with second-placed teams (8)
- those in the same group can not play against each other
- teams from the same country can not be drawn to each other
The above limitations can be used to determine the probability of different pairing in a purely mathematical way, but we are now approaching an alternative.
We used the Monte-Carlo simulation method, which simply means that an experiment (in this case, a draw) is repeated several times and then evaluated the results. During the simulation we used the listed limitations and used a random number generator.
The repeated the draw 3000 times. Based on this method, the most likely 8 pairs are:
Chelsea (ENG) – Beşiktaş (TUR)
Sevilla (ESP) – Roma (ITA)
Real Madrid (ESP) – Liverpool (ENG)
Juventus (ITA) – Manchester City (ENG)
Shakhtar (UKR) – Barcelona (ESP)
Porto (POR) – Manchester United (ENG)
Bayern München (GER) – Tottenham Hotspur (ENG)
Basel (SUI) – Paris (FRA)
If you are interested in more detail, write your question in the comment section and we answer it.
UPDATE (after the draw):
The created simulation works on a strictly probability basis, so the final result was not excluded: we did not guess a single match correctly : /
Afterwards, we looked at how much this was the odds: 18.57%
Which means there are more than 80% chance that we will be better next year 🙂