A post where football meets science again 🙂 This time, it’s about probabilities.
On 11 December 2017 the UEFA Champions League draw will take place. There will be 16 teams which will be drawn one against each other. There are some restrictions:
– 8 teams are seeded, the other 8 are unseeded. A seeded team can only be drawn against an unseeded team
– teams from the same country cannot be drawn against each other
– teams that already met in the previous round cannot be drawn against each other
Based on these elements, I wanted to calculate the associated probabilities, or other words to reveal the question marks in the matrix below:

(first column – seeded teams, first line – unseeded teams, greyed cells – teams cannot be drawn).

Try 1: Thursday night

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%) and, after half an hour spent choosing a color scheme, I put everything in the matrix:

Then I realize that the numbers are slightly different from the ones circulated on social media:

Try 2: the entire weekend

I get a very nice explanation on Twitter from the author of the tool above:

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:

And indeed, the tree simulates the real draw process and reveals the same numbers as the ‘official’ ones:

Since the draw is in less than 12 hours, I have no time to make another script that generates the full tree (that would also be too big to put in a picture). But I trust the numbers from https://eminga.github.io/cldraw/ are correct 🙂

Links:
https://en.wikipedia.org/wiki/Tree_diagram_(probability_theory)
https://www.everythingmaths.co.za/read/maths/grade-11/probability/10-probability-02
https://kera.name/treediag/
http://www.bbc.co.uk/schools/gcsebitesize/maths/statistics/probabilityhirev1.shtml

Football analytics: when football meets science

Written on 12 November 2017, 09:51pm

Tagged with: , , ,

I wrote a piece about football analytics in Romanian: when football meets science. It was one of the articles I really enjoyed writing and it took me over 10 evenings to do it.

Here are the top level details:

Football analytics is all about using data about previous events in order to have an indication about the outcome of future events.
It is not new: it started somewhere in the ’50 and one of the first coaches to use it was a Russian trainer called Valeri Lobanovsky, in an era where a computer was taking up rooms.
I found a correlation about the DIKW pyramid and the usage of football data:
– Data – numbers and metadata collected using manual operators, tracking devices or video tools
– Information – when data is put into context. One indicator that recently became mainstream is the ‘expected goal‘ (xG) – a percentage associated with every shot based on previously aggregated data
– Knowledge – when information is combined with previous experience. Example – aggregating information about indicators like xG (xG for, xG against, non-shot xG, xG difference)
– Wisdom – using previous levels to take strategic decision enabling competitive advantage.

The first two levels are for the football fans, media writers and TV pundits.
The last two levels are for the professional football clubs and for the betting companies. This is where the football analytics takes places and these levels can give indication about future events.

A few examples of football analytics:
1. transfers: before any transfer, the targeted player is analysed from a few perspectives: tactical, physical, technical. The modern clubs are using players databases with custom criteria in order to maximize their match rate.
2. injury prevention: by tracking the way a player runs and measuring how long his feet stays on the ground, one can evaluate the player tiredness
3. predicting outcome of future events by calculating and maintaining a club index (ex. fivethirtyeight.com)
4. penalty shoot-out: statistics showed that the team shooting first has a 20% advantage over the second team. The football governing bodies realized this un-fair advantage and recently changed the order of the shoot-out (now ABBA instead of ABAB)

In the end, football remains a random sport. Using analytics can give indications, and make the clubs better understand some questions, but it cannot (yet) give definite answers. As long as football is played by humans, the human factor will play its part and will keep football random and enjoyable.


The graphics on Fifa 16 are something else