Randomization in Football Strategy a Mourinho Case Study

Updated: Sep 2, 2020



Jose Mourinho, current coach of Tottenham, has made himself famous at winning the most difficult tournaments with the toughest competition. In the UEFA Champions League he won with teams whose players were not nearly as skillful and were of lower market value than most in Europe (Porto, Inter Milan).


Jose Mourinho pioneered a formation which effectively brought struggles for his opposition with the dominant strategy being to play a 4-2-3-1, diminishing the advantages of ball possession and focusing on counter attacking defensive football. As time has gone on however, his strategy has not been as effective. He now is managing historically better performing teams with higher payrolls and skillsets, but has continued using his original formation and strategy.


Below I show his payoffs playing a superior opponent.


His potential payoffs are represented as the number on the left in each box. His opponents potential payoffs on the right, with their decision being to attack or defend.


Example: Mourinho plays his 4-2-3-1 as Porto against Real Madrid. Real Madrid sees Porto and chooses to attack as they see them as a very easy opponent.

If the opposing team is of superior skillset, his dominant strategy is to use the 4-2-3-1.


6 vs. 4 will always be higher than 3 vs. 4 - with no marginal difference for the opponents expected result.


When he plays against worse and inferior opponents he does not get as much utility in differential between the strategies. Looking at the graph below, if he sporadically switched to a very attacking 4-3-3 formation, the opposition would defend but not be nearly as effective in stopping the team.


Like shooting a penalty down the middle of the goal, the opponent will be thrown off guard , which would equate to a higher long-term probability of winning.

Using deductive reasoning the dominant strategy for the Inferior opponent will defend.


Mourinho needs to shift away from his go-to-formation and use other line-ups.


To increase efficiency over the long term one has to demonstrate an ability to randomize in crucial situations. Top coaches including Guardiola, Zidane, and Sir Alex Ferguson are known for this. Asking people what these coaches’ methods will be next game or the following season, the answers are always inconsistent. Nobody will ever be completely sure as to who or how Guardiola, Zidane, or Sir Alex Ferguson will play their teams.

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