A mind game about the European championship squad of the German national soccer team: Let's imagine that Joachim Löw, as a math teacher, had to prepare the students of a grammar school, let's say in Freiburg, for the Abitur.

He would probably be one of the teachers who would not have corrected the exams even after the holidays, but let's not be distracted.

Imagine two years before high school graduation he had deleted several formulas that had proven useful for solving equations from the curriculum because he thought they were no longer useful.

Over the next few months, his students would have approached the solution of the equations every now and then, but in the end made reliable miscalculations.

Let's imagine that he had taken the formulas back into class a few weeks before graduating from high school, because they are probably not entirely unimportant in order to pass exams.

But without ever admitting that you made a mistake.

Something like it is with Joachim Löw, the national coach who has now nominated Thomas Müller and Mats Hummels again for the EM.

The price of his pride: There is hardly any time to test whether and how the formulas help you through the test.