Turkey are in the semi-finals of the European Championship. They have played 414 minutes of football at the tournament, including extra time and injury time, and have been ahead for precisely nine of them. That is all you need to know, really. Anyone attempting to explain the progress of Fatih Terim’s team in any way that is logical will be defeated, as Croatia, Switzerland and the Czech Republic have been in the unlikeliest circumstances so far.

Against the Swiss, Turkey went behind, then equalised, and scored the winner in the second minute of injury time, after which three minutes of additional time were played. Against the Czech Republic, they fought back from 2-0 down to lead 3-2 with a goal that put them in front after 89 minutes, and there were five minutes of injury time played.

Last night, they went one better. At no time in this match were Turkey ahead, yet they won, on penalties, and will now face Germany in Basle on Wednesday.

It has to be the most remarkable sequence of success at any leading international championship, the ultimate in resilience and refusal to accept what non-believers see as the inevitable. There is a word for defeat in Turkish — yenilgi — although it is fair to presume that these players do not know the meaning of it.

Croatia have guts, too, England know that. Yet when this turned into a test of nerve in the last two astonishing minutes of extra time, and during the penalty shoot-out, they wilted when faced with a monstrous opponent, who would not lay down and who could not be killed.

After Rüstü Recber, the Turkey goalkeeper, went absent and Ivan Klasnic, a 97th-minute substitute for Ivica Olic, Croatia’s wasteful striker, headed in Luka Modric’s cross with two minutes of extra time remaining — the initial 90 minutes having ended in a frustrating stalemate — it looked as if Turkey would be beaten at last.

No team, surely, could come back from that. And no team would; except that Turkey are not a team in this tournament, they are a phenomenon, a force of nature. This is a campaign of almost mythical purpose.

And so it was that from a free kick taken by Rüstü, the stand-in goalkeeper due to the suspension of Volkan Demirel, the first choice, the ball landed at the feet of another substitute, Semih Sentürk, after a scramble and his shot flew past Stipe Pletikosa, in Croatia’s goal, as if propelled by an unseen power.

Slaven Bilic, the Croatia coach, complained bitterly that Roberto Rosetti, the Italian referee, played one minute and 14 seconds over time, but he need not have wasted his breath. As he spoke, it was if the life was being sucked out of his team. Bilic, normally so strong, so defiant, reduced to moaning at the fourth official like one of those ineffectual little men on the touchline. Maybe he sensed what was about to happen and could feel the confidence draining from his men, too. Certainly, Croatia looked defeated before the shoot-out even began.

This after-match joust was a disaster for Croatia, from start to finish. They took four penalties, and missed three. We will never know who would have taken the fourth or fifth Turkey penalty, because those players were not required. Luka Modric missed, Ivan Rakitic missed, Mladen Petric had his saved.

Only Darijo Srna came through for the Croats, while Turkey did not draw one blank. Nihat Kahveci, their striker and top goalscorer, had gone off through injury — or maybe a touch of the Nicolas Anelka syndrome — with two minutes of extra time remaining, but it did not matter. Arda Turan, Sentürk and the excellent Hamit Altintop did not fail. Their will was greater, simple as that. Sometimes football transcends the tactical or technical, and that is what Turkey did in the shoot-out here.

The match was something different. Yes, Turkey rode their luck, and had Croatia, and in particular Olic, taken their chances the game would have been long over before the 90 minutes were up, but it is not fair to say the eventual victors were outplayed.