Fact one: Lionel Messi is quite good at football. Reckoned to be the best player in the world, after scoring four goals as his club, Barcelona, demolished Arsenal the other week. Talked up as the player who could win the World Cup for Argentina.

Seriously good, then.

Fact two: José Mourinho was never much good at football. These days he’s an old buffer with grey hair. Put him against Messi in a one-on-one match in the gym and there’s only one winner.

Fact three: on Wednesday night, Mourinho reduced Messi, the best player in the world, to near-impotence. In doing so, he beat Barcelona, the best club team in the world. Mourinho, who can’t play for nuts, is a winner; Messi, who can play like God, is a loser.

What does a coach bring to a sporting operation that a mere player can’t? He operates in three areas simultaneously. The first is strategy. In club football, that’s acquiring and offloading players and developing the chosen style of football. Mourinho is doing that at Inter, a continuous Forth Bridge task.

The second is tactics: the decision on the way each match should be approached, who should play and what assignments they should take on. Inter’s two-leg semi-final against Barcelona was a tactical masterclass. The first leg in Milan, which Inter won 3-1, involved two separate game plans, each scrupulously carried out.

The second leg was always going to be defensive; after the sending-off of Thiago Motta, it became almost parodically defensive.

Mourinho’s tactics worked triumphantly. Barcelona were restricted to four chances, Messi to just one. Of these chances, Messi’s was brilliantly saved, another was disastrously muffed, one produced a goal and the last a goal that was disallowed for a rather unlikely handball. Mourinho’s skill was in restricting his opponents to those four chances — luck bore a part in what came of them. That is often the way of things in football.

Strategy, yes, tactics, yes. But there is something else. There is the third area of expertise — the talent that lies a little way beyond the scope of definition. The existence of this elusive third way was summed up for me for all time when I asked for directions in India: “Continue until the road divides. Then take the central bifurcation.”

Trying to pin down the essentials of the central bifurcation is like the ancient experiment in weighing the human soul. A dying person was set on a bed that was also a weighing machine, so that the instant he died, it registered the sudden decrease in weight as his soul left his body.

The reason that Mourinho’s long-term strategy and his short-term tactics bore fruit so spectacularly in the two matches against Barcelona came down to that third element. To defend for an hour with ten men is a hard task; to do so against the best club side in the world is all but impossible. It required great tactical organisation, it required great fitness. But it also required a great willingness.

Inter won because Mourinho’s players were willing to run themselves into exhaustion to bring off a battle plan they believed in totally. Only at the end, when they were knackered, did Barcelona get close to them. That willingness, that soul, that spirit was ultimately the difference between the sides — that, and the iffy handball, the slice of Napoleonic luck. And that spirit, that third thing, is ultimately the work of the coach.

It is unanalysable, so let’s try to analyse it. We can perceive the hand of the coach in many of the great success stories in sport. Sir Alf Ramsey’s coldness frightened people. It was not a device to cover up weakness. If anything, it covered up strength; he was an implacable man. During the 1966 World Cup — which as you may know, he and England won — there was a move in the FA to force him to drop Nobby Stiles, in the wake of an outcry after the match against France.

Ramsey didn’t listen to any arguments. He just said that if Stiles was dropped, he would resign. The point is that no one thought he was bluffing. Because he wasn’t. And it wasn’t that he had calculated that the FA would back down. Rather, he was standing up for his team, his team against the world, us lot contra mundum. That is what all great coaches do. It is the one absolutely essential aspect of mutual trust.

The FA backed down, and that led straight to Ramsey’s finest moment. As despair hit with West Germany’s late equaliser in the final, Ramsey told his team unforgettably as they prepared for extra time: “You’ve won it once. Now go out and win it again.” This simple summary was the inspiration that his team needed. Ramsey told them, his team believed.

Sir Clive Woodward was England’s head coach on the “Tour from Hell” in 1998, when they played New Zealand, Australia and South Africa in the space of a month, five years before his triumph in the World Cup. On the tour’s final leg, England checked in to a hotel in Cape Town that was decidedly unsatisfactory. So Woodward took the whole squad down to a better hotel and slapped his own credit card down on the reception desk.

Trust could hardly have been established more solidly.

Brad Gilbert, the coach behind Andre Agassi’s renaissance, called his book on coaching I’ve Got Your Back — you don’t need to look over your shoulder, coach is looking after you. Agassi believed that. To make an entire squad believe in you and trust you is a far more complex matter, of course.

Sir Alex Ferguson, of Manchester United, is one of the most successful coaches in club football. Fear is his best-known managerial method, but it is trust that makes his method work. Us against the world, and I’ll see you through. The point here — the point with most great coaches — is that it doesn’t matter what happens objectively. What matters is what you believe is happening.

Bill Sweetenham used a combination of fear and challenge to inspire the Great Britain swimming team. I was there for some of his private coaching sessions. He could be deeply alarming, but to win his approval was a great prize. “Who wants to be ordinary?” he asked his goggle-eyed troops. They believed all right. British swimmers won no medals at the Olympic Games in Sydney in 2000. After Sweetenham had done his stuff, they won six, including two golds, in Beijing in 2008.

Trust, then, trust and belief. Together the founding principle of the coach’s art, the defining characteristic of the central bifurcation. Strategy and tactics, they’re the basics, and don’t leave home without them. But it is in the third element that you find the difference between coach and coach: what allows a great coach to beat a great player. The third element is the special one.