It has been a while since a Müller hat trick won the Bundesliga title for Bayern Munich, but it happened at the weekend when three goals from 20-year-old Thomas Müller effectively sealed Munich’s first trophy of the season after a 3-1 victory over Bochum.

He struck with his chest, his head and his foot. Gerd Müller, the original “Bomber” and Germany’s all-time record scorer, used to do that sort of thing all the time. And though they are unrelated, there is a connection: Gerd, now 64, remains a coach, an example, to Bayern’s apprentices.

Speak of youth, and Barcelona can never be out of the equation. On Saturday, three days after its elimination from the Champions League, Barça resorted to type, selected eight players who have come through its academy, and thumped Villarreal, 4-1, away from home.

Somebody had to pay for Barcelona’s loss of a trophy, and that someone happened to be Villarreal, which had won its previous six home games.

Lionel Messi, of course, scored — twice. Xavi Hernández chipped in with a typical, immaculate Xavi free kick. But the goal of the night, a goal of audacity, intuition and skill that suggest the making of a truly prolific career, came from Bojan Krkic.

The son of a former Serbian striker of the same name, but born in Catalonia, Bojan is 19. He is built in the small, swift mold of Messi, Andres Iniesta, Xavi and Pedro Rodríguez.

And judging from the especially warm hug Bojan got from his coach, Pep Guardiola, it will be a surprise if speculation in the Spanish media is true: They think that Barcelona’s response to its European failure last week is to buy Valencia’s David Villa — and to offer Bojan in part exchange.

Guardiola neither confirms nor denies the interest in the prolific Spanish striker Villa. But by preferring Bojan to Zlatan Ibraimovic and to Thierry Henry for a match that was a test of Barcelona’s character, the coach showed his hand. By hugging the teenager substituted toward the end, Guardiola demonstrably showed almost paternal pride in the “boy.”

Maybe we read too much into a gesture, but ask any coach what young, gifted, vulnerable people need after a letdown. Ask any coach at a top club what their instinct is just days after a youth has blown a shot in front of an empty net from five meters that would have kept his team in the Champions League.

The best coaches, if they believe they have the best of youngsters, put an arm around the lad and send him back into the fray.

Guardiola, still under 40 and in only his second season as Barcelona coach, knows his trade better than most. What the know-alls on studio couches said happened against Inter Milan last week, rushing to denounce Barça as a team with no Plan B, was actually wide of the mark.

Barcelona did change its game against Inter. It muscled up and tried to match the Italian champion in a physical sense.

On Saturday, it was back to the true Barça, back to the irrepressible passing and movement that most teams on earth cannot defend against. If that is Plan A, and such a very stylish Plan A that keeps Barcelona top of the Spanish league, why change it?

Two of the four goals were pure Barça. The first came when Xavi slipped the ball through the heart of Villarreal’s defense, Messi took it on his instep, swayed out of reach of the nearest defender, and then with a low shot that deflected off the boot of Diego Godin, beat the Villarreal goalkeeper, Diego López.

Bojan’s little gem was even more impudent. Xavi, then Dani Alves, played him in, but then Bojan flicked the ball to one side of the big Javier Gonzalo, darted to the other side, and with turbo pace and sure-footed finish he picked his spot to score the goal.

Think Guardiola wants to let this talent go? The coach, rather, has the problem of how and when to give a growing teenager game time in a team that is forever chasing one title or another.

Bayern Munich’s board, led by men who were legends in their own playing time, would give their eye teeth for such a product line of talent. Munich, however, has long known that Thomas Müller could be something special.

In his boyhood, with TSV Pähl, a regional club 65 kilometers, or 40 miles, from Munich, he once scored 120 goals in one season. As quickly as you could say the name Müller, he was signed up by the club where the phenomenal Gerhard Müller scored the vast bulk of his 572 goals in 669 appearances.

The older Müller retired as a Bayern player in 1979. Where he was short and stocky and relied upon an uncanny instinct and an unshakable low center of gravity, the younger Müller is taller, leaner, more versatile.

On Wednesday, when Bayern swept aside Lyon to reach the Champions League final, Müller was the provider, the hard-working foil for his Croatian co-striker Ivica Olic, who scored a hat trick.

Saturday was Müller’s turn. He could have had more goals, and so could others, as Bayern overwhelmed relegation-threatened Bochum. And while Munich was winning so easily, its crowd was singing because news arrived that Schalke, its rival for the domestic title, was losing 2-0 at home to Werder Bremen.

It had been Schalke’s presumption that Bayern, pursuing a league, Champions League and German cup treble, would slip up somewhere along the way. But it was Schalke’s nerve that failed, and Munich that now, with a 3-point lead and a goal difference 17 goals superior to anyone, will be the champion.