The reason? A perfect example arrived in the 42nd minute of Bayern's 8-0 humbling of Hamburg on Saturday, when the Germany international chased down what seemed to be a lost cause. A long ball forward was bound to go out of play - or was it? Where other players might have been happy to let it roll out, Müller got there just in time and kept it on the pitch for Douglas Costa.
Since the Brazilian's shot was blocked and the rebound was converted by Robert Lewandowski, Müller cannot lay claim to the assist, but there can be no doubt that he set the goal up with his selfless running.
Furthermore, the 27-year-old covered 11.07 kilometres at the Allianz Arena – more than any of his team-mates. Coach Carlo Ancelotti, who did not so much as flinch as any of his side's eight goals hit the back of the net, had maintained a perfect overview of the action and, perhaps surprisingly in view of Lewandowski's hat-trick, waxed lyrical about Müller's contribution after the final whistle: "He was the best player on the field, even though he didn't score a goal. He was the key to this win."
From up in the stands, Bayern's CEO Karl-Heinz Rummenigge said he had seen the same lung-busting performance from a man who, having found the back of the net 20 times in the Bundesliga last season, is now making a difference in other ways. "Unfortunately I didn't get a shot in on goal again, but I can live with that," said Müller with a smile, enjoying the victory even without seeing his own name up in lights.
Watch: Highlights of Bayern's 8-0 victory over Hamburg:
It should not be overlooked that while the scorers generally take all the plaudits - especially in such a thumping win - Müller's contribution was being singled out for praise. He had a hand in all three of Bayern's first-half goals, setting up Arturo Vidal's opener with a neat move and pass before earning the penalty which Lewandowski stroked home. And then there was that seemingly hopeless sprint to the goal-line which led to goal number three.
His second assist of the game was symbolic of the maturity of a man whose worth is being weighed in much more than goals nowadays. Faced with just Rene Adler to beat, he altruistically squared for David Alaba, certain that the odds of the Austrian converting into an open goal were much higher than his own chances of beating the Hamburg custodian as he closed him down. "Scoring goals is not everything to me," Müller said. "Especially not when I can help one of my team-mates score."
He has done that time and time again, which explains why he is unlikely to go into double figures this season for only the second time since 2009/10. "Thomas is always important to the team, even when he's not scoring or even when he's not even got the ball," said Arjen Robben. "He makes room for Lewy and myself, when he's on my side of the field."
Moreover, he is valued for his off-field qualities too. "Nobody doubts his technical ability – he's proven himself over the years – but how motivated he is and how he motivates his team-mates is astounding," said Bayern captain Philipp Lahm. "This may be a period in which things are not necessarily going so well for him, but Thomas doesn't just dig his head in the sand, he faces up to things, works hard and leads by example." Like retrieving an apparently lost cause, for the common good.
Watch: Müller was on target the last time Bayern beat Hamburg 8-0, back in 2015: