Martinez once claimed to see in Barkley "bits of Paul Gascoigne and Michael Ballack" and said "he could give us something unique as a nation".
That was three years ago, when local boy Barkley made his England debut under Roy Hodgson, who then took him to the 2014 World Cup.
By this year, however, Barkley's star was fading.
He went to Euro 2016 but was unused and found himself left out of the only England squad named by Hodgson's successor, the ill-fated Sam Allardyce.
Four games into the season, the 22-year-old suffered the humiliation of being substituted at halftime in Everton's game at Sunderland, whereupon the Merseysiders scored three second-half goals for a comfortable win.
"He did not play well and lost many balls," Koeman said on that occasion. "Players of that quality can't lose that many balls. I had talks with Ross that he needs to improve.
"We spoke to him and he understands. We showed him the clips, and there's no escape."
MORE ASSURED
Lesson digested, Barkley looked far more assured in Sunday's 2-0 victory at home to West Ham United.
He provided the brightest moment of a dull first half with a feint and shot that brought a fine one-handed save from Adrian, then started and finished the move for the second goal, scoring with a deft half-volley on his supposedly weaker left foot.
But if he looked much more like the "key player between the defenders and the strikers" that Dutchman Koeman wants to see, the manager still added one barb to his initial praise.
"Ross Barkley had more impact in the last part of our attacking, not only in scoring but he was dangerous throughout," was the good news.
The follow-up was significant: "He can be very good, but it is all about knowing what you need to do. Sometimes I have to shout too much, he needs to run more."
At least and at last the message seems to have sunk in.
"It's a platform today to kick on from," said Barkley.
(Editing by Ken Ferris)
