"I believe that throughout my time with Kevin I've been able to develop a lot of power and a lot of speed," Parker said. "I'm still developing a lot of techniques and skills. It takes time but we're eventually getting there and I'm getting more and more confident in what I can do."
That growing confidence was evident in the noises emanating from the Parker camp during the week. Neither Tyson Fury nor Wladimir Klitschko inspired any fear among the young Kiwi, according to Parker and Barry, and a similar theme emerged last night.
"I believe fully that, if I train hard and work hard, get good guidance from Kevin and good support from my team, I can beat anyone in the world," Parker said. "That's what I truly believe."
That belief is set to be tested in 2016. Parker and, particularly, his handlers might have drawn criticism for the quality up opponents he has battled in his three-year professional career, but that qualm seems set to disappear in the New Year.
The year will begin with a January 23 bout against American Jason Bergman in Samoa, the first southpaw Parker has fought. Ranked No11 in heavyweight southpaws by respected independent site BoxRec, Bergman will immediately pose a tougher test than Martz, but there are much loftier targets to pursue later in the year.
The Parker camp have a stated goal of manoeuvring their charge into a mandatory challenger position by the end of 2016, a feasible aim for a division in a state of flux. In the WBO, for example, Parker is ranked behind only Fury, Klitschko, Charles Martin, Anthony Joshua and Vyacheslav Glazkov, fighters all positioning themselves to clash with one another after Fury's stunning world title win.
Once the men above him have their shot, it will be Parker's turn. But, with time on his side and still short of his physical peak, Parker is in no particular hurry.
"It comes down to a decision with my team," he said. "I'm confident in what I can do in the ring. But I'm not looking at fighting any particular opponent."
First he has another four-week training camp in Las Vegas to prepare for Bergman. And while Parker was unflustered about potential opponents, he was much more concerned with being allowed a festive treat.
"Probably on Christmas I can have something nice to eat - hopefully Kevin allows me. If he doesn't, I might sneak it."