McCarthy came thought the youth system at Hamilton before moving onto Wigan Athletic.
"There's no doubt about it, he's the best player Scotland has ever produced," said McAvoy to evertonfc.com. "Technically he's great, he's got a fantastic right and left foot, he can pick passes and he's got great energy levels to go and support.
"We brought him to our academy, which has produced some great players, but James was certainly the best. We knew as time was progressing we had something special. The Scottish set-up had some top-notch players at the time but we knew James was better than them.
"My honest opinion is that Everton have got a cracking young player who's 22 years of age with a long career ahead of him. I think in the current financial climate the £13million Everton paid for him is fantastic business.
"The manager (Roberto Martinez) knows him well and I think he'll add a real bit of finesse to the team. I certainly think in the long term he'll be a fantastic acquisition for the club."
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