Player is very inconsistent in report and doesn't change, but player is very consistent in games.

I also do not get it. I got very consistent players who constantly get bad match ratings and inconsistent players who constantly get good match ratings. Thou that was more visible couple seasons ago when they both ware same star ratings. 

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A very consistent player has "very inconsistent" in his report.

That's linked to his Consistency hidden attribute. As you've found, it doesn't necessarily mean performances will be inconsistent.

21 hours ago, Furmanbp said:

I got very consistent players who constantly get bad match ratings and inconsistent players who constantly get good match ratings.

Consistency is a hidden attribute. It doesn't necessarily indicate how well a player will perform as there are a million variables at play - his attributes, the tactic, his role, how consistent/inconsistent he is, how much better/worse he is the the rest of the players in the team and league, how consistent/inconsistent the other players in the team are etc

There are also other hidden attributes like Pressure and Important Matches that can affect a player on a match day.