I'd argue that the job of a fullback goes unnoticed, especially when they aren't the greatest offensively. Forcing your winger into putting in a poor quality cross often results in the crosser getting castigated by fans, when in reality, the defenders made it really hard for him to even put one in. In fact, most wingers won't even cross the ball if they don't feel they can wrap their foot around it, and the ball will go back towards the middle; yet again, you won't see the good work of the full back, you'll see a winger trying to make something happen in a more central region i.e. a shot from 20-25 yards, instead of putting in a speculative, hopeful cross.
Likewise, Carrick does the same; slowing down the opposition attack, breaking it up with interceptions, yet a lot of this will go down to 'Oh that stupid idiot, he gave the ball right back to the opposition, whereas, in reality, Carrick will have read the play and cut the pass out. Again, someone like Lionheart Scottie Parker will be considered far superior, because he gets stuck into tackles which you do recognize as an ACTION made by the defending player; something they've done on purpose to cut the play out.
Keeping the ball tidy, far tidier than Parker and his ilk. 90-91% passing completion, with a far better passing range; but all we'll remember is the lack of assists etc.