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Alves was a great fullback at Sevilla, no doubt. That is why Barcelona bought him for the amount they did.
At Barcelona, his role has become much more crucial than just that of the marauding fullback who can defend once in a while.
Pep Guardiola gave Alves license to roam all over the right flank. He could play as high up the field as he wanted to, as long as he came back to defend when needed. This was a singularly brilliant move for two reasons:
1. Alves' presence allowed Lionel Messi to cut inside
Early in Guardiola's time at Barcelona, Messi was still an inside right—a player who cut inside from the right flank to shoot with his left foot.
In football, a winger and a full-back usually handle a wing. With Messi cutting inside, the right wing would be left exposed to counter attacks. Alves' presence served to cut off any early counters, and ensure that the wing was not left unguarded.
2. Barcelona effectively had an extra midfielder to run the show
A very important facet of Guardiola's tactics is the crowding up of midfield with a large number of players who can play the ball among each other.
With Alves playing very high up the field, Barcelona gain an extra man in midfield, which enables them to control the game more effectively.
Alves' shift from marauding fullback to winger/midfielder/defender makes him almost irreplaceable for Barcelona.