tactical analysis of Napoli vs Milan
Imo, it is personal perception of how he influences the game and the players around him. (not good if you ask me)

What I mean by that is, does he alleviate pressure from other players and the team? Is he a safe player to give the ball to when we are under pressure? Will he safely break the other team's press by finding a safe place for the ball, for example a vertical pass behind the line of pressure...or will he panic or just play the ball laterally and still in front of the pressure?

Those are all important characteristics of a player that plays in front of the back line.....and if you ask me, Montolivo does not do any of those things consistently well enough.

Like somedevil said, he very rarely puts the ball vertically behind the opposing midfield line for example. His first thought when we are under pressure is to play the ball sideways or backwards. This only makes the problem even bigger as the opposition gets closer and closer to our goal, and eventually we have to just clear the ball and lose possession anyway. Instead, if he can not panic so much, and simply find a pass behind that first line of pressure (vertically play the ball behind the wave of pressure), than this same line of pressure from the other team will have to actually go back and away from our goal and we gain positional advantage and get into their half of the field. ONE SIMPLE pass, yet it is very difficult, I know. This is what made Pirlo so great, and what makes other world class midfielders great today. Sadly for us, Montolivo does not possess this ability when it comes to "speed of thought" and ability to alleviate pressure.

Statistics can be a very skewed way to look at his performances. Maybe he played a ton of vertical passes, but.....
1. were they vertical passes to Kucka for example just 10 yards away but still not behind the pressure?
2. Was it a pass that was played behind a wave of pressure like I said?
3. Was it a pass made under absolutely no pressure with the opposition happy to just go back and let us simply make that pass OR
4. was it a pass that he made when the opposition had 6-7 players in our half pressuring the hell out of us and he just took all of them out of the game by simply making a pass behind them and forcing them to retract back to defend (meaning all of their hard work of pressing was done for nothing as now they have to sprint back in order to get back behind the ball)?

I don't have the statistics of these, and it will be almost impossible to find them to be honest unless you sit down on a Sunday afternoon during the game and analyze every situation that Montolivo is involved in (and is not involved in but could/should have been involved).......but I am willing to bet that most of his "vertical" passes are of the #1 and #3 nature and very few (if any in some games) are of the #2 and #4 type.