I remember Benitez being particularly hung up on the "final third passing percentage" as a stat he really valued when looking at players. He mentioned it over and over again, so obviously it was important to him. Unfortunately we have little more than those kind of clues when trying to figure out what the statisticians are really doing; none of them are going to put their theories in public as it's a big part of the competitive advantage they're trying to build.
I've been pondering over a stat, myself, and wondering about what it might tell us about a player. Call it "2nd pass percentage" or "2nd pass chance creation." Basically, it would be a stat not of the player's completed pass percentage, but the percentage of passes completed AFTER their pass. Or, alternately, and perhaps more instructive, the percentage of their passes that led to the next pass creating a chance. Or possibly the percentage of their completed passes that led to a chance in that possession.
Many times this might be useless, as Player A passes to Player B, who then gives the ball away attempting to play Player C in. Why should Player A's statistics suffer for a mistake by Player B? However, I think that in the aggregate, you might eventually see some interesting things with these two measures. How often does a player's pass put the player receiving the ball in a good position to make the next pass? Sometimes a midfielder will fizz a ball through a gap to a forward, but just a half-step behind him or too high or something, leading to the forward getting the ball but almost immediately losing it to an opposing defender. When that happens, we need a statistic that will show that the midfielder was partially to blame for the pass selection, even though he completed the pass.
The statistic of "2nd pass chance creation" might be even more instructive; how often does a player's pass lead to a chance? You could measure this either as how often the next pass is a chance created, or how often that possession leads to a chance created. It would be much more instructive than a pass percentage to see how often that pass leads to the creation of a chance at goal.
I'm sure that the professional statisticians that we're employing to analyse the game have thought of these and many more, and are trying to work out which of these stats are being undervalued and how we can improve the most important number, the number of points. However, it seems clear that as of right now, we have not quite worked out all the kinks, as we're creating chances hand over fist, and still losing and drawing a lot of games. I would guess that our results this season will cause something of a rethink about which statistics we should value most highly in the pursuit of wins.