"Remember, it's not about how long it is, but what you are able to do with it! Possession of the ball, that is..." quote from 11tegen11, July 19th 2012.
Probably the most intelligent statement you are ever likely to read concerning the use of possession statistics in football.
Possession stats tell you how long a team spent doing "things".
They don't tell you what those things were. Teams could have been trying to score, they could have been trying to prevent the opposition from scoring by keeping the ball. Polar opposite objectives. Sides could have been comfortably ahead or they could have been comfortably behind. It doesn't tell you how good the players were at carrying out their various tasks.
Ability to Carry out the Game Plan.
None of these factors appear in a catch all possession stat and each of them drives it.
Percentage of Possession should be largely ignored.