I watch a fair bit of aussie rules football, and for years they had the same attitude as most here do about stats, i.e. that they are pretty useless. That was because their stats were like ours are currently, and didn't really tell you much.
what they started doing instead was measuring things that actually made a difference, rather than being pure counts.
Rather than just possession, they measures the ability of team to win contested possessions, the number of passes that were effective (i.e. actually made a contribution rather than sideways/backwards), the times teams got the ball into dangerous areas etc. It allowed them to differeniate between teams having a lot of possession, and being able to use the possession effectively.
It's a particular pet peeve of mine that so many now use shots on target as a measure of how many good chances a team created, dismissing off-target shots as ones of poorer quality. That's just nonsense. Of the four best chances in the Brighton v Reading game, for example, two hit the woodwork, yet neither counts as a shot on target.