2 questions, 4 cents of mine:
Scores are counted in stroke play, and like in real life tourneys, the lowest scores win. Averages are calculated from rated stroke play rounds (s.p.r.), i.e., better players may have lower averages. Low average + a certain number of rated s.p.r. promote a rise in tiers, from Hack to Legend.
(BTW, tourneys deliver a high XP bonus per game, 2x the private s.p.r.)
OTOH, some (or more) players decide not to show their skills in rated s.p.r. thus staying in low tiers. This enables them to play some games as wolves in sheep's clothing - in common wording they are called sandbaggers.
A wedge might well be more of worth than a putter. Putts are merely defined by length & direction, and this is quite well covered by the Starter putter. Custom putters have more&custom scales and hopefully they are still a bit more precise than the first one. OTOH, I've seen a Master play with it, and rumor has it that some Legends stick to it, too.
A better wedge has a broad range of adaptions in it, enabling the player to shape his shots. The most important issue may be backspin - control the roll & let the ball sit where it hits the green. If you set up short putts this way you may tap-in with your olde putter :o)