Here are the missing social features and how they could be designed.
There's no real advantage in being in a group and helping others in group
- A collective group-progress (sum / average of active players) could help
- HP: House points they would be called
- very good skills in a training could earn house points
- winning in a quidditch game could earn house points, too
- every now and then (seasons?) the house cup could be given to the winning house
- winning the house cup could appoint all players of that house additional points / badges
There's no way to connect to players nearby and communicate within the game
- The players currently in the radius of a Pokestop / Gym could be listed (not in a map! --> privacy)
- a chat-channel (per team/house?) could be accessible for all players close to a POI
- there should be a bad-word filter + a flag button to quickly ban players posting bad things
- when attacking a gym / playing in a pitch players involved should have a chat for each team
There's no way to compare with friends and see their progress without meeting and asking them
- Introduce a friends list (both sides have to accept, search by player name or email)
- Importing the address book / facebook should automatically show players playing the game, too
- One shall see the current main progress and number of differenct collectable items collected
- One may also see the badges earned by a user
- There may be a direct chat with friends within the game to organize attacks / events
There's no way of direct battle against a friend
- Introduce direct battle possibility with friends or anybody by using their name
- For fighting against each other they may or may not need to be at the same location (opinions?)
- Fighting statistics against specific friends and overall are available
- An ELO like ranking points is calculated using the last fought opponents and battle results
Here are the missing social features and how they could be designed.