sessions_per_user = visits.groupby(['session_year', 'session_date']).agg({'uid': ['count','nunique']})
sessions_per_user.columns = ['n_sessions', 'n_users']
sessions_per_user['sessions_per_user'] = sessions_per_user['n_sessions'] / sessions_per_user['n_users']
sessions_per_user['sessions_per_user'].mean()