Specifically HGSS, but any other games with the feature would be cool too. I have a score of 920 in my SS with three badges and it would be cool to know what influences that + the maximum.
In Generation IV, the Trainer Card also carries the Trainer's score. A Trainer's score offers no specific purpose in the game and appears to be only aesthetic. The score begins at zero and increases every time a score-altering event occurs. Berry is picked DPPt +1 Battled against a wild Pokémon +2 Battled against a Pokémon Trainer +3 Pokémon Egg is hatched +7 Pokémon is traded +10 Pokémon is evolved +20 Flag is obtained in the Underground +34
Source
It carries on going until 9,999.
Hope I could help.