I see several problems with this.
I suppose some sort of balance _could_ be achieved. If there's a lot of these broad skills, and you can only increase them +1 per session, and you double (or so) the HP awards, you can get the result of slowing advancement in the broad skills while still allowing the characters some room to improve the narrow skills.
However, this presumes that the abilities to be classified as broad are somehow dangerous to the game because they're too useful, while the ones that remain narrow abilities are more for color than utility... I don't agree with this at all. I think most abilities have the potential to be useful in most situations if you use your imagination.
If the perceived problem is that players are sinking all their HP into Close Combat or Tough or whatever, there's a much simpler solution, as others have pointed out: just throw a string of non-combat sessions at them.
Besides, even under the proposed system, the wannabee-combat monster will
simply buy up Close Combat for 3 hero points and his favorite fighting
technique for one more point, and thus achieve an effective +2 increase per
session anyway, for just 1 HP more than before... Only the players who
_don't_ want combat monsters, just a respectable level of fighting ability,
will have their styles cramped because they're forced to spend 2 HP more
than they used to.
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