As a hero, what is unconventional about Romeo in Romeo and Juliet?

When you think about a conventional
(or typical) hero, what qualities come to mind?  I think of brave, physically
attractive, selfless or in some way sacrificial of himself for others, someone who is
naturally goodhearted, talented, a good fighter, often self-made, and a good decision
maker.  Also, most people associate heroes with "winning" in the end.  They fight and
defeat the enemy (who is typically a threat to the greater good), win the love of the
lady, and end up happily ever after.

In many ways, the
conventional hero possess qualities that are the result of both age and experience. 
Romeo, because of his youth, immediately lacks the wisdom that comes from age and
experience.

Additionally, though Romeo is physically
attractive (to Juliet at least) and skilled with a sword, he does not come across as
self-less nor does he seem to aim at goodness.  In fact, he's just the opposite.  He is
quite spoiled and selfish, and all of his decisions are based on his desire for instant
gratification.  He is not a planner.  He is rash, hasty, emotional, and fickle in
decision making.  After killing Tybalt, he ends up in the Friar's cell emotional and
crying to the point that the Friar calls him "womanish."  This is not the courage and
fearlessness we expect of a conventional hero.

Finally,
Romeo does not win in the end.  He does fight his enemy which are
only a threat to the Montagues and not to society, but does not necessarily defeat him. 
He does win the hand of Juliet, but at a very great price.  Rather than living happily
ever after, in the end both die.