Whenever an item is damaged, the item's hardness is subtracted from the damage, pretty much like Damage Reduction.
If the shortbow has 5 hardness, that means that any attack that would do less than 5 damage doesn't harm it.
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You WERE incorrect, and unfortunately I don't have page numbers to reference this, but an item's hardness is akin to damage reduction. when an attack is made against an object, you subtract its hardness from the damage done. In your case, the Mite did 4 damage against a hardness of 5, meaning that it did not do enough damage to overcome the hardness, let alone actually damage the bow. You would have to deal 6 or more damage to start actually damaging the bow.
EDIT: Ninja'd. T_T
Last night, my players encountered some mites. During the encounter, one of the players dropped his shortbow and began to use his dagger. So, one of the mites decided to try and break the shortbow. The mite rolled a 10 on attack and a 4 for damage. So I looked up the rules for hardness and such and found that a shortbow has a hardness of 5, 2 hp and if the damage done is more than half the hp the item is considered to have the broken condition. OK, so I ruled that the bow would have the broken condition. However, one of the more rules knowledgeable players stated this was incorrect as the damage did not surpass the hardness, therefore the damage is basically null and void. I would like to know if I was wrong or not and why?
I believe that for damage to be "done" it must get through hardness first, so to get the said shortbow to the broken condition you would have to do 6.5 points of damage or more. five is absorbed by hardness and you have to do more than 1 more.
however, if you rule that the type of damage is particularly effective against the substance, like fire to paper, or scissors to bowstring,etc, then you can ignore hardness all together, in addition to doubling the damage.(pg.174 corerulbook)edit:semi ninja'd twice
Last night, my players encountered some mites. During the encounter, one of the players dropped his shortbow and began to use his dagger. So, one of the mites decided to try and break the shortbow. The mite rolled a 10 on attack and a 4 for damage. So I looked up the rules for hardness and such and found that a shortbow has a hardness of 5, 2 hp and if the damage done is more than half the hp the item is considered to have the broken condition. OK, so I ruled that the bow would have the broken condition. However, one of the more rules knowledgeable players stated this was incorrect as the damage did not surpass the hardness, therefore the damage is basically null and void. I would like to know if I was wrong or not and why?
Since the bow is not currently weilded, the sunder rules don't apply, but the "Smashing an Object" rules on page 173 do.
Your player is correct:
Hardness: Each object has hardness—a number that represents how well it resists damage. When an object is damaged, subtract its hardness from the damage. Only damage in excess of its hardness is deducted from the object’s hit points (see Table 7–12, Table 7–13, and Table 7–14).
Edit: Ninja'd during cut and paste
Incidentally, the shortbow should probably have 5 hp as well as 5 hardness, at least according to the appropriate Table.
however, if you rule that the type of damage is particularly effective against the substance, like fire to paper, or scissors to bowstring,etc, then you can ignore hardness all together, in addition to doubling the damage.(pg.174 corerulbook)
This is an important point. Specifically, a pair of scissors ignores the hardness of paper, a rock ignores the hardness of a pair of scissors, and most surprisingly, a sheet of paper ignores the hardness of a rock.
Other examples are at GM discretion, but these are written in stone (probably with the aid of paper).|
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however, if you rule that the type of damage is particularly effective against the substance, like fire to paper, or scissors to bowstring,etc, then you can ignore hardness all together, in addition to doubling the damage.(pg.174 corerulbook)This is an important point. Specifically, a pair of scissors ignores the hardness of paper, a rock ignores the hardness of a pair of scissors, and most surprisingly, a sheet of paper ignores the hardness of a rock.
Other examples are at GM discretion, but these are written in stone (probably with the aid of paper).
I'm not sure whether to groan or award you +1 internets.
however, if you rule that the type of damage is particularly effective against the substance, like fire to paper, or scissors to bowstring,etc, then you can ignore hardness all together, in addition to doubling the damage.(pg.174 corerulbook)This is an important point. Specifically, a pair of scissors ignores the hardness of paper, a rock ignores the hardness of a pair of scissors, and most surprisingly, a sheet of paper ignores the hardness of a rock.
Other examples are at GM discretion, but these are written in stone (probably with the aid of paper).
don't forget the particular effectiveness of lizard attacks on paper,
and papers destructive potential when used against spock,|
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however, if you rule that the type of damage is particularly effective against the substance, like fire to paper, or scissors to bowstring,etc, then you can ignore hardness all together, in addition to doubling the damage.(pg.174 corerulbook)This is an important point. Specifically, a pair of scissors ignores the hardness of paper, a rock ignores the hardness of a pair of scissors, and most surprisingly, a sheet of paper ignores the hardness of a rock.
Other examples are at GM discretion, but these are written in stone (probably with the aid of paper).don't forget the particular effectiveness of lizard attacks on paper,
and papers destructive potential when used against spock,
I award 1 Internets to Avalon, and 2 to you, sir. For TBBT makes me giggle heartily.
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In NeoFax's defense, he could have been correct if he had ruled the mite was attempting to break the bowstring and not the bow. If that were the case, I'd say the bow could still be fired if somebody took the time to restring it. I'd normally only allow the bowstring to be broken if the bow was unattended (as was the case) since the string is such a thin target for a sunder.