There's no way that can be right (lol). Using standard gear (neitiznot, fire cape, fury, defender, barrows gloves, dragon boots, berserker (i): The average hit of the rapier is 289.9 The average hit of the longsword is 316 The attack delay of the rapier is 1.8 seconds The attack delay of the longsword is 2.4 seconds Therefore, in one hour, assuming 100% accuracy for both, The rapier should hit 580k damage The longsword should hit 474k damage Now, let's assume the rapier hits 50% of the time. The rapier would deal 290k damage. For the longsword to hit 290k damage, it would need to hit 61% of the time. That means you'd need to get a 22% increase in accuracy from a 21% boost in your weapon attack bonus. That's absurd even by itself (if you already hit 50% or more), but when you also consider that you have 125/99 attack and turmoil it's 100% impossible. Turns out with the accuracy boosting gear, potions, and prayers, the longsword should never be this much more accurate than the rapier.