Rigour is a prayer that was released on the 19 August 2010. It boosts Ranged by 20%, Defence by 25%, and requires 70 Prayer to use. It is unlocked after completing the Knight Waves Training.
Considering the boosts and Prayer level required, this prayer is to be considered the Ranged equivalent of the melee prayer Piety.
The Rigour prayer currently grants the greatest increase to a player's ranged attack (+20%) , and can only be matched by combining Eagle Eye (+15%) and amulet of zealots (+5%) although that will give a large prayer penalty (-8) and occupies the neck-wear slot. However, the amulet of zealots and Eagle Eye are available in free-to-play while Rigour is not.
To make it fair for all 3 combat styles Rigour and Augury will be removed from the dungeoneering shop and your points will be refunded. They will now unlock alongside Piety by completing the knights waves.