RuneScore is a points system used to measure completed achievements. It was added on 29 August 2017 and can be viewed in the Hero tab. Each achievement has an assigned value (between 5 and 75) and upon completing the achievement its value is added to the player's RuneScore.
The maximum possible RuneScore is currently 19,730, coming from 1,848 achievements, as of 19 March 2018. Some achievements that are heavily luck-dependent, such as skill pets, boss pets or boss collection log achievements, do not contribute to a player's RuneScore and have an assigned value of 0.