Abstract: Two novel damped outrigger systems, viscous type (VD) and buckling restrained brace type (BRB), were presented for high rise buildings with outriggers. The probability density evolution method (PDEM) was introduced into the analysis of such systems. Random sources from site excitation and damper parameters were considered, respectively. The Kanai-Tajimi model was used to generate artificial ground motion. The 2.5-times mean square error method with 15 discrete representative points from random normal variables was proposed. The total variation diminishing finite differential scheme (TVD) was applied to provide the probability density evolution of maximal story drift angle, and the equivalent extreme value method (EVEM) was utilized to analyze the relationship between dynamic reliability and targeted story drift angle limit. The research results show that both proposed novel damped outrigger systems can reach higher reliability than traditional aseismatic structures. The VD type outrigger system possesses a high reliability under random site excitation, while the BRB type outrigger system is more reliable in the case of random damper parameters. Therefore, the design of redundant outriggers as damped outriggers is capable of increasing the safety of high-rise buildings and it is worthwhile to popularize and apply them in real engineering.