Wave runup is an important issue that needs to be considered in the design of offshore structure such as wind turbine piles. Most of the recent proposed formulas for the estimation of wave runup height on vertical piles are based on the calculation of wave kinematics using an appropriate wave theory. In this study, regular and irregular wave runups were investigated based on scaling arguments using available experimental datasets. Effective nondimensional parameters were found by considering the physics of wave-pile interaction as well as the correlation based sensitivity analysis. Wave height to water depth ratio and wave steepness were identified as the governing parameters for the estimation of runup height to wave height ratio. New formulas were developed for the estimation of wave runup height using a combination of model tree and nonlinear regression techniques. The performance of the new formulas was also compared with those of previous methods using accuracy metrics. The present method does not need any pre-calculation for the determination of wave kinematics and provides accurate prediction of wave runup (i.e. runup height exceeded by 2% of the waves and maximum runup height) compared to the other methods.