Energy decomposition analysis (EDA) is a widely used tool for extracting physical and chemical insights from electronic structure calculations of intermolecular interactions, as well as for the development of advanced force fields for describing those interactions. Recently, the absolutely localized molecular orbital (ALMO) EDA has been extended from the self-consistent field level to the second-order Moller-Plesset (MP2) theory level. This paper reports an efficient implementation of the MP2 ALMO-EDA that scales optimally, employs the resolution of the identity (RI) approximation for post-SCF matrix elements, and is shared-memory parallel. The algorithms necessary to achieve this implementation are described in detail. Performance tests using the aug-cc-pVTZ basis set for water clusters of up to 10 molecules are reported. The timings suggest that the MP2 ALMO-EDA is computationally feasible whenever MP2 energy calculations themselves are feasible, and the cost is dominated by the SCF itself in this size regime. The MP2 ALMO-EDA is applied to study the origin of substituent effects in anion-pi interactions between chloride and benzene and mono- through hexafluorobenzene. The effect of fluoro substituents was primarily to change the frozen interaction. Detailed analysis supports the interpretation that anion-pi interactions are favorable because of electrostatic interaction with the substituents.