How does the Roman Catholic idea of ex opere operato explain sacramental effectiveness?

In Roman Catholic theology, the phrase ex opere operato—Latin for "from the work done"—is used to describe the effectiveness of a sacrament. This doctrine asserts that the efficacy of a sacrament is derived from the saving act of God in Christ, rather than the personal merits, faith, or virtue of the minister performing the rite.1

Because the minister acts as an agent of the church, their individual holiness or lack thereof does not add to or detract from the sacrament's power. Instead, the rite itself, when performed with the proper "matter" (material) and "form" (words), serves as an effective sign that applies God's grace to the recipient. This concept ensures that the sacrament’s validity is grounded in the objective promise of Christ rather than the subjective state of the human administrator.1

This is distinct from the concept of ex opere operantis ("from the work of the worker"), which relates to the conditions or dispositions required for the worthy reception of a sacrament.2