Step 1: Define efficacy. Vaccine efficacy is the proportionate reduction in disease among the vaccinated group under ideal, controlled conditions — classically measured in a randomized controlled trial.
Step 2: Define effectiveness for contrast. Effectiveness is the performance under routine field conditions in the real population programme.
Step 3: Map the numbers. The 90% is derived from the randomized controlled trial → that is the efficacy. The 85% is the routine/community value → that is the effectiveness.
Step 4: Why efficacy is the higher value. Trials enforce strict dosing schedules, a controlled cold chain, and a selected healthier study population, so the measured protection is at its maximum. Field use loses some of this benefit, so effectiveness (85%) is usually lower than efficacy (90%).
Step 5: Why the others are wrong. 85% is the effectiveness, not efficacy. 5% is merely the gap; 87.5% is a meaningless average. Efficacy is the directly measured trial value.
Key fact: Efficacy = ideal trial performance = 90%.