It serves as emphasis. Most people have interpreted "caffeine has a half-life of X hours" to mean "oh so it's fine to have it just X hours before bed. By expli

It serves as emphasis. Most people have interpreted "caffeine has a half-life of X hours" to mean "oh so it's fine to have it just X hours before bed. By explicitly calling out the quarter-life, it prompts people to think if a quarter of the amount would still affect them.