Have ideas of "gamification" been applied to education?
A popular lit review [1] discusses some game concepts that have been empirically tested to support the idea of gamification. In some cases, these may be very hard to quantify. For instance, the article cites fantasy as one gaming characteristic that engages gamers. Other characteristics, such as having clear, well defined rules/goals seem easier to objectify.

The authors also cite mystery, challenge (something hard but not too hard, with levels of increasing difficulty), sensory stimuli, and user control as important attributes as well.

[1] Garris et al. (2002). Games, Motivation, and Learning: A Research and Practice Model. Simulation and Gaming, 33, 441-467. Retrieved from http://scottsdale.brainadvantage.com/PDF/Games,%20Motivation,%20and%20Learning.pdf