Student retention is a central challenge in systems for learning at scale. It has been argued that educational video games could improve student retention by providing engaging experiences and informing the design of other online learning environments. However, educational games are not uniformly effective. Our recent research shows that player retention can be increased by using a brain points incentive structure that rewards behaviors associated with growth mindset, or the belief that intelligence can grow. In this paper, we expand on our prior work by providing new insights into how growth mindset behaviors can be effectively promoted in the educational game Refraction. We present results from an online study of 25,000 children who were exposed to five different versions of the brain points intervention. We find that growth mindset animations cause a large number of players to quit, while brain points encourage persistence. Most importantly, we find that awarding brain points randomly is ineffective; the incentive structure is successful specifically because it rewards desirable growth mindset behaviors. These findings have important implications that can support the future generalization of the brain points intervention to new educational contexts.