But this would affect any method. So its not really relevant when deciding a method right?
Incentives need to be based on obtainable goals and targeted improvements. Payouts (bribes!) to students for good grades and scores actually really work. Money helps kids internalize the societal value placed on their performance. Similarly, targeted bonuses for teachers work too, but only if formulated relative to the characteristics of enrolled students. See the literature by R. Fryer, for example