Large scale peer assessment is arguably the most critical innovation required for development of MOOCs. Its core principle is to involve students in the evaluation and feedback process of correcting assignments. However, it has been criticized for being less rigorous than instructor assessment, too demanding on students and not reliable or fair due to student biases. This paper is drawn from data and practical hands-on experience from MOOC GdP2, in which assignments were both graded by instructors and by peers. Using data from 4650 papers, each graded by 3-5 peers and by an instructor, we test hypotheses and discuss a series of questions: How to train MOOC students to grade their peers? Is peer grading as accurate as instructor grading? What data pre-processing is to be used prior to testing hypotheses on peer grading? Which grading algorithm is best for processing peer-produced data? Is anonymity in peer assessment preferable to increased student interaction? We also present the improved peer grading systems we implemented in MOOC GdP 3 and 4 thanks to this research.