given probability $p$. In Figure 1, we plot the RMSE (root mean square error) of the predicted mark as a percentage of the 100 marks for varying $p$. Thus a RMSE of 5% means that the PeerRank grade is off with a root mean square error of 5 marks (out of the 100 possible marks). If we map back onto grades out of 10, this means we are off by less than half a grade. For $p>0.6$ (in other words, for where the marks are typically above 60 out of 100), the generalised PeerRank method outperforms simply averaging the peer grades. For $p>0.65$, the error is 4% or less. This compares well with the error returned by simply averaging the peer grades (which is mostly above 10% in this region). Note that for PeerRank to get any useful signal out of the data, we need $p>0.5$. At $p=0.5$, we will often answer (or mark) an exam just as well by tossing a coin. With the PeerRank method, we need the exam to be informative (that is, to have $p > 0.6$), to be able to extract much information from the grade matrix.

![Performance of the generalised PeerRank method on marks 