Encountering the same compiler error repeatedly, particularly several times consecutively, has been cited as a strong indicator that a student is struggling with important programming concepts. Despite this, there are relatively few studies which investigate repeated errors in isolation or in much depth. There are also few data-driven metrics for measuring programming performance, and fewer for measuring repeated errors. This paper makes two contributions. First we introduce a new metric to quantify repeated errors, the repeated error density (RED). We compare this to Jadud's Error Quotient (EQ), the most studied metric, and show that RED has advantages over EQ including being less context dependent, and being useful for short sessions. This allows us to answer two questions posited by Jadud in 2006 that have until now been unanswered. Second, we compare the EQ and RED scores using data from an empirical control/intervention group study involving an editor which enhances compiler error messages. This intervention group has been previously shown to have a reduced overall number of student errors, number of errors per student, and number of repeated student errors per compiler error message. In this research we find a reduction in EQ, providing further evidence that error message enhancement has positive effects. In addition we find a significant reduction in RED providing evidence that this metric is valid.
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