We use elections data in which a large number of ties in vote counts between candidates are resolved via a lottery to study the personal incumbency advantage. We benchmark non-experimental regression discontinuity design (RDD) estimates against the estimate produced by this experiment that takes place exactly at the cutoff. The experimental estimate suggests that there is no personal incumbency advantage. In contrast, conventional local polynomial RDD estimates suggest a moderate and statistically significant effect. Bias-corrected RDD estimates that apply robust inference are, however, in line with the experimental estimate. Therefore, state-of-the-art implementation of RDD can meet the replication standard in the context of close elections.