In many regions the strength of El Niño—Southern Oscillation (ENSO) teleconnections has varied over the last century. It is an active area of research to investigate how such changes can be related to long-term climate variability or climate change. However, fluctuations due to the limited observational record and low signal-to-noise ratio also contribute to variations in the apparent strength of the teleconnections. These contributions are considered at 658 precipitation stations around the globe. For each station the probability is estimated that the observed decadal variations in the effect of ENSO on precipitation are explainable by random statistical fluctuations of a constant teleconnection. The number of stations with statistically significant decadal variations is much lower than the number with statistically significant ENSO teleconnections. It is close to the number expected from chance alone. The observed period is too short to reliably detect multiplicative decadal variability in ENSO precipitation teleconnections.