Avoiding dangerous climate change necessitates the decarbonization of electricity systems within the next few decades. In Germany, this decarbonization is based on an increased exploitation of variable renewable electricity sources such as wind and solar power. While system security has remained constantly high, the integration of renewables causes additional costs. In 2015, the costs of grid management saw an all time high of about € 1 billion. Despite the addition of renewable capacity, these costs dropped substantially in 2016. We thus investigate the effect of natural climate variability on grid management costs in this study. We show that the decline is triggered by natural wind variability focusing on redispatch as a main cost driver. In particular, we find that 2016 was a weak year in terms of wind generation averages and the occurrence of westerly circulation weather types. Moreover, we show that a simple model based on the wind generation time series is skillful in detecting redispatch events on timescales of weeks and beyond. As a consequence, alterations in annual redispatch costs in the order of hundreds of millions of euros need to be understood and communicated as a normal feature of the current system due to natural wind variability.