Recent food crises have highlighted the need to better understand the between-year variability of agricultural production. Although increasing future production seems necessary, the globalization of commodity markets suggests that the food system would also benefit from enhanced supplies stability through a reduction in the year-to-year variability. Here, we develop an analytical expression decomposing global crop yield interannual variability into three informative components that quantify how evenly are croplands distributed in the world, the proportion of cultivated areas allocated to regions of above or below average variability and the covariation between yields in distinct world regions. This decomposition is used to identify drivers of interannual yield variations for four major crops (i.e., maize, rice, soybean and wheat) over the period 1961-2012. We show that maize production is fairly spread but marked by one prominent region with high levels of crop yield interannual variability (which encompasses the North American corn belt in the USA, and Canada). In contrast, global rice yields have a small variability because, although spatially concentrated, much of the production is located in regions of below-average variability (i.e., South, Eastern and South Eastern Asia). Because of these contrasted land use allocations, an even cultivated land distribution across regions would reduce global maize yield variance, but increase the variance of global yield rice. Intermediate results are obtained for soybean and wheat for which croplands are mainly located in regions with close-to-average variability. At the scale of large world regions, we find that covariances of regional yields have a negligible contribution to global yield variance. The proposed decomposition could be applied at any spatial and time scales, including the yearly time step. By addressing global crop production stability (or lack thereof) our results contribute to the understanding of a key aspect of global food availability.