We train and compare the performance of two different machine learning algorithms to learn changes in winter wheat production for fields from the southwest of Sweden. As input to these algorithms, we use cloud-penetrating Sentinel-1 polarimetry radar data together with respective field topography and local weather over four different years. We note that all of the input data were freely available. During training, we used information on winter wheat production over the fields of interest which was available from participating farmers. The two machine learning models we trained are the Light Gradient-Boosting Machine and a Feed-forward Neural Network. Our results show that Sentinel-1 data contain valuable information which can be used for training to predict winter wheat yield once two important steps are taken: performing a critical transformation of each pixel in the images to align it to the training data and then following up with despeckling treatment. Using this approach, we were able to achieve a top root mean square error of 0.75 tons per hectare and a top accuracy of 86% using a k-fold method with k=5. More importantly, however, we established that Sentinel-1 data alone are sufficient to predict yield with an average root mean square error of 0.89 tons per hectare, making this method feasible to employ worldwide.