A second experiment was carried out with an even simpler task of explaining the predictions of the molecular weight. However, the poor performance (r 2 of 0.67, SI Table ), especially for such a simple task, indicated a faulty model. Using the Myerson values to explain some of the predictions highlighted an immediate problem of the model, as the Myerson values showed negative contributions of some atoms (Figure ) instead of just positive contributions, with higher values for heavier atoms (Figure ). The problem was identified as using a mean as the invariant function for the pooling of the node embeddings into a graph embedding. Here, the purely additive nature of molecular weight interferes with the aggregation method which, in case of the mean, loses a lot of information regarding the graph size. Using sum pooling instead improves the model to the expected very high performance (r 2 of 0.999, SI Table ) and the Myerson values correctly highlight the expected positive atom contributions (Figure ). This example illustrates how the use of Myerson values can help in identifying flaws in model design and erroneous predictions. Looking at (the error of) the actual Myerson values per atom (Figure ), we see that the explanations are still not perfect. This restricts a potential use case of Myerson values, where the Myerson values could be used to obtain a new model for atom contributions of a molecular property (similar to how clogP is calculated based on individual atoms). While better GNNs may be able open the door for this application, we did not explore it further in this work. After this promising proof of concept, we investigated the explanatory power of Myerson values on an experimental dataset of kinase inhibitors. Kinase inhibitors are well known for binding in the hinge region of the protein, so a successful explanation should highlight the atoms important for binding. We employed a simple GNN with three GAT layers, followed by sum pooling and a single linear layer. Our model has an accuracy of 0.83. We first investigated a subset of the dataset with 2018 molecules. Among these, there were 418 true positive predictions, 1203 true negative, 131 false positive and 326 false negative. Looking at an example of a true positive prediction (not from the dataset) in Figure , we can not only see the expected H-bond donors and acceptors that could bind to the hinge region, but the surrounding scaffold appears to contribute positively to the prediction as well. The crystal structure confirms that the correct substructures were highlighted (Figure ). Interestingly, the crystal structure reveals that the hydroxy group of the molecule is important for binding but is seen as neutral by the GNN. This indicates that either the model and training dataset does not provide enough information for this prediction, or this hydroxy group is not as important as might be expected from the crystal structure. This can be possible since replacing a water interacting with the protein by another hydrogen bonding partner does not always lead to improved activity.