Additive Noise Models (ANMs) are a common model class for causal discovery from observational data and are often used to generate synthetic data for causal discovery benchmarking. Specifying an ANM requires choosing all parameters, including those not fixed by explicit assumptions. Reisach et al. (2021) show that sorting variables by increasing variance often yields an ordering close to a causal order and introduce var-sortability to quantify this alignment. Since increasing variances may be unrealistic and are scale-dependent, ANM data are often standardized in benchmarks. We show that synthetic ANM data are characterized by another pattern that is scale-invariant: the explainable fraction of a variable's variance, as captured by the coefficient of determination $R^2$, tends to increase along the causal order. The result is high $R^2$-sortability, meaning that sorting the variables by increasing $R^2$ yields an ordering close to a causal order. We propose an efficient baseline algorithm termed $R^2$-SortnRegress that exploits high $R^2$-sortability and that can match and exceed the performance of established causal discovery algorithms. We show analytically that sufficiently high edge weights lead to a relative decrease of the noise contributions along causal chains, resulting in increasingly deterministic relationships and high $R^2$. We characterize $R^2$-sortability for different simulation parameters and find high values in common settings. Our findings reveal high $R^2$-sortability as an assumption about the data generating process relevant to causal discovery and implicit in many ANM sampling schemes. It should be made explicit, as its prevalence in real-world data is unknown. For causal discovery benchmarking, we implement $R^2$-sortability, the $R^2$-SortnRegress algorithm, and ANM simulation procedures in our library CausalDisco at https://causaldisco.github.io/CausalDisco/.

Additive noise models are a class of causal models in which each variable is defined as a function of its causes plus independent noise. In such models, the ordering of variables by marginal variances may be indicative of the causal order. We introduce varsortability as a measure of agreement between the ordering by marginal variance and the causal order. We show how varsortability dominates the performance of continuous structure learning algorithms on synthetic data. On real-world data, varsortability is an implausible and untestable assumption and we find no indication of high varsortability. We aim to raise awareness that varsortability easily occurs in simulated additive noise models. We provide a baseline method that explicitly exploits varsortability and advocate reporting varsortability in benchmarking data.