Native speakers can judge whether a sentence is an acceptable instance of their language. Acceptability provides a means of evaluating whether computational language models are processing language in a human-like manner. We test the ability of computational language models, simple language features, and word embeddings to predict native English speakers judgments of acceptability on English-language essays written by non-native speakers. We find that much of the sentence acceptability variance can be captured by a combination of features including misspellings, word order, and word similarity (Pearson's r = 0.494). While predictive neural models fit acceptability judgments well (r = 0.527), we find that a 4-gram model with statistical smoothing is just as good (r = 0.528). Thanks to incorporating a count of misspellings, our 4-gram model surpasses both the previous unsupervised state-of-the art (Lau et al., 2015; r = 0.472), and the average non-expert native speaker (r = 0.46). Our results demonstrate that acceptability is well captured by n-gram statistics and simple language features.