In this paper, we propose linear branch entropy, a new metric for characterizing branch behavior. The metric is independent of the configuration of a specific branch predictor, but it is highly correlated with the branch miss rate of any predictor. In particular, we show that there is a linear relationship between linear branch entropy and the branch miss rate. This means that the metric can be used to estimate branch miss rates without simulating a branch predictor by constructing a linear function between entropy and miss rate. The resulting model is more accurate than previously proposed branch classification models, such as taken rate and transition rate. Furthermore, linear branch entropy can be used to analyze the branch behavior of applications, independent of specific branch predictor implementations, and the linear branch miss rate function enables comparing branch predictors on how well they perform on easy-to-predict versus hard-to-predict branches. As a case study, we find that the winner of the latest branch predictor competition performs worse on hard-to-predict branches, compared to the third runner-up; however, since the benchmark suite mainly consisted of easy branches, a predictor that performs well on easy-to-predict branches has a lower average miss rate.