Finite element (FE) models are often used to study the biomechanical effects of traumatic brain injury (TBI). Measures based on mechanical responses, such as principal strain or invariants of the strain tensor, are used as a metric to predict the risk of injury. However, the reliability of inferences drawn from these models depends on the correspondence between the mechanical measures and injury data, as well as the establishment of accurate thresholds of tissue injury. In the current study, a validated anisotropic FE model of the human head is used to evaluate the hypothesis that strain in the direction of fibers (axonal strain) is a better predictor of TBI than maximum principal strain (MPS), anisotropic equivalent strain (AESM) and cumulative strain damage measure (CSDM). An analysis of head kinematics-based metrics, such as head injury criterion (HIC) and brain injury criterion (BrIC), is also provided. Logistic regression analysis is employed to compare binary injury data (concussion/no concussion) with continuous strain/kinematics data. The threshold corresponding to 50% of injury probability is determined for each parameter. The predictive power (area under the ROC curve, AUC) is calculated from receiver operating characteristic (ROC) curve analysis. The measure with the highest AUC is considered to be the best predictor of mTBI. Logistic regression shows a statistical correlation between all the mechanical predictors and injury data for different regions of the brain. Peaks of axonal strain have the highest AUC and determine a strain threshold of 0.07 for corpus callosum and 0.15 for the brainstem, in agreement with previously experimentally derived injury thresholds for reversible axonal injury. For a data set of mild TBI from the national football league, the strain in the axonal direction is found to be a better injury predictor than MPS, AESM, CSDM, BrIC and HIC.