Simulations of combustion and reacting flows often encounter stiffness in the equations governing chemical kinetics. Explicit solvers for these ordinary differential equations offer low computational expense, but typically cannot efficiently handle stiff systems. In contrast, implicit methods demand greater expense but offer unconditional stability—as a result, most reactive-flow solvers rely on these methods by default (other than explicit direct numerical simulation solvers). However, explicit or stabilized explicit methods can instead be used to reduce the computational expense while remaining stable and accurate if the chemical kinetics systems exhibit low-to-moderate stiffness. In this thesis I investigated five stiffness metrics, with the goal of identifying one capable of efficiently and robustly determining the least computationally expensive category of integrator required. I applied the stiffness metrics to three test problems to demonstrate their capabilities and limitations, and then extended my analysis to simulations of hydrogen/oxygen and methane autoignition using initial conditions representing realistic turbulent combustion, obtained from partially stirred reactor simulations. I compared the metric values against the computational expense measured using five different integration methods that ranged from fully explicit to fully implicit, with different levels of integrator tolerances used. Lastly, I extended the comparison to a large set of initial conditions sampled from partially stirred reactor simulations. My analysis demonstrated that the stiffness metrics alone provide insufficient information to predict the computational cost of integrating a chemical kinetics simulation at each point and time step. The accuracy requirements of each integrator and the lack of detection of these requirements in the stiffness metrics are potential causes of the lack of correlation.