In this paper a new fundamental constant asociated with a \(P\)-matrix is introduced. It is showe, that this constant has various useful properties for the \(P\)-matrix linear complementarity problems (LCP), and is sharper than the Mathias-Pang constant in deriving perturbation bounds for the \(P\)-matrix LCP. The new fundamental constant defines a measure of sensitivity of the solution of the \(P\)-matrix LCP. In addition, it is also examined how perturbations in the data affect the solution of the LCP and efficiency of Newton-type methods for solving the LCP.