We investigate the write-error rate (WER) of spin-transfer torque (STT)-induced switching in nanoscale magnetic tunnel junctions (MTJs) for various pulse durations down to 3 ns. While the pulse duration dependence of switching current density shows a typical behavior of the precessional regime, WER vs current density is not described by an analytical solution known for the precessional regime. The measurement of WER as a function of magnetic field suggests that the WER is characterized by an effective damping constant, which is significantly larger than the value determined by ferromagnetic resonance. The current density dependence of WER is well reproduced by a macrospin model with thermal fluctuation using the effective damping constant. The obtained finding implies a larger relaxation rate and/or thermal agitation during STT switching, offering a previously unknown insight toward high-reliability memory applications.