We present a numerical study of the wave breakup and soliton formation in a standard single-mode fiber pumped by variable pulse lengths in the range from $20\text{to}400\mathrm{ps}$ in the presence of noise. The average power and the standard deviation of the trailing soliton were calculated. We calculated also the average distance at which the soliton time delay reaches 1.5 times the pulse width. We found that for pulses longer than $100\mathrm{ps}$ the breakup starts from the amplification of the noisy modulation of the amplitude by the modulation instability mechanism even for very low noise power, while for pulses shorter than $20\mathrm{ps}$ the breakup starts from the pulse collapse. For intermediate durations, wave breakup starts from the pulse collapse at low noise power, while for higher noise power, modulation instability prevails.