To predict pulse detection performance when implemented in high speed photoreceivers, temporally resolved measurements of a 10-stage InAlAs/InGaAs single carrier multiplication (SCM) avalanche photodiode (APD)'s avalanche response to short multi-photon laser pulses were explained using instantaneous (time resolved) pulse height statistics of the device's impulse response. Numeric models of the junction carrier populations as a function of the time following injection of a primary photo-electron were used to create the probability density functions (pdfs) of the instances of the avalanche buildup process. The numeric pdfs were used to generate low frequency gain and excess noise models, which were in good agreement with analytic models of multiple discrete low-gain-stage APDs and with measured excess noise data. The numeric models were then used to generate the instantaneous and cumulative instantaneous low order statistics of the instances of the impulse response. It is shown that during the early times of the impulse response, the SCM APDs have lower excess noise than the pseudo-DC measurements and the common APDmodels used to describe them. The methods of determining the time resolved low order statistics of APDs are described and the importance of using time-resolved models of APDgain and noise is discussed.