Why Is the Non-Conducting Half Cycle Included in Half Wave Rectifier Efficiency Calculations?

If the half wave rectifier does not conduct current to its load during one half, then why is that half cycle considered in the calculation of efficiency of the circuit?

Since efficiency is the ratio of power, how does it make sense to include the second half when the second half does not produce and power output. 

If the half wave rectifier is 40% efficient, it means that 60% of the power is wasted. If that is true then where is it going and where is it wasted?

the half wave rectifier is 50% efficient because it uses half of the wave in rectification. the other 50% is going nowhere because it is blocked by the diode.

while the full wave rectifier uses all waves for rectification thus it is more efficient than the half-wave rectifier because no signal is blocked.