A question about impedance matching

For the maximum power transmission, we use conjugate matching. Observing from the 50 ohms load, the output impedance is also 50 ohms. My question is coming that only half of the power can be obtained by the load, for an amplifier, that is to say half of the power is lost. I know it is a misconception, but i don't know how to explain it.
Thx in advance！

Dear Patriot,

Please reframe your question. Explain your situation rather.
your wordings are confusing.

You mean to say your 1dB compression point is down by 3dB.