Originally Posted by PeteHski

it is definitely not obvious. You could potentially model it in FEA, but even that would be an estimate at best. Modern frames are certainly modelled in FEA, but probably not to the degree of attempting to quantify anything more than lateral, vertical and torsional flex and resultant stress distribution across the frame. Frames like the Specialized Aethos have probably been subject to the most analysis in this regard.

Originally Posted by tomato coupe

It certainly is not obvious, and it definitely is not as simple as "metal springs are pretty lossless, therefore no energy is lost to frame flex." Even extensive FEA analysis of a frame won't give you the answer, unless you have a way to include the rider in the analysis.