To anyone who has been through the analysis/math: are fake punts considered "going for it"? I assume they are. The following is possible: the surprise element

To anyone who has been through the analysis/math: are fake punts considered "going for it"? I assume they are. The following is possible: the surprise element of a fake punt makes going for it on 4th down more advantageous than it otherwise would be. It could make P(good outcome | going for it on 4th down) > P(good outcome | punting) if and only if the defense expects a punt, which they no longer would if a team adopts the strategy of routinely going for it on 4th down.