very much this. I’ve cried a little during…
It’s also possible to over-estimate by pacing it too much, meaning you can suffer for naught. You really do need to go all-out from the start. Like full gas sprint trying to hit a new all-time PR at every second from 1 through 180 sec. You ride like the finish line is perpetually 1 meter in front of you and you just need to go as hard as possible for one more pedal stroke. Also note you’re blinded to time and power - you just go until you hear the blessed beeps.
There is literature suggesting 3min all-out CP test overestimates actual maximal steady state (max lactate or max VO2 steady state) although there is just as much saying it is valid. So your results may vary. Don’t take this as fact, but I hypothesize that some of the over-estimation could be the result of too much pacing during the effort, or inexperience with the protocol.
My most accurate result tested against MLSS was around the third time I did it, when I ended up crying a little . Hit new all-time peak power from like 50sec through 1:30, then was just cross-eyed pedalling bricks for the final 2min. Fun times.
It’s an interesting feeling to be essentially at VO2max and all that’s coming out is critical power.