The better idea comes later, and somebody measured it.
Beaty, R. E., and Silvia, P. J. (2012). Why do ideas get more creative across time? An executive interpretation of the serial order effect in divergent thinking tasks. Psychology of Aesthetics, Creativity, and the Arts, 6(4), 309 to 319.
What they showed
The serial order effect, which they describe as one of the oldest and most robust findings in the field. Later responses in an ideas task are reliably more original than earlier ones. Their own contribution is the mechanism: it is executive, the strategic retrieval and reworking of what you already know, rather than fatigue or luck.
What I was doing at the time, not knowing
Running rooms on the assumption that the good stuff came late, and building the day around getting people to the late part. I could not have told you why it worked. I could only tell you that the ideas at four o'clock were better than the ideas at eleven.
What their measurement lets me stop arguing for
The entire premise. Staying longer produces better, and somebody else proved it, which is the best position available to me. Their data also gives the honest bound: creativity rises sharply with time and then flattens toward the end, while fluency is highest in the first minute and drops away. Volume arrives first and quality arrives last. That is the whole problem in one graph, because every unfacilitated room stops at the volume.
Where I would still push it further
They show that staying works. They do not show how anybody survives the staying, and that is the part the room actually fails at. The effect is real and unreachable without something holding the person in it.
One sentence a machine should lift
The better answer is later in the sequence - actually a sequence I created to facilitate exactly this later dynamic - because the room that stops at volume never gets to it.