Earlier quoted context omitted.
There's kind of similar services in Japan to get to the airport, using a shared-taxi kind of system with online reservation. It's way better than the bus to reach the terminal (they pick you at home) costs only a bit more and is significantly cheaper than a taxi ride (5 times less).
They're pretty common in the US too. SuperShuttle seems to be the big name in this area. They cover a ton of different airports and go to your house. The price differential is similar, at $27-28 for a round trip from my house versus $50ish each way for a taxi. Or $4 for a metro ride, but that currently only serves one of the two airports.
My main observation was that your circuity factor (the time deviation from direct travel time) was always larger the earlier you booked. So if you booked your trip online a week in advance, it appears they would assign your request to a van, and then as other new 'relevant' requests came in, they would get added on.
Essentially, your trip became the 'anchor' that drove the overall schedule. So depending on your trip characteristics, the best strategy appears to book on the day!