In message of Wed, 20 Feb
2008 07:40:59 in uk.transport.london, asdf
writes
On Wed, 20 Feb 2008 04:13:41 +0000, James Farrar wrote:

Your long post omitted to mention the service I use when I must use
Heathrow and can choose the mode - Heathrow Connect (HC)
http://www.heathrowconnect.com/.
30 minute service interval and about 30 minutes travel time.
Roughly half as expensive as Heathrow Express (HE) which has double the
service interval and half the travel time.
Roughly double the cost of London Underground and half the travel time.

Depending, of course, on where in London the traveller is travelling
to/from.

Indeed. I'd say HC actually takes longer on average than the Picc for
most destinations, due to having to wait up to half an hour for a
train (versus 5 mins on the Picc).

Assuming random arrival, you have an argument.
Given the knowledge that it leaves Heathrow T123 at 26 and 56 minutes
past the hour and Paddington at 3 and 33 minutes past the hour, random
arrival is not sensible. (I work on "get there just before the hour and
half hour".) Sunday is another ball game.
--
Walter Briscoe