How much is a connection?

My company requires us to purchase the “cheapest logical fare” for trips.  Out of CLT at the 7 day mark (because I often book 2 clients in a week and change fees get really messy) that usually is not the direct flight.

The math for these calculations is easier if you work for a company that bills for travel time.  Obviously if a direct flight is 2 hours or a connecting flight is 2 hours + 2 hours + 1 hour connection it makes the math slightly different.  My company does not bill clients for travel time so they get billed for the airfare only.  Since time is not billed for, to my company that takes time out of the equation and they really force us into the cheapest airfare.  The booking engine seems to disregard schedule parameters I put in so to book a basic flight that must leave after 5:30 pm I must first look on SideStep and find the flight/airline that will be the cheapest within my time parameters, then manually find it on the corporate travel site.

What I’m trying to get at is this week I needed to go from CLT to PIT.  I was scheduled on a 2:15 pm flight on Delta connecting in CVG.  That flight was canceled this morning pushing me to depart at 4:38 pm to connect in ATL.  That’s great, but weather on the East Coast was a mess so that flight left 30 minutes late, then the flight to PIT left 2 hours late.  I was originally supposed to get into PIT around 6 pm but got in around 11 pm.  I look at US Airways’ flight status and they had a flight leave CLT at 2:45 and arrive in PIT at 4:11.  My DL ticket cost $250 which means that US ticket probably was around $600 when I booked.  I wasted 5 hours in connection limbo and wasted almost 8 hours over the direct flight…but probably saved around $350

So what criteria should I use to determine if a connection is worth it?  I know some say I should always take a non-stop over a connection out of principle.  Others will say I should always connect to get more miles.  Right now I look at departure time first.  If a flight leaves too early it’s out.  If a flight doesn’t allow me to work a full day at a client and then leave it’s out.  After that I go by connection city.  I avoid EWR, JFK, IAD (always canceled for mx reasons), and PHL.  I try for connections in CVG, or DTW.  I’ll take an ORD connection because  I can’t avoid them.  I avoid connections that involve reclearing security.  After that I’m left with a connecting ticket at X an a direct ticket at 2X.  Since X is usually at least $300 and often $500 in peak months 2X is $600-1,000.  Not exactly chump change to people who aren’t used to paying airfare for vendors.  A misconnect resulting in a hotel room is usually less than $170 so the connecting flight is still significantly cheaper than the non-stop.  What math should I use?