I don't know your travel dates or requirements. I checked the routing you mentioned using travel dates of Sept 21 and 22 and nwa.com came back with a fare of $236.50.

Using a routing of BWI-DTW-STL-MEM-SDF-MEM-STL-DTW-BWI, nwa.com came back with a fare of $132.00. 8 legs with 500 minimum miles = 4,000 miles.

On a per mile basis, my routing is better. Plus, unless you have biz in LA, other than mileage, the on-the-ground expenses may be easier on the pocketbook.

Need more?