This might turn into a pennywise, pound foolish scenario once you factor in the price to rebuild your engine...
Jokes aside, I find the savings by running longer oil change intervals. I run 0w20 Mobil 1 Advanced whatever whatever formulation, and their Fram Ultra Synthetic filter, and I run them out to 15k miles. In the long run, that's cheaper than using junky oil and junky filters. I paid $33 for the combo last ($25 5 qt jug, $8 filter).
To put that into perspective, if you're doing 3k mi oil changes, that'd be like spending $6.60 per oil change. If you do 5k mi changes, $11/change. The regular Mobil1 non-advanced is good to ~10k miles, so if you actually follow their recommendation, it'd still be $22/change.
Don't do extended drain intervals on cheap oil though, that's just asking for sludge.