I've been working with synthetics for about 25 years. From my personal experience and a fleet I managed for 5 years the gains varied from 1.5-8% depending on winter/summer and/or short trip versus highway driving.
Bottom line is yes, synthetics can give some added mileage.
Per extended drains? Absolutely, no question. The length will vary on the type of oil used, the type of driving done and to some extent the vehicle.
Most of my personal equipment gets an oil change once a year which is on average about 10K miles and I also use a synthetic based filter versus the cheaper or OEM filter when possible.
Will synthetics save you money? In my case it does.
One thing too about synthetics is we simply use less oil & fewer filters to clog the landfills where recycling filters isn't available.
It can depend on the mileage and type of driving you do. This should be handled on a case by case basis. To many variables are involved to make a blanket statement.
Was rushed for time last night & I should add something.
During my years of fleet maintenance it was found the biggest mileage gains, thru oil useage was in changing all the drive line fluids to synthetic.
In every case where we changed all the drive line fluids to synthetic gains were realized. The biggest gains were seen in the winter, which common sense should suggest as well when doing a proper flush to synthetics in both the trany and final drive for units that had both.
We also used synthetic grease on wheel bearings that weren't sealed and synthetic oil in hubs that required oil baths.
This fall I'll be flushing the trany on our 5 speed Kia Optima 07 vintage W/I-4 that has been averaging 38 MPG at 65 MPH on the Interstate during fair weather. Should be interesting to see what this does. I doubt if the gains will be dramatic since most of the miles logged are on the highway but other benefits will be obtained with the change over.
I've never used synthetic, but have always used regular 10w40 of various brands changing it at 3K-4K intervals. Over the life of the '88 Escort with 477,000+ miles I would say I have changed brands 5 or 6 times so I don't think there is much difference in conventional oils.
This actually part of the maintenance routine in some cars now. Honda is one.
Even if the filter was still "good" I don't like the idea of mixing 4 quarts of fresh, new oil with 1 Qt of old, used oil... I'm really anal about my oil changes. I always pour 1 quart in the top of the engine, and let it run until clear, then reinsert the drain plug. I also fill up my oil filter with oil before installing it too.