Ever since computers started controlling ignition timing, there has been a debate about octane and performance/economy/etc. Before the computer was there, you had to dial in the timing to not knock too bad on whatever fuel you used. Some older cars even had an "octane" knob on the distributor. I used a fully programmable ECU in my turbo conversion on a 1983 Toyota Celica. It was fairly radical for the time, with 9.0 compression and 13 psi of boost. Pumping a real 300+ hp out of 2.4 litres with just one cam and 8 valves. Ignition timing was CRITICAL. and it HAD to run 93 or better octane. Even going to the west coast 91 pinged it so hard I ruin the rings. And that was with backing the timing down and lowering the boost to 11 psi, it would not go lower without a different wastegate. It did have a knock sensor, and I dialed it in to retard timing up to 15 degrees if it kept "hearing" knock. When I tuned it on 93 octane, I dialed it in so the knock retard would just hit 2 degrees. This made it so you barely ever heard even a single ping, but the ECU heard it and dropped that timing within a rotation of the crank. I did a couple hundred hours of data logging to get it right, and it paid off big time. That beast of a car would run 0-60 in under 5 seconds, and it also got 28.5 MPG.
So, what does this have to do with the C-Max????
Back the, my programmable ECU was an 8 bit processor running at 2 Mhz, with my couple hundred hours of data logging to dial it in. Todays ECU's have 32 bit processors running in the Ghz range, many times more memory, and the factories spends THOUSANDS of hours dialing in the base maps and very elaborate learning routines that I could not have come close to back in the mid 90's. What does that mean? These ECU's are what make it possible to run 12:1 and higher compression ratios on regular gasoline. Even back in the 90's the factory computers were quite good, and would set an error code if the knock sensor did not show any knock. The base maps do run close to the limits, and not just at full throttle, in fact, the maximum timing advance is under part throttle light load. At higher loads, the timing backs off a lot. Every fuel has a certain burn rate. The ideal timing is when the burn creates the maximum cylinder pressure without detonating with the crank at the correct angle to turn that pressure into torque. Getting it right at light load is where highway fuel economy comes into play. Have the spark a few degrees late, and you lose torque, so you need to burn more fuel for a given amount of power. Even my 2004 Camry 4 banger would ping a tick once in a while at part throttle, going up an incline in 5th gear is one example. Pushing the throttle a bit more, it would stop immediately, because the map had to retard timing at the higher load. All modern ECU's walk a fine line to get the most out of the fuel. In most cases, part throttle efficiency can increase a bit with higher octane fuel, but there is a flip side. Rarely will the increase cover the cost difference. The additives can also reduce the energy a little nulling any economy increase from the greater possible timing advance. Some engines actually run better with a faster burn rate (long stroke and wankel come to mind). Atkinson cycle is a bit of an odd ball. I really do not know how it effects the true cylinder pressure. It obviously creates less compression pressure, but since it still does have the longer expansion, I am sure the timing is still very picky if not more so. I have never tuned one, so I do not know how the burn rate of the fuel will effect it.
I have only run regular so far in my C-Max and I have been getting very good mileage, with my last 2 tanks running very close to 46 MPG. If I do decide to try premium, I will have to run at least 2 full tanks through to make sure the learning routines in the ECU can correct for the change. Just going to a different brand took a good 120 miles before my mileage was back to "normal". When I filled up at 7-Eleven instead of my normal Chevron, my MPG went from nearly 47 at the end of the previous tank to 43 for the first 1/8 tank plus with the same driving. But now at the 1/2 tank mark of this same tank, my average is back up to 45.9 with close to 48 on my last few trips. It certainly takes the ECU a bit of time to optimize the fuel in the tank. Just one tank of premium will not tell you much. And switching up and back with never tell you anything.
Cheap gas that advertises higher amounts of detergent sure sounds like a bad thing to me. Detergent does not contain energy, it is displacing fuel for soap. I would much rather have clean gasoline and a little detergent to just keep the injectors and valves clean. Would you wash your clothes in mud by just using twice the laundry detergent? "Top Tier" gas vs "Premium" gas is a different discussion. High quality 87 octane is better than 94 octane crap. My fuel ups in the C-Max are so far apart, it is tough to try to test multiple fuels. I will try a few tanks of Shell as that was what my Camry ran best on. Chevron is just the most convenient on my way home and also has a $0.20 per gallon discount when I use my Von's club card. Shell has the same deal if I went to Ralph's, but I do not shop there enough. I have used Sam's club gas in my Camry with decent results, so I may try them as well. Arco was BAD, to the point I would not even try a second tank to let the car try to learn it. The car would surge an buck even while on cruise control on a flat highway. My MPG dropped far more than the cost savings. I only will use them if I can't find any other station and my distance to empty is ZERO.