[vibrating_cake]

I will have to butt in here.
No, the ICE in a Hybrid is no more or no less efficient than the ICE in a non-hybrid.
I have a honda CRZ (yes i am one of the few!) basically a manual transmission IMA system, that never runs on full electric.

Now, the hybrid system on this car is not a high percentage of the cars weight (5% from what i worked out when i first got it) so that in its-self is rather negligible to mpg over the lifetime of the vehicle.

Here is where i bite.
I can drive more efficiently in NORMAL mode rather than ECO mode.
ECO mode basically runs minimal ICE and a high percentage electric power (all of which is recovered from braking/during steady state driving at approx the 50mpg(uk) mark.
NORMAL mode runs the ICE on a "normal" ICE setting, i.e. normal pedal map, normal timing, normal usage. But when you use more than a certain percentage throttle input the electric (which has previousley been harvested from going down a hill) gives it a good shove, but it does it only on say 30% plus throttle input

This does not make the ICE more efficient in its self, but it allows the ice to say run 80% of the throttle seen for the same total output ICE+IMA
Same scenario without IMA you are running say 90% throttle application for the same output.

(guesstimating numbers)

so, we know under acceleration the IMA helps output per amount of fuel ratio.

Now steady state on the motorway (highway)
Same thing, steady state driving 30% throttle application @ 70mph
BOTH cars with and without IMA run exactly the same MPG, same throttle position etc.
but you loose nothing for your weight (if you are on level ground)

Steady state driving uphill motorway (highway)
you are now running 30% throttle with 10% IMA
40% throttle on the non IMA equipped car, therefore, the engine is no more efficient, but your mpg doesn't drop as low as it would without the help of the few bhp output from the electric motor.

and again, downhill motorway (highway)
DFCO + REGEN IMA (harvesting)
DFCO + no IMA regen (rolling)

equal mpg for the both.
BUT you can DFCO longer with no IMA REGEN, (rolling/coasting) so you get a +1 on the non hybrid.

At lights, lets say we have auto stop on both cars, equal

so...
hybrid vs non hybrid

acceleration advantage hybrid (say 5%)

steady state advantage non hybrid (weight, say 2.5%)

Uphill steady state adv hybrid (say 5% again)

Downhill steady state, tricky one, i'd say equal advantages between the two.

Now, stopped, IMA equipped cars have a larger capacity battery, so it can be stopped without the engine on (with ancillaries on) for longer, so +1 for the hybrid, but no percentage gain unless you are really stopped for long periods.

If you end up adding all of these up, for a specific number input (petrol/gas in litres/gallons) Hybrid has the advantage, but it's pretty marginal depending on the situation.
Say high use of motorway/highway, i see them being equal.
High use in a city, stop start, i see hybrid on top, nearly every time!
High use mixed... hybrid probably takes the biscuit, but not by much.
High use in a mountainous area (where you fully deplete the battery on the hybrid) the non hybrid has the advantage.

We can see this in the estimated MPG numbers, highway are pretty much even the hybrid eeks it out on the mixed and city cycle.

So in real terms, they are marginally more efficient, all things being equal, as long as you don't live in the mountainous parts of the world or do mega highway miles.

It all depends, can you regenerate the percentage of ENERGY lost for the weight of the hybrid system in your situation. Most of the time yes, a few situations, no.
But the few situations equal a small percentage of the total hybrid use, so yes they make sense.
unless you are commuting over the alps, or you do a majority of motorway(highway) miles, then a diesel is your best bet.

A couple of numbers,
43mpg UK 1.5 petrol IMA Honda crz. Petrol is £1.06 average
43mpg UK 2.2 diesel Honda civic. Diesel is £1.13 average

My last commuter (12.5miles motorway/highway)
50mpg UK 1.5 petrol IMA Honda crz
63mpg UK 2.2 diesel honda civic....

Thats my two cars, on exactly the same commute, averaged over 6 months of summer-winter driving, 18miles each way.
I had to eek everything out of the diesel to get that MPG, the CRZ does that even if i do drive like i just passed my test on a country road!

Go figure!