My imagination has painted a picture (bear with me here.) of the dished pistons advantage. As the piston draws down on the inlet stroke it would be sucking air fuel mix from the carbie. A dished piston combined with an inlet valve placement on the side of the combustion chamber would be more likely to start a controlled swirl (tornado style) inside the combustion chamber running from top to bottom. This swirl would act as a bit of a self perpetuating syphon to draw more air fuel in using less force. It would also aid more even air fuel mixture in the combustion chamber.
It works great in my head and has sold me on dished pistons for life.

. I wonder if in reality it works anything like this?
Oh and wiki says.
Combustion chamber
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A combustion chamber is part of an engine in which fuel is burned. The leftover hot gases produced by this combustion tend to occupy a far greater volume than the original fuel, thus creating an increase in pressure within the limited volume of the chamber. This pressure can be used to do work, for example, to move a piston on a crankshaft. The energy can be converted to various types of motion or to produce thrust when directed out of a nozzle as in a rocket or jet engine.
In a reciprocating engine, the moving pistons are flush with the top of the cylinder block at top dead centre, and the combustion chamber is therefore the recess in the cylinder head which contains the valves.
Some engines use a dished piston and in this case the combustion chamber can be considered as partly within the cylinder. Various shapes of combustion chamber have been used, such as L-head (or flathead) for side-valve engines, "bathtub" and "hemispherical" for overhead valve engines and "pent-roof" for 16-valve engines.
The shape of the chamber has a marked effect on power output, efficiency and harmful emissions; the designer's objectives are to burn all of the mixture as completely as possible while avoiding excessive temperatures (which create NOx). This is best achieved with a compact rather than elongated chamber. The intake valve/port is usually placed to give the mixture a pronounced "swirl" (the term is preferred to "turbulence" which implies uncontrolled movement) above the rising piston, improving mixing and combustion. Finally, the spark plug must be situated in a position from which the flame front can reach all parts of the chamber at the desired point, usually around 15 degrees after top dead centre. It is strongly desirable to avoid narrow crevices where stagnant "end gas" can become trapped, as this tends to detonate violently after the main charge, adding little useful work and potentially damaging the engine.
The term is also used to refer to an additional space between the firebox and boiler in a steam locomotive. This space is used to allow further combustion of the fuel, providing greater heat to the boiler.
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