Take a look at the Cylinder Pressure Decay chart and then let's go through the characteristic difference (computed taking into account typical heat losses) between a high-compression cylinder versus a low-compression one. For a moment, let us imagine that both the 15:1 and the 2:1 cylinders start off at TDC with 1,000 psi. As the piston of each cylinder moves down the bore, the drop in pressure follows a distinctly different line. The 15:1 cylinder drops pressure much faster than its 2:1 counterpart because of its more rapid change in volume. It only has to go down the bore a short way for the original volume to have doubled, whereas the 2:1 cylinder must travel to the bottom of the bore to double its original volume. At the bottom of the stroke, the 15:1 cylinder has dropped down to about 25 psi above atmospheric whereas the 2:1 cylinder is still at some 260 psi. In simple terms the high-compression cylinder, when the exhaust valve opens at BDC, is only dumping 2.5 percent of its original pressure whereas the 2:1 cylinder is dumping 26 percent!

Up to this point we have assumed that both cylinders start with 1,000 psi. In reality, the best that the 2:1 ratio cylinder would generate is about 200 psi. That produces the lower curve (light blue line) on our graph. Both the 2:1 and 15:1 cylinders will draw in about the same amount of fuel and air. But we can see that the 15:1 cylinder has more area under the curve by an amount equal to the green shaded area. The addition of the green shaded area under the curve amounts to about a doubling of the power output from the same amount of fuel and air. That means from the same heating value of fuel we have doubled the thermal efficiency and in so doing extracted twice the power.
You can run 11:1 or even 12:1 compression on your pump-gas street motor, but you'll need this simple advie to make it happen.