As a thumbrule 12-14 HP per point of compression. So increasing compression from 8:1 to 12:1 you could potentially gain 50 HP on compression alone. There are many other variables involved too, so don't rely too heavily on this rule of thumb. Combustion chamber shape, camshaft profile, ignition timing, induction and exhaust flow all play an important part when optimizing a combo for a given compression ratio.
Also, when compression gets very high, like 15:1 for example, the added benefit from increasing compression decreases per point added. I don't know why this is, but practical octane limits may come into play here.
E85 racer and E85 carb builder
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68 Camaro, E85 powered 427" small block. 9.96 @ 133 MPH, 1.319 sixty foot on motor. 5.92 eighth @ 116 with a 1.42 sixty breaking beams with back tire on the bottle