8:1 needs lower octane 87-89 while something like 12:1 would need around 110.
High compression, higher octane. Putting 110 octane in a car that has about 8:1 compression will not hurt the motor. How ever if you put like 87 in a 12:1 compression motor there goes your motor.

There is no actual formula determining exactly what fuel is right for what compressions and different vehicles are going to vary based on timing and what not. Basic rule of thumb is to use the lowest fuel grade that does not cause early detonation or pinging in the motor. (if you hear pinging you need higher octane)