There's a lot more to understanding compression ratios than simple bore x stroke, as has been said.
Combustion chamber volume has to be known and factored in, but also, if you want to know the
actual CR at cranking speeds, compared to the
theoretical one, then cam timing also has to be factored in.
For example, if your inlet valve closes at, say, 70 degrees ABDC, then at cranking speeds, where the engine is turning slowly, you're not compressing
anything (much) prior to that point. So you would then need to calculate how far up the bore the piston has travelled by that point, then subtract that figure from the actual stroke to find the
effective stroke (for compression ratio purposes) at cranking speeds. Using that figure for the stroke in your calculations will give you a better idea of your actual CR at cranking speeds.
Wilder cams designed to deliver power at higher revs will, naturally, produce a lower (shorter) effective stroke at cranking, and therefore a correspondingly lower CR.
So from this, you can see that, with wild cams, and even with a high theoretical CR, your actual CR for starting may not be so high - may even be lower than the standard engine with standard cam.
So why, then, are high compression engines slow to turn over when cold starting you may ask? Well, as has been mentioned, it's more likely to be related to advanced ignition timing than compression ratios: tuned engines generally run more advance than standard engines, so at cranking speeds the spark is arriving effectively a little too early for what the engine wants at cranking speeds, and this early spark (and so early combustion) slows the piston travel as it approaches the top of the cylinder.
If you want to know for sure, then simply crank your engine with the ignition disconnected - if it spins faster than with the ignition on, then it's advanced timing that's slowing it down.
