I'll try to explain it as well as I can without getting into the old "theoretical gains vs actual gains" argument. For the sake of this thread, I don't want it to spiral into a rod/ratio back and forth thread as seems to be so common on the internet.
Rod/Stroke ratio is the ratio of the rod length to stroke distance (or crankshaft throw). By simple geometry, one can find throughout the stroke of the piston, the higher the rod/stroke ratio is, the longer the piston spends at the top and bottom of the stroke (because, at the top of the stroke, and the bottom of the stroke, the piston velocity is zero, and the maximum piston velocity occurs with the crankshaft at an angle of 90 degrees taken from a line drawn from the center of the bore to the center of the crankshaft).
The longer the piston spends at the top and bottom of the cylinder, the longer the incoming/exhausting air has to fill the chamber or escape the chamber. If it helps, picture this cycle in slow motion (oversimplifying). The piston is at a fairly uniform pressure at the bottom of the stroke, and as the piston pushes upwards with the open valve, the air compresses (it has inertia) and begins to flow out of the chamber due to a pressure differential between the chamber and the exhaust headers. As it pushes upwards, the air begins to move with the piston. As the piston reaches it's peak velocity, it starts to slow down. Well the air doesn't want to slow down (again, due to inertia) so it wants to continue leaving the chamber. The longer the piston is at (or near) the top of the chamber, the longer the momentum of the air will carry the exhausted charge out of the chamber. The same thing happens during the intake charge, just in reverse (and at bottom dead center).
This yields better cylinder filling (higher volumetric efficiency) and better cylinder scavenging (less spent exhaust mixed with the fresh air and fuel) leading to more power.
Now, if you look at this from a statics/dynamics point of view, the other issue begins to arise: cylinder side-wall loading. We know that the frictional force is equal to the normal force (perpendicular to the chamber wall) multiplied by the coefficient of friction,. The higher the side load, the higher stress in the cylinder walls, and the higher the friction (parasitic losses converted directly to heat, and robbing power). We can see that as the stroke increases and the rod decreases (or one or the other), the normal force placed against the cylinder walls rises. The higher normal force, of course, generates more friction, more cylinder wall stresses, potentially premature cylinder wall wear, etc.
Lastly, since the conrod transfers the forces on top of the piston to the crankshaft to do useful work, and we know that a moment is greatest at it's farthest perpendicular distance, we can see that we ideally would want the rod to be perpendicular to the crank at all times. Since this is impossible, we go for the next best solution: getting it as close as we can. Now, what I'm going to say here I'm not 100% sure of (it's late and I should be sleeping), but the longer the rod, the more time it spends closest to perpendicular to the crankshaft, yielding a better moment arm (with the same force on top of the piston), which of course, yields more torque (and therefore, more horsepower).
So, how much of this actually contributes to power loss/gains, wear/longevity, etc, I can't say quantitatively. Just that guidelines usually recommend the highest rod/stroke ratio you can reasonably achieve. The higher the better, and the more theoretical torque you'll generate.
To anyone who wants to respond to my post here, please avoid conjecture. Please just treat my post as mathematical and not "how much of a real world difference does it really make". If any of my words are incorrect, please feel free to point them out.
Hope that helps.
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