Shelf Sag Deflection
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Deflection is how much the shelf bends downward under load, measured at the point of maximum sag (usually the center of an unsupported span). It's normal for any shelf to deflect a small amount; the question is whether that amount is visually and structurally acceptable.

Span length matters the most by far, since deflection increases with the cube of the span; doubling the unsupported length increases sag roughly eightfold for the same load and material. Thickness is the next biggest factor, since deflection decreases with the cube of thickness.

Bending stiffness scales with the cube of thickness, so a shelf that's 50% thicker isn't 50% stiffer, it's roughly three times stiffer. This is why adding even a small amount of thickness, or a front edge banding strip, dramatically reduces sag.

A commonly used guideline is limiting deflection to about 1/360th of the span for shelving under sustained load, though visible sag can bother people well before it reaches a structurally risky level, so many woodworkers aim tighter, like 1/500, for shelves holding heavy books.

Yes, through the modulus of elasticity (MOE), which measures a material's inherent stiffness. A shelf in a low-MOE species like pine will sag more than the same dimensions in a high-MOE species like maple or in plywood with its cross-grain layers, even under identical span and load.