Just for fun, let's compare the theory of scaling for fiber with the theory of scaling for copper conductors.
In the fiber-optic case there are two predominate bandwidth-limiting effects: modal dispersion and chromatic dispersion. Both bandwidth-limiting effects vary inversely with distance. If you go twice as far,  you get half the bandwidth.
 Theoretically, once you exceed the mode-coherence length for a fiber-optic cable, the bandwidth descends only with the half-power of length, but since no cable manufacturers specify the mode- coherence length, this fact is not useful to designers of fiber-optic links.
Fibers are also afflicted with a fixed transmission loss. The transmission loss in dBmW varies directly with length. The further you go, the less signal comes out the far end of the cable.
In a practical optical transmission system, as the cable is stretched further and further, one of two things eventually goes wrong. In some systems the bandwidth becomes a limiting factor, in which case the received signal has plenty of power, but the bits are slurred into each other. In other cases the power is a limiting factor, meaning that at great distances the signal looks okay, but simply becomes too small to reliably detect. In either case a 10% reduction in length results in a 10% improvement in signal quality.
For a skin-effect-limited copper medium, a 10% reduction in length generally results in a 20% improvement in signal quality, because copper bandwidth in this zone varies with the length squared. Copper systems are generally more sensitive to length than are fiber systems.
Fiber cabling exhibits enormous variations in bandwidth and loss. For example, a typical length of cable with a bandwidth-distance specification of 500 MHz-km may have an actual bandwidth two or four times higher than the specification. The same holds for attenuation. The experience of technicians in the field is that fiber systems often go much further than advertised.
Not so with copper. The performance of a metallic interconnection is heavily affected by its physical construction, which is comparatively well controlled in the manufacturing process. Metallic transmission systems have a relatively hard, fixed upper limit on distance that should never be exceeded.
POINT TO REMEMBER
Transmission Line Parameters
Pcb (printed-circuit board) Traces
Generic Building-Cabling Standards
100-Ohm Balanced Twisted-Pair Cabling
150-Ohm STP-A Cabling
Time-Domain Simulation Tools and Methods
Points to Remember
Appendix A. Building a Signal Integrity Department
Appendix B. Calculation of Loss Slope
Appendix C. Two-Port Analysis
Appendix D. Accuracy of Pi Model
Appendix E. erf( )