OK, lets get to the bottom line here. All strings move on ball contact. The difference is in how much they move and how they work against each other (mains vs. crosses). Tensile strength and enlongaton has a major impact on how a string performs, along with racquet stiffness. The stiffer the string the less movement; the softer the string the more movement.
OK, even though poly strings say that they resist movement, slow motion video says that they do move but because of their slick surface thay return to the original positions with minimal wear. This is why they last longer than softer strings. It's also why they give you a bit more control. However, they can be very harsh on the arm and wrist if you do not hit the ball cleanly.
Some players have requested stringing with hybrids of poly and natural or synth gut to get the best of both worlds. Natural or Synth gut in the mains will give you a softer feel with more power, however, polys in the mains with natural or synth gut in the crosses will be stiffer and deliver more ball control. Of cource, tension and racquet type have a major impact also.
With over 130 string types out there, a USRSA certified stringer can help you in finding the string that best serves your playing style.
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