Professional baseball players agree that rotation increases bat speed, and pro golfers agree that rotation creates more club speed, resulting in harder baseball hits and longer tee shots. Similarly in football hip rotation increases the angular momentum—foot speed—which imparts more force into the ball.
Postgame: Fun Facts about Pro Kicking
Smaller kickers. Back in the days of toe-ballers, kickers tended to be bigger. Because a straight-on kick could only generate a limited amount of foot speed, the key to hitting longer field goals was to have bigger leg muscles. Placekickers today are generally smaller because they can rely on the soccer-style hip rotation to create foot speed.
Higher salaries. In 1964 the Buffalo Bills, a team in the young American Football League, signed Pete Gogolak, the first pro soccer-style kicker. He proved so valuable that in 1966 the New York Giants, a team in the longstanding National Football League, "poached" him from the Bills, by offering more money. At the time, team owners generally did not sign players from the "other" league, an arrangement that reportedly lessened competition for players and helped prevent salaries from escalating. Poaching increased noticeably after the Gogolak deal and salaries rose, which allegedly helped convince AFL and NFL owners to merge into one league before competition for players became too expensive.