Perhaps the simplest answer (though not the only one) is that whites tend to have stronger and more accurate throwing arms. Take, for example, Major League Baseball. There have been many great black players in Baseball, but very few great black pitchers. The vast majority of truly dominant pitchers have been white, and that remains true today. Likewise, if you take a look at record holders for throwing sports such as javelin and shot put, you will see that white athletes have traditionally dominated in these areas, and continue to do so today.
The quarterback is a throwing position and will always be dominated by players with an ability to throw quickly and accurately (obviously). White athletes are the best throwers in the world, and consequently, most quarterbacks are white. This is not to say that there are not some black athletes that are strong and accurate throwers, this is just to say that whites have a natural advantage in this area.
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