Switch to math concept for a moment. Either x > y, or x = y, or x < y. Technically, there are 3 possibilities; runner came first, out came first, or there was an exact tie. By the actual wording of the rules, the runner is not required to beat the out, the out is required to beat the runner. Therefore, tie must go to the runner.
By the next extension of science, what is the actual possibility of an exact tie in time and space, when time can be broken into an infinitesimally small component? My argument isn't that ties don't go to the runner; I submit that I have never seen one; in fact, at some point, the human eye is incapable of judging anything that infinitesimally small, even with slow motion replay, at times.
Bottom line is my judgment, which I trust to be sharper in the vasy majority of cases than the coaches or fans (who see with their hearts, not just their eyes). If the ball beat the runner, I have an out; if the ball didn't beat the runner, I have a safe. I refuse to discuss ties (I know I'm not wearing one!!). All I will state in response is if the ball did or didn't beat the runner.
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Steve
ASA/ISF/NCAA/NFHS/PGF
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