Actually, you're more likely to have a tie within a given range of time the larger that range is (ie, more likely to tie within 1 second than within .5 seconds). The less precise you are, the more likely you are to tie.
Accuracy*, not precision. A less accurate measurement will always allow for greater precision, because the results are significantly more repeatable within a very low margin of error.
Semantics aside, that's only if you're talking about recording events to a significant figure. Even if you record events only to a significant figure where they're the same, before rounding it can be quite obvious that the two events did not happen at the same time and that the "simultaneous" nature recorded is, in effect, only the result of a rounding error. Truly simultaneous events don't occur until the Planck scale, where time becomes quantized and there's no further "division" of time possible; at that level, things really happen "at the same time", because there's no "in between" for them to happen in, and even if there were there's no possibility of distinguishing between them.
For example I can't accurately time off a tenth of a second myself, but I can damn sure tell you things that happened a tenth of a second apart didn't occur at the same time, even if the accuracy of my timing doesn't allow for record keeping that reflects that. I couldn't count off "one-one-thousand, two-one-thousand, etc." to time the Olympic 100m out to 0.001 second, but I could still tell you who crossed the line first, even if I had to record five runners with a time of 10 seconds.
And now that we're done with our completely useless science lesson for the day...
If it's very close, but I feel the ball really did get there first I'm going to ring up the out. If I think you beat it, then you're safe. No matter what I call, fifty percent of the players are going to be pissed.
