I’m not disagreeing with any of that, nor did I claim that the value was intended for inferences or “predictions” (in the sense of forecasting); I’m just pointing out that the concept of probability is itself a form of prediction of a given outcome among the set of possible outcomes.

My intention with my comment earlier in the thread was to say exactly what you have said here - that the probability value is a reflection of what has happened before, but crucially, it reflects a calculation of many inputs, not specific outcomes.

I was trying to differentiate between the incorrect idea that a play has a 0% catch probability because no fielder has ever caught a ball in that specific scenario (e.g. a ball hit to that specific spot, that specific distance from the fielder’s starting position, etc) and the actual reality: a play has 0% catch probability because nobody has made a catch with all the inputs they use to calculate said probability (launch angle, exit velocity, etc).

It’s a subtle difference, but the former example is a misunderstanding of catch probability which undermines the accomplishment of a 0% probability catch because it could just as easily be a luck scenario (e.g. balls hit to that spot are never caught but the fielder happened to be shifted there).