Here's another problem with attempts at mathematical determination of real world phenomena. How was the 30% for any individual shot determined? It has to be based on the real world experience of shooting shots. What was the pool that the average for each individual shot was determined from? What was the distribution of the pool? Was the distribution really averaging every third shot or were there clusters of shots made versus missed. All of that would change the actual probability of making a certain number of shots in a row.
Maybe the player is coming down with flu. Maybe the table was moved last night and has a new roll. Maybe ....
The point is to guess as well as you can how likely something is, based on limited knowledge. If you know how much data went into assumed percentages, you can say how accurate those percentages are. For example a FargoRate with a robustness of only 200 is expected to have something like 25 points of error compared to the player's true average performance in competition. With 10,000 games recorded, the rating is expected to be much closer to the player's true ability.
But, the particular point being discussed is a theoretical one: given that the player is exactly x% to run a rack, and there is no real-world, extraneous interference, and everything goes according to theory, what is his chance to string N racks together in T tries?
Such theoretical understanding can help with real-world predictions.
