These alleged fields don't really convey any constructive information. You can't really verify the probability of something, as outcomes are determined by other conditions, for example, I will throw a dice from such an initial state that it land on a 5, although the initial states are not the same, it is not really meaningful to say the probability is 1/6 as it does not convey information as to whether I should bet on a specific outcome as that depends more on the exact initial conditions and not all the possible outcomes.

Statistics falls more or less in the same ball park, with collecting data and doing some arbitrary arithmetic that isn't really informative. I would describe Statistics as "meaningless arithmetic"