Quantum mechanics offers some statistical reasoning for small pieces of length in the Universe (please correct me if I'm wrong). To some extent everything has uncertainty. We might even say that it is random to some degree.

Is it possible that these small pieces of randomness produce a deterministic picture at the end?

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    The moving of the gas molecules in your room is completely random. Neverthelss the pressure at all eight corners remains constant.
    – Wilhelm
    Apr 21 '18 at 12:53

Not deterministic exactly, but orderly yes. Limit theorems and laws of large numbers mean that random behavior by large number of identical elements leads to orderly patterns in aggregate. We can trace these effects in much detail in classical statistical mechanics, where random behavior of individual particles leads to very "deterministic" chemical and thermodynamic phenomena. Pockets of order may emerge out of chaotic substrate that may not even be governed probabilistic laws, like quantum particles. Quantum statistical mechanics exhibits similar effects, and even quantum probabilistic laws themselves may emerge from something else at a finer scale, e.g. from strings.

Nancy Crtwright, one of the Stanford Disunity Mafia philosophers of science, calls such pockets of aggregated order "nomological machines". Dupre, her fellow mafioso, in Metaphysical Disorder and Scientific Disunity illustrates how determinism may not go "all the way down" on the example of baseball:

"Even where empirical regularities of the right sort can be found, this in no way requires that they be grounded in underlying single-case propensities. This last point can usefully be illustrated by looking briefly at a topic about which there has been a great deal of investigation of statistical regularities, though without much effort to construct elaborate theoretical models, the game of baseball. The performances of baseball players are subject to analysis in terms of a battery of statistical measures, the most familiar being the batting average and the pitcher's earned-run average...

Over a number of years earned-run average will very reliably distinguish an outstanding pitcher from a marginal pitcher. The same handful of batters average over .300, or drive in 90 runs, with considerable consistency. But whereas with sufficient time such statistics can give a good idea of the capacities of baseball players, this possibility does not depend in any way on the assumption that the particular events codified by such statistics are subject to any fully determinate and completely specifiable causal influence."

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