For many real world data sets, what we actually observe is that the smaller digits are more likely, with 1 tending to be the most common digit.
Statistical models, like those used to predict the weather, deal with uncertainty. This runs counter to our expectations for mathematics. Factor in a reliance on probabilities, which are deeply unintuitive, and it’s no wonder we find these models hard to understand. Nevertheless, they can actually be quite useful.
Humans and statistical models both make errors sometimes. But we understand the human errors because we make the same kinds of mistakes, while statistical models can be wrong in surprising ways. Perhaps we think those errors are worse simply because they are different.
We need to resist the urge to wonder “What are the odds this one specific person would have predicted this one drawing?!?!?” Instead, we should ask the statistical question: “Have enough predictions been made about enough lotteries to get positive results?”
What distinguishes statistical modeling from New Age predictions? Plenty, but maybe not exactly what you’d intuit.