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The Ref Was Right, How to Talk About Probability in March Madness, also in Average April, May Too…
The sun comes up in the east and sets in the west, you may have different words an for these things and ascribe them different meanings but the underlying physical thing is extremely consistent. In the world of null hypothesis testing, you should be completely comfortable rejecting the null. Coin flips are interesting, they are wobbly. I once had a large room of people flip coins, after the aggregated first round of flips (>500) we had a definite preference for heads, the second round had a less intense preference toward tails, surely after another round we would have settled in around 50/50, but with some wobbliness.
In many ways it does a great disservice to teach probability from a stochastic basis. For the most part, there are no coin flip models in life or research, but there are also not many interesting models like the sun either. Proving that fire is hot is not a particularly interesting insight. Yep, it is hot. The interesting stuff comes in degrees of belief for events that are neither random nor determined. This is the heart of the Bayesian turn which animates everything from chess rankings to political polling. Basically, what if instead of thinking of the world as a bunch of coin-flips, what happens when we take our priors seriously and change them with care?
