The New York Knicks and the martingale property of calibrated probability forecasts (with some simulation and R code)

This long post covers four topics: 1. The Knicks’ stunning series of come-from-behind victories to win the NBA title in 5 games; 2. The martingale property of probability forecasts; 3. An example of learning from simulation; 4. How we (sometimes) do research in probability and statistics. I don’t know enough about this blog’s audience to know which of the four topics will appeal to most of you. For the internet as a whole, it’s #1; for most of you, it might be #3. I’m interested in all four, which is why I’m writing this all up right now. I’m embarrassed to say that it took several hours to do this. I was originally planning to post this Sunday morning after the game but it took time for me to get to the task. Most of the effort came from writing the code, not from writing the text. And there’s actually not much code, as you can see if you scroll to the end of this post. The main effort was not figuring out the syntax or even debugging (although there was some of that) but in working…