I have retired from Berkeley, effective end-June 2018. However I will continue with light-duty research and professional activities. In particular I have been updating and expanding my open research problems page. But I am focussing more on my ongoing "Probability and the Real World" activities, below.
A more sophisticated analysis [see details of what follows] exploits the probabilities for each match winner. This allows us to attach more weight to "major upsets". We use a formula that represents the overall "extent of upsets" on a scale of 0 to 100, where 0 means "every match won by the favorite" and 100 means "every match won by the underdog". The formula is designed so that, before the tournament starts, each number between 0 and 100 would be equally likely.
The bottom line is 90. That is, in only 10% of tournaments would one expect more than this level of upsets. The single main upset, as most would agree, was Russia's win over Spain.
FYI A BBC article on other aspects of the World Cup
(June 2018): This page shows an unexpected literary appearance of my old Poisson Clumping Heuristic book (in Helen DeWitt's Some Trick). Presumably some real mathematician had this particular eclectic selection of books -- who could that be?
(March 2018): $200,000 prize money is being offered in the current IARPA Geopolitical Forecasting Challenge, but there is a curious Prediction Tournament Paradox which says that the winners are not so likely (as you might imagine) to be the best forecasters. So maybe my performance in the 2017 HFC Challenge pre-season was just luck.
|Probability Approximations via the Poisson Clumping Heuristic||Springer, 1989|
|Reversible Markov Chains and Random Walks on Graphs (with Jim Fill)||Draft chapters|
E-mail address: firstname.lastname@example.org