Dr. Green and White Sports Authority

The 2018 NCAA Men's basketball tournament had some pretty special moments. From the controversial quad system to a 16-seed beating a 1-seed to an 11-seed making the Final Four to crazy finishes, it was a pretty a fun 3 weeks (except for MSU fans. It honestly kind of sucked for us). But, was it really such a strange tournament? I mean, they call it "March Madness" for a reason, right? Well, as we will see, it was really not that strange at all, at the end of the day. As for the total number of upsets (by seed only) the 2018 Tournament produced a total of 20 upsets in 67 games. The average number of upsets per year back to the 64 team expansion in 1985 is 17.6 ± 3.  But, as you can see from the histogram below, there is a fair amount of scatter in the data with a minimum value of 12 and a maximum of 23.  While 20 is a bit high based on the average, it is actual the mode (most frequently appearing value) of the distribution. If we instead look at the upset distribution o...

It has been almost three weeks since Villanova cut down the nets in San Antonio, and with that, three weeks since the beginning of great annual 5 month gap between meaningful college sports. While we patiently pass the time this summer until the real fun begins again this fall, I thought that I would reflect back on the NCAA basketball tournament with a series of my math-infused musings.  Today's topic: why did it take 34 years and 136 attempts before a 1-seed finally lost to a 16-seed while a 2-seed has fallen on average about once every 4 years? The answer, as it turns out, is the same answer that I often find when I decide to dig deep into some of these topics: because, math. My journey to solve this mystery began a few years ago when I made the observation that the probability of an upset in the NCAA tournament occurring scales roughly linearly with the difference in value between the two seeds.  The correlation is quite strong for the most common seed pairs (i.e. those ...