By Daniel Alpert
Round one of March Madness 2016 is in the books. From 15-seeded Middle Tennessee taking down Michigan St. to UNI hitting a half-court buzzer-beater to sink Texas, this year’s first round was full of upsets. Since the tournament expanded to 64 teams in 1985, there has been an average of about 6 upsets (double-digit seeds winning) per first round. Ten upsets occurred this year, more than any year in the past. Excluding the 8 vs. 9 matchup, this year had more upsets than ever before (and tied the record with thirteen if you do include that matchup).
All upsets, however, are not created equally. A 15-seed stunning a 2-seed is far more surprising than a 10-seed beating a 7 (something that is still an upset but happens nearly every year). I wanted to find not which round had the most upsets, but which round had the most stunning upsets. To do this, I weighted each upset. I used historical data from 1985 to weight each upset based on how often the upset had happened in the past. The weights were determined by (100/# of times upset had happened in the past). One flaw with this weighting method is that all of the previous years weighted upset scores are calculated using all 32 years of data. When the first 15 vs. 2 seed upset happened, it would have had a weighted score of 100 then, not 12.5.
With the weights, I recalculated the magnitude of upsets in the first round each year.
I found that while this year had the most upsets, it only had the second most “weighted upsets.” This makes sense, as 2012 yielded nine upsets, two of which were 15 seeds over 2 seeds.
To find how unlikely it was that each year would produce as many upsets and weighted upsets as it did, I used a logspline density estimate to fit the distributions.
Looking at this year again, according to the density estimates, there was only a 1.3% chance that there would be 10 or more upsets. There was a slightly better chance (4.2%) that we would see as many weighted upsets as we saw. In 2012, there was a 5.2% chance we’d see nine or more upsets, but only a 2% chance we’d see as many weighted ones.
Two interesting years I found were 1993 and 1994. In 1993 there was an 88.9% chance we would see as many or more than the four upsets we saw, but only a 31.9% chance of having more weighted upsets. On average, each upset was a significant one. The next year, there was a 68.0% chance of having more upsets, but an 89.0% chance that the upsets would be more significant. The upsets weren’t very significant.