The Daily Think

The NCAA men’s and women’s basketball tournaments are upon us and the well over 128 teams (play in teams included) have a chance for glory, by simply winning 5 games straight in a single elimination competition that watches the field drop from 64 to 1. Everybody gets that and is familiar as enthusiasts and casuals alike also participate in “filling out a bracket” and seeing how you do against your friends, who may/most likely are filling out brackets too.

What really brings these two seemingly opposite levels of interest for college basketball still come together for a friendly competition of who picked more games correctly?

Is it the players? Not really, the system now has competition for future NBA talents, like the G-League and overseas stints and the projected top 2 men’s NBA draft picks in 2023 may not have played in college. See Victor Wembanyama “Wemby” & Sterling “Scoot” Henderson (great names Sterling and Scoot!) Got to just say shout out to Sterling Sharpe, a fantastic Green Bay Packer Wide Receiver in the 90’s and Tecmo who had too short a career. Also Shannon “Unk” Sharpe’s older brother. But anyway, the players in the NCAA tournaments on the men’s side will not be household NBA names. A different story for the women’s Tournament, as more pros will come from their ranks and really build on a great run in the tournament, with name recognition as they progress to the WNBA. More on that in another article about college cache over development leagues.

Is it the college names? I mean sure we all recognize the big names like Kansas (pick them they won a couple of these right?) the North Carolina’s (oh wait that’s not the usual North Carolina blue I see) the Duke Blue Devils, because really you can never get rid of the devil (hey it’s in their name!) But other names you constantly see but don’t know anything about until March, like Gonzaga, um, NorthWest school, has some pro players. Or a Providence, they always seem to be in that double digit seed, they don’t seem like a big college name, but they always play hard! Maybe you’ve heard of Xavier, as a friend said to me as to why they picked them “the bald X-man guy right?” from the Marvel Comics’ X-Men. Or the VCU’s maybe a friend went to med school there. But clearly we don’t know anything about a majority of these colleges outside of our own colleges. So its not the teams.

Is it the simple mathematical formula tournament with plenty of error and parity that has a rank system that doesn’t always favor the lower/perceived better seed? Yes! Let’s give it up for math, as it creates a great equal tournament that exposes the top seeds to play a variety of opponents from the far reaches of the NCAA landscape from San Diego State to Iona. From a Farleigh-Dickinson to a Saint Mary’s or maybe you’ve heard of Marquette and Butler. A little more on that formula.

To understand the mathematics behind the format, let’s first look at the number of possible matchups in each round. In the first round, there are 64 teams, so there are 32 matchups (64/2 = 32). In the second round, there are 32 teams left, so there are 16 matchups (32/2 = 16). In the third round, there are 16 teams left, so there are 8 matchups (16/2 = 8). This pattern continues until the final round, where there are only 2 teams left and they face off in the championship game.

To calculate the total number of possible matchups in the tournament, we can simply multiply the number of matchups in each round together. That is:

32 (first round matchups) x 16 (second round matchups) x 8 (third round matchups) x 4 (fourth round matchups) x 2 (championship game matchup) = 2^6 x 2^4 x 2^3 x 2^2 x 2^1 = 2^16 = 65,536

So, there are a total of 65,536 possible matchups in the NCAA tournament format of 64 teams. The mathematical principle behind a single-elimination tournament made of 64 participants is often referred to as a “binary tree” or a “bracket.” This is because the tournament’s number of participants is halved, forming a tree-like structure that ends with a single winner. Each round of the tournament is represented by a branch in the tree, with the winners advancing to the next branch and the losers being eliminated. The binary tree structure is a widely used and efficient way to organize and manage large-scale single-elimination tournaments like the NCAA basketball tournament.

THE SEEDENING OF THE BINARY TREE!

With those regions, there is a ranking by a committee from 1 to 16, so that means there is 4 number 1 seeds, 4 number 2 seeds, so on and so forth. And one thing we enjoy seeing as the tournament is seeing a lower seed, a 2,3,4,5 or dare we say it, a 1 seed!? It has only happened twice in the history of the tournament, and only recently in the past few years, is this a commentary on the talent levels in college these days where many basketball teams are pretty equal? No, that’s more of a macro conversation, lets keep this on these seeds.

Why do we like these seeds?

Well, there are so many combinations and possibilities, but the rankings are always the same…a number 1 vs. 16 a number 5 vs. 12 or a 8 vs. 9 match-up. We don’t know much outside of the name or the history with that school that occupies a seed, and that is where the crap shooting begins. It becomes a guessing game that rewards our perceived brilliance, but mostly our dumb but calculated luck. However, the perfect bracket competitions exist, with many contests and an estimated $8 Billion in wagering, so it comes with the slight amount of skin in the game and also bragging rights (most importantly) through countless pools across the country.

A Perfect unifying event

In addition to being a perfect wagering event as the first-place player in your pool in the first week can be your last place player by the end (its mathematically possible, it can happen!) But also, a perfectly formatted binary tree that fairly distributes invites to the many colleges and universities out there, but its a UNIFYING event. Sure, we may not like Duke or UCLA, but we like to pick against them and gloat, I mean share that we picked Princeston to defeat Arizona. For a few weeks, many people are doing the same thing, focused on the same thing, and that’s how is my bracket doing, alongside many others, united in math! Plus who doesn’t like an event with an unusual number of upsets that makes you feel like you picked a winning bracket when the 12 seed you picked beats the 5 seed every year (don’t worry, it won’t happen to many of us, its math.)