Visualizing all of the Ways to Win Our March Madness Pool
By: Ryan Harrington
Tags: March Madness, Data Science, Data Visualization

March Madness. The best time of the year. The collective American public goes nuts for 64 teams duking it out game-after-game for basketball glory. We enter tournament pools. We build brackets. We momentarily care deeply about teams and players that mere days prior we (mostly) couldn’t have even told you existed.

Like the rest of America, the CompassRed office also went nuts for March Madness. While I’m a basketball fan, I don’t pay much attention to the college basketball season as it’s happening¹. However, March Madness…this is my time to show that knowing a few random rules² and nothing else about picking teams can lead to office pool glory.

Now, I don’t know about you, but as each game in the tournament progresses — especially in the later rounds — I find myself trying to do the mental calculus of which games need to go which way so that I can win my pool. Here is a recent video of me doing this:

Typically, my thought process goes something like “even though I have Virginia in the Final Four, if they lose now, then that means that Darren, who has them winning, would lose more points overall than I would, meaning that I might be able to leap frog him in the standings”. Now do this for every possible game. My allegiance to teams waxes and wanes as quickly as I decide what is the best route for me to win.

Of course, there’s a better way to do this. We could actually calculate every possibility and figure out every outcome.

Me, f̶i̶g̶h̶t̶i̶n̶g̶ ̶T̶h̶a̶n̶o̶s̶…calculating possibilities.

It doesn’t really make sense to do this for the first round of games. Entering that first game, there are 2⁶³ possible outcomes³. That is a decidedly large number. However, that exponentially decreases to the point that by the time teams head into the Elite Eight, fighting to make it to the Final Four, there are only 128 possible outcomes remaining for the final seven games⁴ of the tournament. I’m no Dr. Strange, but I can handle this.

There are two data points that we need to start off with. First, heading in to the Elite Eight, what did the points⁵ of everyone in our office pool look like?

Darren — 72 Eugene — 68 Frank — 68 Jeff — 68 Tom — 68 Bob — 63 Patrick — 58 Ryan — 57 Aru — 57 Gabby — 54 Pat — 34

Second, what were the matchups heading into the Elite Eight?

East Region — Duke (1) vs. Michigan State (2)

— Duke (1) vs. Michigan State (2) West Region — Gonzaga (1) vs. Texas Tech (3)

— Gonzaga (1) vs. Texas Tech (3) South Region — UVA (1) vs. Purdue (3)

— UVA (1) vs. Purdue (3) Midwest Region — Kentucky (2) vs. Auburn (5)

Given that starting point, we can generate every possible outcome for the tournament. A great way to visualize those outcomes is with a Sankey diagram:

If you follow each strand, you can see every possible path to winning the NCAA tournament. We can also highlight all of the outcomes that lead to each team winning:

Now that we have all of those scenarios, we can figure out all of the different outcomes for our office pool. We do this by comparing each of the 128 scenarios to each pick that everyone in the office made for all of the remaining games. While typically people want to optimize the number of points that they get from their bracket, I’d rather maximize my rank. I want the glory of winning. Remember — if Virginia losing (spoiler: they don’t) means that Darren loses more possible points than me, even though I also picked Virginia, then I’m happy. Here’s what that looks like:

There’s some interesting takeaways here:

It looks like Darren is more than likely going to win. Even if everything goes wrong for him, then the worst that he can do is 5th place. Eugene will probably do well, but he can never win. Frank and Tom both have a shot at winning. Aru, who is in 9th place at the beginning of this round, actually has a chance to win. There’s a chance that I (Ryan) can end up doing pretty well, but I can never win. So much for the glory of winning the office pool. Pat is completely and utterly screwed.

It looks like Darren, Frank, Tom, and Aru all have a chance of winning. Of the 128 possible scenarios, how many of those scenarios does each of them win?

It appears that Darren will win in 56 of the 128 scenarios (43.75%). Tom will win in 32 of 128 scenarios (25%). Aru will win in 24 of 128 scenarios (18.75%). Frank will win in 16 of 128 scenarios (12.5%).

The next question is — which of those 128 scenarios leads Darren, Tom, Frank, or Aru to glory. For that, we can consult another Sankey diagram:

Now we can see all of the paths that might occur that would lead to each person winning our office pool. Let’s separately highlight the scenarios that would lead to each person winning:

Now, of course, we know what actually happened in 6 of those 7 games.

After all of those games, we’re down to only two scenarios left — either UVA or Texas Tech is winning the whole tournament tonight. For our office pool, that means that there’s only one possible winner left. Congratulations Darren! Go ‘Hoos!