The NCAA Men’s Basketball Tournament began last night with a couple play-in games between two 16-Seeds and two 11-Seeds. This tournament is single-elimination. The winners advance to what is referred to as the official first round. The losers do not advance. They return home.
68 teams will compete this tournament over the next few weeks. 67 games will be played. 1 team will emerge the winner. 2 games are already in the books. There were 2 winners and 2 losers.
But this is the tip of the iceberg. Prior to this, the NCAA had all these teams and many more competing in the regular season.
351 teams play in the NCAA Men’s Division 1 Basketball league. They occupy 32 divisions. These teams competed over an entire season. From November to March, thousands of games were played by hundreds of teams with all manner of upset wins and surprise stories and titanic clashes.
Every team gets a chance to win. By winning, they claim a spot in the tournament to pursue the big prize.
Seems fair, right?
Tournament Systems Are Sorting Systems
Fairness is a very difficult thing to achieve even in the best of circumstances. But fairness in sports should be easy. After all, sports involve well-designed games with clear, objective scoring and inarguable results. Someone always wins; someone always loses. And aside from the occasional bad decision from the officiating crew, everyone understands that there is equal opportunity. Superior talent and/or tactics wins the day.
All the same, fairness gets dicey when you start to think about tournaments. It begins with the limitations of a “sudden-death” single elimination format. Consider the upset victory.
The impossible happened in last year’s tournament. A 16-seed team defeated a 1-seed. Prior to that moment, 16-seed teams had a perfect losing record of 0-135. But somehow, the University of Maryland-Baltimore County came out of nowhere to defeat the 1-seed Virginia Cavaliers. Who also happened to be the top ranked team overall. In the entire league.
The odds of this upset victory were practically negligible. Las Vegas wasn’t concerned about whether or not Virginia would win. That wasn’t the question. They just worried about the margin of victory. The betting line, in terms of over/under, was 22.5.
ESPN calculated the actual probability of a loss. It was 1.5%. Such a low probability and yet it happened. It was an incredible sight to see.
So back to fairness. By virtue of their win, it’s obvious that Maryland-Baltimore County was the better team, right?
Of course not. The Virginia Cavaliers were the best team in the entire nation based on the whole record of competition. Over the course of 33 games in the 2017-2018 season, the Cavaliers only lost twice. This upset was only their third loss of the entire year. By the record alone, they were the better team. They just happened to suffer a rare 1.5% event on that day.
In fact, one could say that this regular season result, by virtue of its comprehensive record, is always where the best team is discovered. As tournament designs go, the regular season is something closer to a round-robin format. It isn’t exactly the same but it’s close.
A round-robin format gives every team a chance to play every other team and progress by avoiding a certain number of losses. With repeated games come repeated observations and the best team can be judiciously determined through steady, consistent exposure to every possible combination of adversary. In terms of fairness, this works really well. It’s not perfect, but better.
Only trouble is time. If the NCAA instituted the pure format of a round-robin method, the result would be a basketball season that never ends. The effort necessary to make 351 teams play each other in a single round is absurd. No one has time for that.
Would it create equal opportunity and clearer measures? Yes.
Would teams like the Virginia Cavaliers have a better chance of proving themselves? Certainly.
Would upset victories carry the drama and intrigue and excitement? No.
Would anyone watch this sort of competition? No.
Fairness is hard. Efficient fairness is practically impossible. Delivering a fair system of broad opportunity requires significant time and resources. Those things are always in short supply.
So we shortcut it. We take a bunch of teams, assign subjective value to their performance via the tournament seeding (why is 23-win Purdue ranked as a 3-seed but 24-win Colgate ranked as a 15-seed?), put them in a single-elimination sorting machine, and let the games begin.
It’s the most fun of all formats. It’s the most efficient. It is the least fair.
Sorting Machines In Everything
The tradeoff between fairness and efficiency really becomes apparent when you examine all manner of sorting methods from the book Algorithms to Live By. Brian Christian and Tom Griffiths give us a fascinating view into this corner of computer science where techniques like Bubble Sort and Bucket Sort and other kinds of “-sorts” have intricate strengths and weaknesses that depend on the scale of your problem and the overall objective you wish to achieve.
So when you go for the methods that are more efficient, especially at scale, you choose to forgo the methods that are most fair. You get fluke results. A 16-seed somehow defeats a 1-seed.
There are easy correlations to other sorting mechanisms. The college admissions scandal shows the deranged behavior that results from sorting mechanisms that are less systematic than the NCAA tournament and certainly less transparent.
Or how about Google’s PageRank? Once that mechanism was understood, people started to game it. Search Engine Optimization is a standalone industry these days. All sorts of tricks and manipulations are tossed at the machine. Seth Kravitz has a fascinating article on the broad phenomena. It’s startling.
I could list more examples but you get the point. The job interview process is a sorting machine. Our own public schools are a sorting machine.
Entire cities are sorting machines. Want to be the best in tech? Naval Ravikant says you need to move to SF. This is a sorting mechanism. He doesn’t like it. His words to budding tech professionals are,
Unfortunately, I’d say, move to SF.
So that’s what you have to do. Unfortunately.
Improve The Sort To Improve The System
The more mindful we are to these sorting effects, the better we can assess our situations. Some sorting methods are misery-in-the-making. Specifically, pairwise comparison is an awful way to sort things. Not just from a fairness or efficiency standpoint. From an accuracy standpoint, too. Because for some of us, these rankings are not the goal.
For example, I have eight Twitter followers.
Can you believe that? Who has a mere EIGHT twitter followers? Me. That’s who.
In an “ordinal” measure of ranking, this is ghastly. I might as well have zero followers. It would look better in pairwise comparison for me to just not even bother.
But I don’t sort myself in that way. Neither should you. Twitter isn’t for sorting. It’s for connection. So I’m looking for the opportunity where someone, like a book author, acknowledges my thoughts on their wonderful work. Did that happen? Great. Did it not happen? That’s okay. No sorting. No ranking. No competition. Just outcomes sought and occasionally achieved.
Nonetheless, competition still exists. But there’s a great line from our aforementioned authors that I think really helps me think better about the act of sorting. It is the approach I want to take in competition. It has to do with a sorting method based not on pairwise competition, a’la the NCAA tournament, but on individual competition against a standard, a’la the marathoner’s final time in a race:
This move from “ordinal” numbers (which only express rank) to “cardinal” ones (which directly assign a measure to something’s caliber) naturally orders a set without requiring pairwise comparisons.
If you want fairness and efficiency in a sorting mechanism, the best way is to look at a cardinal measure. Look at your performance against your standard.
So you didn’t get into the top university. Or you didn’t defeat the 16-seed. Or you weren’t selected for the job. I think it helps to remember that these sorting machines are all flawed.
But your standard for yourself? The time you want to make as your personal best? That’s less flawed. Never perfect but much more robust and resilient. That standard, as a mechanism, helps you sort your best efforts from the ordinary ones. It helps you sort what’s right and wrong. Your standard might not be as high as others. You might not be ranked at the top of the leaderboard. But that’s okay so long as it isn’t how you let yourself be sorted.
As these things go, it fits with the idea of the self-authored strategy.
Make no mistake about it: tournaments are fun. Sorting is fun. Rankings and competitions are fun. But they’re still games.
So let the games begin. Just don’t let them consume us. It’s still your race, your standard. Sort yourself thusly. As Tony Horton would say, do your best and forget the rest.