You’re Invited: A March Madness Challenge Where Skill Prevails
It’s that time of the year when I bemoan NCAA March Madness bracket rules, mostly because they’re terrible.
To see how my thinking has evolved over the last two years, you can check out the 2014 and 2015 versions of this article, but the key point of contention with traditional bracket rules is that they severely limit the sample size upon which the victor is selected. This happens for two fundamental reasons:
- There isn’t matchup parity. As the most extreme example, a #16 seed has never defeated a #1 seed in the first round. As such, everyone in the pool is likely to choose the #1 seed, which has the effect of eliminating it as a game which identifies skilled pickers.
- Legacy errors abound. In traditional brackets, if you select a team to make a deep run and they lose early, that mistake stays intact in future rounds, reducing the sample size.
Way back in 2014, we addressed these issues and structured rules that would maximize the sample size, thereby virtually guaranteeing that the winner was actually the most skilled. Our ideal scoring system looked like this:
- Score each game relative to the inverse odds that a team will win.
- Have each game picked only after the exact matchup is known.
- Have every game scored via the same system without regard to the tournament round.
Of course, this system is functionally unmanageable and…well….boring. Recognizing these shortcomings, in 2015 we changed tack by suggesting an “auction” approach. Each participant was allocated a faux budget from which they submitted blind bids on teams. The largest bid won the team, and whomever owned the winning team won it all. This approach was particularly intriguing because it had implications for both investing and economics. At the time, we wrote:
As Investors, we are keenly interested in this method because it has implications for diversification and portfolio design. Am I better off buying two #1 seeds or three #3 seeds or every seed worse than #6? Would I be better off with two #1 seeds from different regions or the #1-3 seeds in a single region? What are the relative values between teams?
As Economists, auctions represent a microcosm of the broad theory of supply and demand. Though we didn’t consider it last year, an auction solves a lot of the problems involved in a traditional bracket because unknowns and risks are all baked into the initial auction price required to “own” a team. This eliminates many of the in-tournament considerations; Legacy picks, as an example, become completely irrelevant because at all times, every team remaining in the tournament is owned by someone.
The auction approach was greatly preferred to traditional scoring systems, but it still had flaws. Most prominently, it doesn’t solve the issue at the heart of the matter: sample size. This was because post-auction, only the highest bidder would win the team, such that each team had only one owner. Particularly for those whose relatively large bids won the top teams, success and failure was once again pinned to a small set, or even one single team.
Which brings us to our most recent revelation: the entire goal of March Madness brackets is fundamentally flawed. Under both the auction system and the traditional bracket rules, in order to win most pools of meaningful size, a bracket had to pick the right Champion. This necessity forces players to over-pick top-seeded teams, which, as previously noted, undermines sample size. So how would things look if, rather than structuring rules that emphasize picking the Champion, we set the rules to optimize more for return on investment?
With this in mind, here’s how our 2016 March Madness Bracket Challenge is going to work:
- At the outset of the tournament, each team is assigned a point value equivalent to the natural log of their inverse proportion of winning the entire tournament. For example, If Kentucky has a 1/20 chance and Wisconsin has a 1/50 chance, Kentucky’s value will be LN(20)=2.99 points and Wisconsin’s will be LN(50)=3.91 points. We do this because the natural log scale seems to create reasonable balance between favorites and longshots. A team with a 1/2500 chance of winning would be awarded LN(2500)=7.8 points/win.
- A team is awarded their point total for every win, such that their entire value is the product of the point value multiplied by their win total. This yields some interesting effects inasmuch as, using Kentucky and Wisconsin again, three Wisconsin wins has roughly the same value four Kentucky wins (3*3.91~4*2.99).
- Finally – and this is where things get really interesting – a portfolio of teams must be selected. Brackets will assign a portfolio weight to however many teams they want, so long as the percentages add up to 100%. As an example, if you place 5% of your portfolio on Kentucky and they won 4 games, the bracket would be awarded LN(20)*4 wins*5% allocation = .78 points.
Basically, we’ve created a scoring system that disincentivizes “chalk” by awarding greater points to lower-ranked seeds. At the same time, we’ve shifted the issue of legacy errors – which used to be an inherent systematic flaw – to a problem that only exists to the extent a bracket chooses to take the risk.
But what really makes this an interesting and compelling exercise is the portfolio management implications of Rule #3. Brackets are allowed to place anywhere between 0% and 100% weight on any given team, meaning that they can concentrate their entire wager on a single team, maximally diversify across all 64, or set any exposures in between. Furthermore, brackets can add exposure to multiple teams who will play each other, thereby hedging (guaranteeing a balance of wins and losses), or they may choose to try and guess winners, potentially juicing their points, but almost certainly increasing the dispersion of outcomes in the process.
And so we come to the end of our 2016 March Madness update, except to say that this year, we want to invite you all to play along. There’s no fee to enter, all you have to do is visit this page to register. You won’t receive an immediate confirmation email when you register, but there will be more information coming next week and after the seedings are announced.
Since there’s no money involved, the only prize we can offer is significant dap in our post-tournament wrap up. And trust me that when I say “significant,” I mean it; we’ll make sure you can lord your victory over your colleagues for time eternal. After all, that’s the point, right?
So, make sure to invite all your colleagues and friends!
Again, click here to join the fun.