This is cross-posted from SkewU, our sister blog. We don’t normally do this sort of thing, but this is important because:
1. You should check out SkewU, as it’s quite a bit different than GestaltU. Our posts over there are more diverse and whimsical if that’s something that interests you.
2. And more importantly, standard March Madness bracket rules are the most awful, terrible, nonsensical, annoying things in our lives right now.
So, we channeled all that frustration into our own unique March Madness Challenge, where skill actually matters. You can read how our vastly superior rules work below, but c’mon…we’re friends…so just register.
There’s no entry fee, but make no mistake, there is a glorious reward awaiting the champion (which you can read about below).
It’s that time of the year when we bemoan NCAA March Madness bracket rules, mostly because they’re terrible.
To see how our thinking has evolved over the last two years, you can check out the 2014 and 2015 versions of this article, but our 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:
1. 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.
2. 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:
1. Score each game relative to the inverse odds that a team will win.
2. Have each game picked only after the exact matchup is known.
3. 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 were 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, the objective was return on investment?
With this in mind, here’s how our 2016 March Madness Bracket Challenge is going to work:
1. 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)=2.995 points and Wisconsin’s will be LN(50)=3.912 points. We use a log scale because some teams will have absurd longshot odds, and the log scale means that when – just picking a team at random, here – Michigan’s odds are ultimately revealed to be 1/2500, their assigned point value will be LN(2500)=7.824.
2. 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*3.912~4*2.995).
3. 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 = .599 points.
Basically, we’ve created a scoring system that dis-incentivizes “chalk” by appropriately awarding more 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, submissions 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.
That said, as with all March Madness pools, there will be a certain amount of people who submit chalk brackets. And while there exists no specific rule against these submissions, it’s a generally accepted principle that such submissions are the exclusive purview of cranks, curmudgeons and cowards!
And so, to save everyone the embarrassment, we thought it would be a useful service to lay out the March Madness portfolios – under our rules – that would be considered “chalk” submissions. Basically, in our post-tournament wrap-up, these are going to be the benchmarks against we will judge the performance of the entire pool of entrants.
1. Equal Weight Portfolio. This bracket allocates equal weight to every team. This is a reasonable starting point for people who feel they have no informational advantage.
2. Rank Weight Portfolio. This bracket allocates across all 64 teams in proportion to the seeding (top seeds are more heavily weighted).
3. Hot-Hand Portfolio. This bracket will allocate equally to the “power conferences” champions (Big 12, Pac 12, ACC, Big East, Big Ten, and SEC), regardless of region or seed. The idea here is that most of them won a conference tournament, and would be heading into the tournament with some positive momentum.
4. Concentrated Portfolio. This portfolio will allocate equally to the top 2 seeds in each region.
5. Rank-Seed Weight. This portfolio will rank weight the top 4 seeds in each region.
6. Potential Point Weight. This portfolio will weight teams in direct proportion to the total points a team would accrue from winning the championship. Heuristically, the idea here would be to target equal expected points from every team in the field.
And ya know what? Just for kicks:
7. The 12-seed Equal Weight Portfolio. Because 12-seeds always seem to punch above their weight.
So, there ya go. Chalk brackets beware: our March Madness challenge is not for the feint of heart!
(SCHEDULING NOTE: The 2016 Tournament field will be announced on March 13. For registrants, we will send the submission spreadsheet via email on March 14, which may or may not include the garbage teams participating in the “First 4” games on March 15 and 16. The first round begins March 17, and your portfolio submissions will be due by 11:59PM EST on March 16.)