Guest contribution from David Gimpel and Matt Zerker, our resident NCAA fans
As quants and sports fans we often find ourselves analyzing statistics from the sports world. And seeing as college basketball dominates the sports landscape for the next few weeks, it’s no surprise we are inspired to write about the NCAA Men’s Basketball Tournament, aka March Madness.
One of the great sports traditions is to participate in an office pool, whereby participants complete a tournament bracket. In doing so, they select a winner for each game, and ultimately the “best” bracket wins.
But there’s a problem: most March Madness bracket challenges reward only some random idiot; the “best” picker – you, obviously – is rarely victorious. You spend hours analyzing teams, weighing matchups and seeking out that perrenial “Cinderella” only to find that on top of your entrance fee, you’ve sunk a lot of time into a losing effort. Here’s the good news: it’s not your fault. Really, it’s not. The scoring system is to blame.
Before we tackle specifics, it makes sense for us to come to a philosophical understanding about how we would go about identifying the best picker in a bracket challenge. Here are our basic criteria:
- We should allow for the largest sample size possible.
- We should create “matchup parity.”
On maximizing the sample size, there are two considerations. First, if we are really concerned with identifying the most talented picker, then it stands to reason that each game ought to be scored in the same way. Increasing points as the rounds pass has the effect of rewarding pickers who are lucky enough to select teams that go far in the tournament, regardless of whether or not they picked the most correct games overall. Stated another way, using a standard scoring system, the picker with the most correct picks in the early round could easily lose to someone who did relatively worse early on, but happened to pick the eventual tournament champion correctly. So, in order to maximize sample size, every game ought to be treated in the same way, regardless of when it happens in the tournament.
Second, and more troublingly, we would ideally have every entrant pick every game in the tournament after the matchups were known in each round. In other words, pickers wouldn’t make their 2nd round picks until the entire 1st round was completed, and so on. In this way, every person could pick every game, regardless of whether or not the teams they selected in the previous round advanced.
Adopting the standard bracket rules is undesirable because every incorrect choice has the effect of reducing the sample size upon which we judge the best picker. These incorrect picks stay on your bracket as legacy errors, eliminating every subsequent game from the set upon which you are judged. This reduces the sample size, and in the world of statistical reliability, smaller sample sizes increase the randomness of possible outcomes.
And let’s be perfectly clear, here: random outcomes in March Madness bracket challenges will never, ever, ever go your way. If you want to be lauded as the “truly talented” picker that you are, the legacy errors have got to go, and thus, so do the old-time scoring systems. Every matchup should be selected, but only after every matchup is known.
Unfortunately, anyone who has ever had the misfortune of running an office pool understands the logistical impossibility that this imposes. If one used the alternate system we are proposing, then a new set of picks would need to be submitted after every round, for 5 rounds! Some people wouldn’t get their picks in on time, others would be frustrated by such a system, and everyone would hate you: the unenviable plight of the lowly pool manager.
Moving on to “matchup parity,” it comes down to this: we want the picker to be completely neutral with regards to which team is chosen to win. Ideally, if the rules are set right, half the people in your bracket would choose one team, and half would choose the other, even in the most lopsided games. How do we encourage this distribution of picks? By appropriately rewarding those who correctly predict an unlikely outcome – upsets!
As an extreme example, let’s think about the all-but-overlooked #1 seed versus #16 seed in the first round. In the entire history of the NCAA tournament, a #16 has never defeated a #1. Not ever. Of course this doesn’t mean it’s impossible, simply that it’s highly improbable. In order to entice half of the pool to chose something that has literally never happened before, we must create a powerful incentive to do so. To wit, we want to make the expected returns equal regardless of which team is selected. To see how this might work, imagine that the #1 seed has a 99% chance of winning, meaning the #16 seed has a 1% chance. From the perspective of expected returns, it might make sense to award 99 points to anyone correctly selecting the #16 seed in that matchup and 1 point for anyone correctly selecting the #1 seed.
To make the expected return of each team equal, we simply set the payoff for correctly choosing the favorite equal to the underdog’s chance of winning and the payoff for correctly choosing the underdog equivalent to the favorite’s odds. In the real world, the odds for each team can be backed out by a simple examination of the betting lines. It might not be perfect, but if you believe in the wisdom of crowds, the “sharp money,” or the completely accurate notion that book-makers are profit seeking enterprises with a vested interest in getting lines “right,” it’s a good enough proxy.
Therefore, if the goal is to actually reward the most talented picker in your pool the ideal system might look something like this:
- Score each game relative to the odds that the selected team’s opponent 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, we’re not stupid: Nobody does this, and nobody is going to do this because it’s tedious and more importantly, it’s BORING.
As with picking an NCAA Tournament bracket, the hope in all endeavors is that true skill bears out over time. In the investing world, time is our sample size. Any manager can look like a genius over a year or two, but it is the truly talented ones whose ability bears out over much longer and more significant periods of time. We want the odds on our side as often as possible, and we want the rules of the game to reward those with a true informational edge. Understanding the virtuous-spiral-inducing recipe of large sample size, statistical robustness and compound growth, we’re happy to win thousands of small bets over our investing lifetimes even if the “action” in the interim isn’t nearly as thrilling. Indeed, the recipe for long-term success is to be on the proper side of a small win over and over again. If you’re excited about your investments – even if it’s for the right reason, like great performance – you may want to think twice about whether or not that strategy is appropriate for you, since the investment’s evocative nature stands a good chance of undermining your success down the line.
In the world of NCAA March Madness brackets, however, we are more often excitement-seeking. And that’s quite problematic to our goal of identifying the best picker, because even we must admit that in the case of March Madness brackets, excitement adds to our overall enjoyment even when it diminishes our chances of winning. And there’s the rub: investors often feel the same way, seeking thrilling investments that ultimately undermine their odds of success. And while it might be alright for your office pool, it’s not going to help you achieve your financial goals.
The process whereby you identify the best picker is mutually exclusive from the process by which you maximize overall pool excitement; the process whereby you maximize your odds of financial success is mutually exclusive from the process by which you maximize the thrill of investing.
In both cases, the decision is yours.
In the case of the NCAA tournament, most people will go with the excitement angle. We understand; Sports are exciting, and the idea of winning gloriously and just owning your colleagues is certainly appealing. But the most likely outcome of a standard bracket challenge is that you’ll have once again contributed your hard-earned money to someone else’s bank account.
Hopefully, though, once you’ve repeated the embarassing annual ritual of awarding the championship money to the person in your office who knows the least about basketball, you’ll think twice about making similar mistakes with your investments.