A Newfound, we try to embrace March Madness as an opportunity to foster some good-natured competition within the company.
This year we decided to mix things up and go with our own version of ReSolve's unique March Madness Challenge.
When Corey originally suggested the idea, my initial reaction is probably best conveyed with this Puff Daddy lyric:
"Put your money on the table and get your math on."
And boy did he get his math on, authoring what was referred to as "the nerdiest sports blog post of all-time*."
* I may or may not have completely made this up.
My approach, while nerdy in its own right, was a bit simpler. Like Corey, I used the dataset available at FiveThirtyEight. In the contest, each team is assigned a points-per-win (“PPW”) score that they accumulate for each win. The objective is to pick a portfolio of teams that is designed to maximize the total number of points earned over the entire bracket.
Using the FiveThirtyEight data in conjunction with each team's PPW, I computed the number of points we expect each team to accumulated during the tournament. I also computed the standard deviation of each team's score.
Below we plot the expected value of each team's cumulative score (y-axis) vs. the standard deviation of that score (x-axis).
Source: Data from FiveThirtyEight, Calculations by Newfound Research
Some observations from this chart:
- Generally speaking, higher seeds have higher expected scores.
- The 1 and 2 seeds seem to offer superior risk/reward trade-offs.
- Standard deviation (or variability) seems to have a peak in the 5 to 12 seed range. Teams seeded 1 through 4 and 13 to 16 have lower variability. This is consistent with the historical observations that "Cinderellas" tend to come from the 5 to 12 seed lines.
- While you can't quite see this on the graph, Sharpe ratio (or expected score divided by standard deviation) consistently decreases with seed.
I also noticed a couple of other important features of the contest.
First, we are able to perfectly diversify our exposure by appropriately weighting teams whose success is negative correlated. In fact, it is possible to guarantee a certain number of points if we allocate properly. In other words, we can lock in our score regardless of how the tournament plays out. Whether every favorite wins or every underdog wins, we will score the same number of points. How do we do this? It's actually pretty simple, we weight our portfolio in inverse proportion to PPW (i.e. give more weight to teams with lower PPW values or in other words overweight favorites). For the PPW values we are using at Newfound, the risk-free score we are able to lock in is 5.36.
We can see why this is the case with a simple example. Consider one game. In this one game, we get X points if the first team wins and Y points if the second team wins. Using the inverse weighting scheme, our allocation to the first team will be (1/X) divided by (1/X + 1/Y). With some algebra, we can see that this equation is also equal to Y / (X + Y). If X wins, you will therefore receive XY / (X+Y) points. The same math for the second team shows that the points received should it win will also be XY / (X+Y).
Second, the optimal portfolio will be highly dependent on the payout structure of the contest. At Newfound, we only are rewarding the top three finishers. With 18 entries, an "average" outcome will be worthless. So while I could lock in a return of 5.36 through the method above, it probably wouldn't be in my best interest. While I do want some diversification in my bets, I don't want to completely eliminate variance. Variance is exactly what gives me hope of a strong enough performance to finish in the money.
With all this being said, I decided to go with what might be referred to as a "multi-factor" approach. I constructed three different equal weight portfolios, each screened using a different metric. The three sub-portfolios were then blended together to get the final result (Confession: I did slightly modify weights for teams I love or hate.) The metrics I used were:
- Sharpe Ratio (Expected Number of Points Divided by Standard Deviation of Points)
- Expected Return (Expected Number of Points)
- Volatility (Standard Deviation of Points, here I actually wanted the higher volatility teams in line with my desire for some healthy risk in my portfolio).
The Sharpe Ratio Portfolio is heavy on the 1-4 seeds (green and dark blue in the above scatterplot) since this is where we get the highest number of expected points relative to risk. The Expected Return Portfolio is generally very similar to the Sharpe Ratio Portfolio. The Volatility Portfolio is dominated by the cloud of teams on the right in the scatterplot (mid-seeded teams).
I decided to deal with diversification using a simple heuristic. Namely, each sub-portfolio was limited to only one team from each four team first round pod of four teams* (i.e. only one of Kansas, Austin Peay, Colorado, and California). I choose this method with a eye towards preferring low correlation to negative correlation. I care about risk, but remember that I do want to preserve variance. In portfolio terms, you might say that I want to be diversified, but not hedged.
* Again, I exercised a bit of discretion based on some more subjective love/hate feelings for certain teams.
The chart below shows my final portfolio.
Unfortunately for Corey, our mantra that simplicity trumps complexity does not seen to have translated over to March Madness. As a result, I'm predicting a massive victory in my totally unbiased opinion.
Enjoy the Madness.