By Benedict Brady
During the week leading up to the start of March Madness, hundreds and hundreds of articles are written on understanding the bracket, dissecting which upsets are the most likely and modeling “important” first round matchups. But how much does this stuff matter? Every major bracket challenge site has a similar scoring system, under which every round is worth the same total number of points. This means that correctly picking 7 more upsets than your dad in first round is worth less than picking one additional final four team, and less than a quarter of picking the correct national champion.
Think back on your last few March Madness pools. Did the eventual winner pick the correct national championship? If your pool is of a decent size, chances are they did. If the winner did not pick the national champion, odds are that no one in the pool managed to get it correct. For this reason, especially in smaller pools, individuals tend to gravitate toward the favorites for their champion, for fear of getting eliminated early. But is this really the best strategy?
Everyone seems to innately understand the logic of picking an early round upset that none of your friends have, it differentiates you from the pack in a very dramatic way. But if this is a marginally beneficial strategy with the first round, it should be substantially more important with picking a winner. Why, then, are most blog posts written about choosing a winner focused on the team that is most likely to win? The key insight to understanding the correct strategy is that you will always be a longshot to win your march madness pool. In a 100 person pool, the best you can hope to do is up your chances from 1 percent to 2 or 3 percent, not 20 percent. The key to gaining this sort of edge is not picking the winner that is the most likely, but the winner that is the most undervalued. This can be best explained using an example year.
Assume that in this hypothetical year (unlike 2017) there is a fairly clear favorite. We have a Kentucky team with a 25% chance of winning it all, and a Villanova team with a 12% chance of winning. You are in a an office pool with 100 contestants and a $1.00 buy in. In this pool, 35 of them have Kentucky winning it all, and 8 of them have the less likely Villanova. Given that you pick the correct winner, you have approximately the same probability of winning as everyone else who picked the winner. So as someone who picked Kentucky, you have a 25% chance of picking the winner, and a 100/35 expected value given that Kentucky wins, for a total expected value of $0.71 dollars. However, choosing Villanova will yield a 12% chance of picking the winner and a 100/8 expected value conditional on Villanova winning, for a total expected value of $1.50. So, how does this apply to this year?
ESPN releases the data on the selection patterns for everyone who makes a bracket on their website*. Using that data, we can combine this with projection models to classify the common championship picks. We will use fivethirtyeight, kenpom, and vegas projections to gauge championship odds.
A few notes on this chart. In the second column, we have the ESPN ownership of each winner, followed by the probability of that team winning it all under three different metrics. Finally, the last three columns are the expected payout on a $1.00 entry fee. The Vegas expected values should be taken with a grain of salt. These lines have vig in them, so the championship odds add up to 98.5% while the 538 and kenpom add to 73% and 65% respectively. Taking the lines with vig does not very accurately translate to the probability of an event. Additionally, we know that betting lines are designed to be a reflection of public sentiment, so will probably correlate closely with actual ownership. In reality though, we care less about the precise expectation than the ordering of the results.
The second important caveat is the pool size issue. Consider a pool with 10 people. If you pick Louisville, all of a sudden they have a 10% ownership and they are significantly less valuable. Because of this, I have included a minimum pool size, under which by selecting a team, they will not immediately surpass their ESPN ownership. In reality this is probably not quite enough cushion, your selection will adversely influence the ownership of the team you choose. It is important to try and gauge the tendencies of your pool. Smaller pools will probably gravitate toward favorites. If you go to Kentucky, a Kentucky national champion will probably have extremely negative value. If you have no inside information though, these patterns are your best bet for what will happen in your own pool.
So, what does this chart tell us?
We can see that the obvious value picks are Oregon, Louisville, West Virginia, and Gonzaga. As we noted earlier, there are some issues with picking Oregon, Louisville and West Virginia in smaller pools. They do not actually have a very substantial chance of winning it all, but their low ownership gives them value. Because of this, if you are in a medium sized pool, the clear choice is Gonzaga. The advanced metrics are in love with Gonzaga, and even if you don’t buy the hype, vegas has them at mid to high level value. Additionally, all of these expectations are taken without considering that you can win without getting the national champion right. On ESPN, these listed teams make up 87.5% of the championship ownership while accounting for probably closer to 70% of the likelihood. Winning with each of these teams given that no one has chosen the champion is probably roughly proportional to the chance that each team wins the championship (since final four probabilities are roughly proportional to championship odds). Without speculating too much on this case though, it is clear that there is additional value beyond what is shown in the chart. Gonzaga is probably solidly in the 2-3x range.
This chart also highlights the bandwagon picks that are of obvious negative value. Teams like Duke, Kansas, and UCLA are substantially over-owned for their respective championship odds.
Finally, we can find some additional value by selecting an undervalued runner up. For the sake of simplicity, let’s assume you have chosen Gonzaga as your national champion. If you have gone with Louisville or Oregon, your fate is probably nearly all tied to your national champion choice. However, if you choose Gonzaga you may have some additional work to do to differentiate yourself. Based on the scoring, you will probably not get this bump from choosing a few 12 seeds to make it to the round of 32, but instead by choosing the correct runner up. So, what are your possible options?
If you are in large pool, there is obvious value in Louisville and Oregon. If you are in a medium sized pool, Kentucky is probably the best way to go. If you are in a smaller pool, you probably want to just go with the most likely options of Kansas or maybe UNC. It is important to note that these expected values assume that your only chance of winning is if you correctly pick the winner and the runner up. This means that you can nearly triple your expected value even if you can only win on a Gonzaga-Louisville final. In all reality, your win probability will be much higher than this, just picking these two teams to the final four would skyrocket you to the top of your standings.
These calculations do not hinge on incredibly precise matchup probability calculations. The 538 and kenpom projections vary wildly, yet they generally agree on which side of the value spectrum each choice is on.
So, now that we have outlined a strategy for picking your March Madness winner and runner up, what is the best strategy for the rest of the bracket? According to Ed Feng, you will win a 5 person pool 43% of the time by just choosing the favorites. This would suggest that once you have narrowed down your pool to the 5 people who have chosen Gonzaga, or in a larger pool the 5 people who have chosen Gonzaga and Louisville, you are best served going chalk. There is very little additional edge to be gained from selecting undervalued upsets, instead your best strategy is to rack up the points that you can get conditional on your one or two big value plays. So take a chance, and understand that every bracket outcome is a low probability event.
*This data was collected around 12 ET on Wednesday, March 15th.