Maximizing Win Probability
When filling out your March Madness bracket, remember that your primary goal is not to pick the most likely bracket, but rather the bracket that has the best chance of winning your pool. Maximizing win probability requires the player to consider not only a team’s odds but also the distribution of picks of the other participants in his pool as well as pool size.
For example, consider a single entry into a 100 bracket pool. One would expect to win this pool (and the corresponding bragging rights) about 1% of the time, and our goal as a savvy entrant is to increase that probability. Most hoops fans are aware that Villanova cut down the nets last year and drew the #1 overall seed in this year’s tourney. Sports books in Las Vegas estimate their chances to be around 10-12%.
So, history is bound to repeat, right? Not quite. A quick glance at the pick distribution tells us that 16% of the brackets filled out thus far have selected Villanova as their champion. Even if you choose Villanova, and they do win, you still have only a 1/16 chance of winning your pool! By picking Villanova, your win probability (‘pool equity’) has dropped from 1% to 0.7%.
What about another talented power basketball school? The Louisville Cardinals might not be quite as good as the defending champs, but they’re a much better pick when filling out a bracket. Las Vegas has given them a 7-8% chance of winning the tournament, but only 2% of Yahoo! pool entries have chosen them. So, if you decide to pick Louisville, the one out of 7-8 times that they win, you’ll be more likely to be crowned champion of your 100 person pool. (You’ll get a ton of points that nobody else gets for picking a more rare champion, as well as tons of points from their run through prior rounds, your ‘pool equity’ rises from 1% to 3.2%).
Villanova and Kansas are great picks if you want to get the winner correct, but pretty bad selections if you are trying to win a big pool. Louisville, Duke, and Kentucky would be much wiser selections in large pools. This year is a wide open field, with Vegas giving 7 teams (Villanova, Kansas, UNC, Duke, Arizona, Gonzaga, and Kentucky) 10/1 odds or better, with no team with better than 6/1 odds.
Compensating for Pool Size
An astute reader may have noticed that this doesn’t hold true for smaller pools, where your baseline win% is higher. We apply the exact same concept, but on a smaller scale in small pools. Powers like Kansas and Villanova now become viable options, but we still must diversify our bracket with picks that are both somewhat likely, but also unpopular.
As a rule, the smaller your pool is, the more conservative your bracket should be. As the pool size grows, we must induce positive-expectation variance by picking more unusual teams to make runs, and for those runs to be deeper.
This should be inherently obvious — in a two-person pool, you would pick all favorites. In an 8-person pool, you would pick almost all favorites, with a couple small surprises. In a 40-person pool, you’ll induce more variance with one or two surprises Final 4 teams, and some early round upsets, and so forth.
Picking Your 2017 Champion
Duke, despite the #2 seed, was given the best odds to cut down the nets by Vegas in the preseason, and after their ACC conference championship now have the most probable odds again. Yet in a wide open tournament, the Blue Devils have only received the 4th most votes by the people filling out brackets.
Against 50-100 competitors, Oregon, Baylor, Florida State, and West Virginia become good options for uncommon champions if you pick the rest of your bracket conservatively. Because of the aforementioned wide-open field, even highly seeded UNC, Duke, Arizona, and Gonzaga are still good choices, if you pick more boldly.
The balance between pool size and variance is the top advice from a game theory perspective. If you pick West Virginia to win in a 100-person pool, you’ve done enough! If West Virginia wins, you’re already golden, so don’t blow it by picking a bunch of ridiculous upsets.
Picking Your 2017 Final-4 / Elite-8
If you need a team to make a surprise Final 4/Elite 8 run there are plenty of good choices. Riskier choices for a pool large enough to accommodate their value are Kentucky, Louisville, Oregon, West Virginia, and Purdue who have a 10%+ chances to reach the Final Four but have each been picked by less than 5% to make it that far. Even further along the risk-reward curve are SMU, Virginia, and Florida each has been given a 5-10% chance to make the Final Four by Vegas, yet each team has been given less than a 0.5% chance by the bracket picking public.
Kansas has been selected to reach the Final Four at the highest rate of 38%, yet is in a tough Midwest regional and their likelihood of reaching the final four is only in the 30-35% range (vig-adjusted Vegas odds).
Picking Your 2017 Round of 32 and Sweet 16
In the second and third rounds, there is a ton of room for personal preference and creativity. There is enough data available online for you to infer solid selections, and it’s up to you to mix and match the appropriate number of early round upsets with one or two deep runs or a surprise champion to create a high-value bracket. Remember, the larger your pool, the more aggressively you want to pick upsets with value!
Picking your 2017 First Round
The first round is easy. Everyone likes to pick cute upsets, but generally, these don’t create a ton of value. It’s better to just pick solid teams with a couple of higher seeded that are basically coin flips. For example, #12 Middle Tennessee is actually a pick’em against #5 Minnesota, and yet only 44% of people have picked them.
Another underdog to consider is #10-seed Oklahoma State with only 21% picked and over a 40% implied Vegas Win Probability versus #7-seed Michigan. Another #10-seed, Wichita State is a talented team that got mis-seeded by the committee with a 70% Win Probability against Dayton and while many already know it, still only 65% of players are choosing the Shockers.
For the sake of simplicity, raw odds from Vegas are used. You’ll have to modify these odds with extra information that you may be able to obtain. For example, Dr. Bob, is able to create more accurate bracket probabilities, and you’ll have to apply these concepts to those numbers.
Likewise, the Yahoo! numbers are reflective of fans nationwide, and they may not be the same as fans in your area. If you are with your co-workers in Ann Arbor, Michigan, do not think it’s a good idea to select the Wolverines as your “surprise” champion.
The purpose of this article is to help you maximize your chances of winning your pool. Most March Madness pools feature many contestants, but pay out only the top few, so we want to embrace high variance. Picking a conservative bracket with a common champion will get you to finish in the top 20% of your pool almost every year, but it will be difficult for you to win. If you pursue these strategies, you’ll come in dead last fairly often, but you’ll also win and profit more frequently.
Dr. Bob’s NCAA Tournament Best Bets are 56% over 28 years and have gotten better recently, going 122-93-3 (57%) the last 13 years and 47-31-1 (60%) the last 5 years. Designated ‘opinion’ games are 86-74-4 (54%) the last 5 years in the NCAA Tourney.
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