Buttons won $10,000 in a 2010 Yahoo! Sports NCAA bracket contest. Buttons is a guinea pig.
The rodent’s owner, University of Tennessee MBA student Jake Johnson, was peeved at how often his sister won the family bracket contest. The sister didn’t watch basketball. Johnson figured that Buttons was more ignorant than his sister and therefore ought to do better. He read the team names to Buttons and picked the one that made the creature purr the most loudly. It worked. Johnson donated part of his winnings to a local guinea pig rescue shelter.
Buttons’s victory demonstrates that sports outcomes are more random than we think and that our ability to outguess the game is often an illusion. Another conclusion is that—with all that misplaced confidence—sports bettors are leaving a lot of money on the table, for someone else to scoop up. In dollars wagered, National Collegiate Athletic Association (NCAA) bracket betting rivals the Super Bowl.
Ever since Gilovich, Vallone, and Tversky’s 1985 paper, gamblers have been trying to mint a sports betting system out of the hot hand. In its literal meaning, the hot hand pertains to the sequence of baskets or misses by an individual player. You can’t normally bet on that. There are analogous beliefs about a team’s sequence of winning and losing games, in basketball or any other sport. These beliefs must drive many bracket picks.
To win the NCAA championship, a team must win six games in a row. By normal standards, that’s a hot streak. Of course, the tournament guarantees that exactly one team will achieve just that. Thinking about the needed streak of six wins prompts bettors to pick teams that they believe to be on a hot streak already. The sports media supplies an echo chamber for such thinking. Anytime a team wins a few games in a row, ESPN pundits dissect it and take it as a portent. “Will Duke go all the way? Only time will tell.” Most of these streaks are meaningless, with little or no predictive value going forward. The result is that bracket bettors are much too inclined to favor a few “hot” teams.
In an office contest, bettors pay a fixed entry fee and fill out a tournament diagram (bracket) predicting the winners of all sixty-seven games of the NCAA Men’s Division Basketball Championship. It’s a single-elimination tournament where the first loss disqualifies a team from further play. Winners are matched against fellow winners, funneling down to the one undefeated team that becomes the tournament champion.
Each bettor must submit a complete bracket before the tournament begins. The picks have to be logically consistent. You can’t predict that a team will be eliminated in one round and then have it reappear later on. Bettors score points for every winner they predict, and the bettor with the most points either wins the pot or gets the largest share of it. Note that predictions about losers are irrelevant. You might, for instance, predict that Ohio State will beat West Virginia in a second-round game. As long as Ohio State wins that game (against whomever), that counts as a correct prediction.
Many pools offer decreasing shares of the pot for runners-up. Ties are uncommon with most scoring systems. Perfect brackets—picking all the winners correctly—never happens. That’s because the number of possible game outcomes is 267, an utterly astronomical number exceeding a hundred million trillion. If everyone on earth picked a bracket randomly, the chance of anyone coming up with a perfect bracket would be something like 1 in 20 billion.
Most picks are far from random. Since 2011 the tournament begins with the “First Four” games between eight evenly matched teams. These games are hard to call. After that, the first round pits sixty-four teams in thirty-two games. In each of four divisions, the teams are ranked from best (“#1 seed”) to worst (“#16 seed”), based on their record. The #1 seed team always plays the #16 team. That’s an extremely lopsided contest, so much so that in twenty-five years, no #1 team has ever lost to a #16.
The #2 team plays the #15 team, the #3 team plays the #14, and so on, down to a near-even matchup between the #8 and #9 teams.
The bracket form almost always gives the seeding rank, so this is public information that the most casual player can use. Serious bettors have many other sources of information. There are prediction markets that handicap teams, and scores of experts post their picks on the Web. You’re free to copy them. There are clever apps that will pick your bracket for you. You can use them, and your coworkers may be using them against you. With all that allegedly good advice out there, is there a way to outguess an office pool in the digital age?
The first thing to realize is that there are three distinct goals in filling out a bracket:
• to predict as many winning teams as possible.
• to score as many points as possible.
• to win the pool.
Most bracketeers imagine these goals to be interchangeable. It’s true that a bracket genius who can predict all the winners will max out points and win the pool. But you’re not going to predict all the winners. Points are a fake currency that has value only insofar as it helps you win the pool. How many points you need depends on the competition. It’s like the joke about the hunter who puts on running shoes in bear country. “You think you can outrun a bear?” asks his friend.
“I don’t have to,” the hunter answers, “I just have to outrun you.”
The good news is that you can expect to pick about 58 percent of the winning teams in your bracket (around thirty-nine out of the sixty-seven games, on average). The bad news is, everyone else has about the same advantage.
Some think they can predict more accurately by listening to sports shows or copying brackets of the smartest experts. Good luck with that. That’s one message of a 2001 paper in Management Science by Edward H. Kaplan and Stanley J. Garstka of Yale. They wrote,
The authors of this paper have unsuccessfully participated in NCAA pools for more than a decade. Simply put, we decided that we would like to win once in a while.… Surely there must be better and worse strategies for garnering points in an office pool, but our experience suggested that we had only mastered the latter.
They compared several readily available sources of information: the seeding, the pre-March performance of the teams (converted into a “strength rating” to allow comparisons), the Las Vegas point spread, and such expert rating systems as Sagarin, Massey, and the Ratings Percentage Index. Their finding was that all the sources performed much better than random picking, and none was much better than any other. “Going with the seeds”—always picking the higher-ranked team—called games correctly 56 percent of the time (in four NCAA and NIT tournaments, 1998–1999). Sagarin was right 57 percent of the time, and picks based on the Vegas line or pre-March performance were each right 59 percent of the time. These differences were not statistically significant.
You may have discovered already that picking the seeds, or piggybacking on expert picks, is not the lazy man’s road to riches. There are several reasons for that. One is that the other players have similar sources of information. Another is the scoring formula. Almost all pools award successively more points to correct picks in later rounds. Typically, the points double with each round. A big bucket of points goes to anyone who picks the tournament winner. It’s rare to win unless you pick the tournament winner.
Some pools award extra points for calling an upset game, one where a lower-seeded team beats a higher-seeded team. The rationale is that upsets are harder to predict and therefore ought to be worth more points. This has consequences, some of them unintended. It can be best to pick an underdog because it’s an underdog and will be worth more points, should it beat the favorite.
A lot of math, computer science, and psychology professors are basketball fans. They have studied point-maximizing strategies extensively. One takeaway is that there is no one-size-fits-all strategy. The optimal point strategy depends on the granular details of the pool’s scoring and on how strongly the other bettors favor “hot” teams.
In their 2001 paper, Kaplan and Garstka looked at how four point-maximizing algorithms would have performed in an upset-bonus pool run by mathematician Erik Packard in 1998 and 1999. In both years a point-maximizing app would have won Packard’s tournament, had one been entered.
Computer scientist Tom Adams followed this up with an ambitious digital simulation. In effect, he simulated 100,000 Mad Marches in 100,000 parallel universes, using the estimated win probabilities that existed in this world, in 2001. Every possible match-up of Team A versus Team B was modeled as a biased coin. The estimated chance of A beating B equaled the chance of the coin coming up heads. The simulation essentially flipped that coin 100,000 times. The software tallied how well specific bracket entries would have fared in both of Packard’s pools.
The computer-generated picks all did very well. The top three brackets, all algorithm based, together won 21 percent of simulated tournaments. Someone betting the top-performing bracket could have expected to more than triple his money on average.
Adams also did a simulation of another pool that didn’t have upset bonuses. In this pool the humans beat the apps. The top six brackets were all by living, breathing fans.
Why the difference? All the computer entries picked Duke to win the tournament. Duke was the favorite, and Duke won. Common sense says you can’t go wrong by picking the winner. But this is a case where common sense is wrong.
Though Duke did win, any reasonable model would allow that this was not preordained. A freak loss, anywhere in the tournament, would have nixed Duke’s shot at the championship. All the expert models granted a substantial probability to Duke’s not winning. Adams’s simulation took that into account. Duke won in some of the simulated games and not in others.
The problem was that Duke was overbet. In general, pool players are too inclined to pick favorites. Harvard economist Andrew Metrick, who looked at twenty-four pools in cities from Boston to San Francisco, found that 78 percent of brackets picked one of the four #1 seed teams to win the tournament. But the record books show that these four teams win only about half the time.
This is partly a hot hand belief. A single-elimination tournament is like a pinball game, subject to a good deal of randomness. The teams that win tournaments are usually good and lucky. Fans underestimate the luck part. They suppose that the team’s recent performance is representative of its underlying talent, and that a regular-season hot streak will persist into March.
The preference for favorites also demonstrates a failure to understand bracket strategy. Look at what happened in Adams’s simulation. In the virtual games where Duke won, those who called it were competing with many others who had also picked Duke. That decreased the chance of any individual Duke-favoring bracket happening to be the one to score the most points. This is the same principle discussed earlier that applies to picks of popular lottery numbers.
The most successful brackets in Adams’s simulation were contrarian. They picked Stanford or Michigan State to win. Though the chance of this happening was less, when it did happen there was less competition. Contrarian brackets stood a greater chance of winning the pool.
Adams’s simulation also confirmed that the best strategy depends on the precise scoring formula. When a pool rewards players who pick upsets, that can override everything else. Though upset bonuses were intended to make the game more interesting, the average person is unable to factor them into a set of picks. Software prevails over humans, not because the software is better at predicting winners but because it’s able to optimize for the scoring system.
Pools with upset bonuses have therefore opened a gap between merely human and computer-aided players. Should your office pool have that kind of scoring, you’ll need to use an app. There are a number of good, free ones online. Make sure you pick one that lets you enter the details of the scoring formula (like Tom Adams’s Poologic.com).
Why doesn’t everyone use an app? When Poologic first came out, efficient-market types insisted it would be useful only for a couple of Marches. Then everybody would start using it. This hasn’t happened. “In spite of the publicity, Poologic gets only a few thousand hits per year,” Adams told me. The fact is that many players enjoy betting on teams they like. With a small office pool, there’s a fairly good chance you’ll be the only one using a point-maximizing app.
Let’s follow the money. A typical pool costs $10 to enter. Most pools have no commission (sometimes the pool manager reserves the right to submit a bracket without paying). You need to have an expectation of winning back your $10 to break even.
It’s impractical to figure your return from experience. March comes but once a year. In a big office, a bracket entry is like a lottery ticket. You may never win, as long as you work at the company. So Jarad B. Niemi, Bradley P. Carlin, and Jonathan M. Alexander estimated bettor returns from three years of a Chicago office pool they entered. They found that 60 percent of the submitted brackets were net money losers. But about 15 percent were good enough to double the player’s money. Even richer opportunities are out there. Metrick estimated that a bracket picking Arizona in 1993—an underbet team that did in fact lose—offered expected returns as high as 423 percent. A $10 bet would get you $52.30 on average, in a pool of 200. It’s hard to top those odds.
This and other profitable brackets were both probable (Arizona had a decent chance of winning the tournament) and contrarian (not too many were betting on Arizona). When the outcome deviates from the favorites, the winning bracket will be one that has predicted some upsets. This is true even when the scoring system doesn’t give extra points for upsets. As a result, the winning bracket will almost always be quirky. This is behind the folk wisdom that you need to challenge the experts; that people who don’t follow basketball beat fans; that guinea pigs beat humans, sometimes. The question is when to go rogue and by how much.
“People tend to pick upsets early and go conservative in the Final Four,” explained Bryan Clair, a Saint Louis University mathematician and avid player. “If you’re in a big pool, you need to flip-flop that: Go boring in early rounds, and slightly strange in the Final Four.”
I’ll describe a practical way to fill out a bracket for a small office pool.
1. Listen to the other bettors. You’ll probably hear plenty of hot hand magical thinking. Such-and-such a player or team is on a streak that is sure to continue. You should pay attention to this talk. You won’t learn who’s going to win but you will learn how your coworkers are going to bet.
With many pools, you can review the last year’s entries. This is informative, too, for most bettors don’t change their strategy or favorite teams much from year to year. If, for any reason, you’re not able to learn your coworkers’ picks, there are other sources of information. Yahoo!, ESPN, and other websites supply pick frequencies for the current year. While a website’s national data needs to be tailored to your office’s geographical loyalties, they give a first approximation of how your coworkers are filling out their brackets.
2. Get a printout or link to the exact scoring formula.
3. Go to Poologic or another good app. Enter your pool’s scoring formula. It will generate a point-maximizing bracket. You won’t be using it as is, but you will use it as a template to be customized.
4. Change the bracket’s tournament winner. The most favored team rarely has much of an advantage over other highly favored teams. The people who insist on picking the top team are overpaying for a small advantage.
The research suggests that the sweet spot for a tournament winner pick is the team ranked second to sixth overall. That would be the four #1 seed teams minus the favorite and the two best #2 seed teams.
Many bettors pick a team that’s close over one that’s far away. “I live in a Big Ten town, so as a rule, the Big Ten is overbet,” said Bradley Carlin, a biostatistician at the University of Minnesota. “Because everyone has seen a lot of Gopher games, they’ve seen Purdue, Indiana, Illinois. They’re thinking, ‘I saw them play the Gophers, and they were pretty good that day.’ ”
This is another example of how people think their limited experience is representative of an uncertain reality. Find the high-rated team that is most underbet in your office. You replace the app’s tournament winner with the moderately contrarian one applicable to your office. Then work backward, changing any app picks to be consistent with that champion.
5. An optional step is to switch a few other picks for close games—in each case going for the slight underdog. This will help to distinguish your bracket from someone who might have used the same app.
In most bracket pools there is no taboo against submitting more than one entry. You might want to play several brackets that differ only in the pick of the tournament winner. Apps can provide guidance here, too. Poologic has an ROI (Return on Investment) calculator that estimates the profitability of the various choices for tournament winner. You enter as much information as you know or can guess: how many people in your office are picking each team as champ, and the total number of brackets in the pool. The calculator guesstimates the likely return, in dollars and cents, for betting on each possible champ.
A team with a return of $1 would be a break-even bet. A wild bet on a low-seeded team might return a billionth of a cent. In general, only about four teams are judged to be profitable bets. Those betting just one bracket should pick the most profitable one. When submitting more than one, stick with the profitable bets.
It won’t come as a big surprise that some NCAA pools are hostile to app picks. Adams has many tales of harassment. In Chicago, Bradley Carlin won three out of five years. “The pool was disbanded and then reorganized, and he was uninvited to play.”
Another algorithmic player, New York Times editor Victor Mather, won a first, a third, and a fifth place over a six-year period, in a 250-player pool. He wrote Adams,
… Last year the pool organizer sent me an e-mail saying I was cheating by picking so many long shots!
Then this year’s pool contains the following note:
“The Board has discovered that some entrants in previous years have used a formula for trying to pick upsets. This runs counter to the spirit of the pool and the awarding of bonus points. The purpose of the pool is to pick winners of games and be rewarded by identifying unlikely victors. It is not to capitalize on a formula and gain an edge on entrants who are playing by the spirit of the rules. Therefore any entry deemed by the Board to be a ‘formula play’ will be rejected.”
Pool managers aren’t always quick to see the ramifications of the rules they make. Adams tells of one manager who decided—just for fun—to offer a substantial prize to the bracket that did the worst. Naturally, the worst-bracket winner was a guy who just bet all the worst seeds. The pool manager never saw that coming. He disqualified the worst-bracket winner for violating the spirit of the game.
I’ll leave it to you to decide whether you care to subject your coworkers to your superior bracket outguessing. Victor Mather offers these observations: “No matter how successful you are, few people will copy you. And you’re not likely to develop a reputation as a basketball oracle, either. Instead, if my experience is any guide, you’ll be viewed as a nut, or at best an absentminded professor, who seems to get awfully lucky in the pool every year.”
• Try to learn how other pool players are betting, or check last year’s brackets.
• Enter your pool’s scoring formula in a bracket app like Poologic.com. The app tells you the bracket most likely to win, but that is not necessarily the most profitable bet.
• Pick an underdog for tournament winner—a team ranked second to sixth overall that is not favored by other pool members. Make any necessary changes to the app’s bracket. In large pools you may want to pick another close underdog in the Final Four.