# NCAA Tournament Pool: Leveling The Brackets

##### Mar 16, 2010 By Chris Gorski

That whirlwind of cubicle activity greeting office drones reporting to work this week is not a frenzy to finish last week's sales reports.

Those buzzing copiers and intensely-focused workers parked at their computers are in the midst of a country-wide cram session, completing brackets for the 2010 NCAA Men's Championship tournament pools. It's that rite of spring during which the field of 65 takes over the sports landscape.

Most pools use simple scoring systems that award one point for picking the winner of a first round matchup, 2 points for correctly choosing second round winners, then 4, 8, 16, and 32 for the subsequent rounds. However, those familiar systems consider each game in a given round equal, emphasizing the final few games. They may not sufficiently reward those whose picks display the most extensive basketball knowledge.

"That system makes a certain amount of sense if you assume that each of the two teams in any particular game has a 50 percent chance of winning," said Ted Gooley, a biostatistician at the Fred Hutchinson Cancer Research Center in Seattle.

Teams are assigned to four regions that are ranked and seeded from 1 - 16. The better teams are assigned what are called the higher seeds (numerically smaller, like 1 or 2), and the lower-ranked teams with lower seeds (the highest numbers). For the first round, the 1 seed plays the 16 seed, the 2 seed plays the 15 seed, and so on.

Gooley's love of the tournament -- and frustration with simple scoring systems -- led him to borrow a technique from his professional research called logistic regression. He used it to develop his alternative scoring system.

"Why not base a scoring system on essentially the likelihood that a particular seed wins a particular game?" said Gooley. "There are clearly many games in the tournament that are far from a 50-50 proposition."

Gooley's system analyzes each NCAA Men's Basketball tournament from 1985 to 2009 and determines the probability of a particular seed winning a particular game. He found that the higher-seeded team has won 75 percent of all games.

"The way I would assign the points would be 1 divided by 25 percent for the lower seeded team, or 4 points, and for the higher seeded team, you take 1 divided by 0.75, which is 1.33 points," said Gooley. "I wanted a little motivation for people to pick upsets, which always happen."

The mathematics is a little more complicated than this, because Gooley's model looks at each possible match up, how often it has occurred, and creates additional terms to provide the best fit of the model to the historical data. For example, a 13 seed team could play a 3 seed in a regional final, but several unlikely events would have to happen. The 10 seed differential is also a rarity, but there have been plenty of games between teams 9 and 11 seeds apart. By smoothing the data between those two points, Gooley formed an estimate of appropriate point values.

Gooley also found that his model improved if he considered not just the difference between seeds, but also what the highest seed was, because a 1 seed team has been more likely to beat a 5 seed team than a 7 seed team has been to beat an 11 seed.

Taking those components, Gooley developed a system that awards points for each seed winning each game. An 11 seed team that reached the Final Four -- like George Mason University did in 2006 -- would earn 170 points for the regional final win. But that has only happened twice in 25 years.

That's a lot of points, and more than the entrants that have won the last three pools Gooley organized with this system. The rationalization is that someone with the foresight to correctly predict that rare event should win. He designed the system that given an infinite number of tournaments, the average score for the brackets should be around 63 points, or 1 point for each game.

There's math in those simple systems, too. Tim Chartier, a mathematician at Davidson College in N.C., has developed his own mathematical methods for predicting tournament outcomes, one of which beat out 97 percent of the 4.6 million entrants in ESPN's Tournament Challenge last year. He developed a ranking system that uses regular season game scores to assess the relative quality of teams. If the team he ranks 43 were scheduled to face the team ranked 45, no matter what the seeds, he picks the team at 43.

As a fan of basketball and math, he appreciates Gooley's efforts. "For true sports analysts and people who really look carefully I do see it as a really intriguing system," said Chartier.

He was especially interested to know if there were people who were able to consistently outperform the mean of 63 points, which would indicate some sort of advanced basketball knowledge, or exceptionally advanced luck.

"I love what one of my friends said. He said, 'look, you're trying to model and understand the behavior of 18 - 22 year old guys,'" said Chartier. "There's an unpredictable component."

Gooley feels that his system emphasizes basketball insight, that if a fan can identify that a certain team has a collection of players that will present difficulty to another, more accomplished, higher seeded team, they should be rewarded with more points than for automatically advancing a 1 seed over a 16. "I think this is the most logical way to assign points," he said.

Basketball fans need not worry that a massive changeover to this advanced scoring system would leave them unable to compete with the mathematically and statistically-inclined, however.

"Based on my performance in the last three pools, I think it's pretty clear my next area of work needs to be to focus on how to win pools other than how to score them," said Gooley.

Explore further: Optimising the future with mathematics

## Related Stories

#### Odds are, seedings don't matter after Sweet 16, professor says

Mar 16, 2009

For budding "bracketologists" busily weighing picks for their annual March Madness office pool, a University of Illinois professor has some advice on how to pick winners: In the later rounds of the tournament, ...

#### Expert: Bracket seedings irrelevant after Sweet Sixteen round

Mar 15, 2010

For the average college basketball fan looking for an edge in a March Madness office pool, a University of Illinois expert in statistics and data analysis has some advice on how to pick winners: After the ...

#### 'Match' Madness: Picking upsets a losing strategy

Mar 04, 2010

Soon Americans nationwide will begin poring over NCAA men's basketball tournament brackets in their annual attempt at glory -- and maybe even a little cash -- in winning the ubiquitous, albeit illegal, office ...

#### Web bookies not worried by NCAA underdogs

Mar 30, 2006

Although heavy underdog George Mason University, who once sat at 400-1 odds, is two victories away from winning the NCAA Basketball Tournament, it's not the team that has online betting sites most frightened.

#### New Algorithm Ranks Sports Teams like Google's PageRank

Dec 15, 2009

(PhysOrg.com) -- Sports fans may be interested in a new system that ranks NFL and college football teams in a simple, straightforward way, similar to how Google PageRank ranks webpages. The new sports algorithm, ...

Mar 09, 2010

(PhysOrg.com) -- Millions of Americans, including President Obama, fill out their “brackets” when the NCAA Tournament field is announced each March, but does that really affect their work? It certainly ...

## Recommended for you

#### Giving dangerous employees socialization, close supervision can avoid problems

7 hours ago

Two UT Arlington management professors argue that employers can prevent workplace violence by keeping dangerous employees positively engaged and closely supervising them to ensure they get the help they need.

12 hours ago

When it comes to shopping for gifts, we try to select things we think people both want and need. According to a new study in the Journal of Consumer Research, focusing too much on the gift recipient can lead to giving the gi ...

#### What's the upside of feeling too sad for chocolate?

12 hours ago

The instant gratification and the pleasure derived from consuming excessive chocolate and deep-fried foods can lead way to a double-edged sword of negative consequences ranging from weight gain to feelings of low self-esteem. ...

#### Study shows men and women both biased against women's math abilities

12 hours ago

(Phys.org) —A study conducted by business and economic researchers Ernesto Reuben, Paola Sapienza, and Luigi Zingales, has found that both men and women hold biases against women's math abilities. In their ...

#### Power play: Empowered consumers are more likely to switch brands

12 hours ago

As consumers, we form favorite brands and select services providers from a plethora of choices. According to a new study in the Journal of Consumer Research, how powerful we feel in our daily lives may impact our likelihood of swi ...

#### Study finds investors prefer good-looking male backed entrepreneurial ventures

12 hours ago

(Phys.org) —A study conducted by a team of researchers from Harvard, Wharton and MIT has revealed that venture capitalists prefer to back entrepreneurial opportunities when pitched by a man and that they ...

## More news stories

#### Study shows men and women both biased against women's math abilities

(Phys.org) —A study conducted by business and economic researchers Ernesto Reuben, Paola Sapienza, and Luigi Zingales, has found that both men and women hold biases against women's math abilities. In their ...

#### Study finds investors prefer good-looking male backed entrepreneurial ventures

(Phys.org) —A study conducted by a team of researchers from Harvard, Wharton and MIT has revealed that venture capitalists prefer to back entrepreneurial opportunities when pitched by a man and that they ...

#### Study suggests more than two hours of homework a night may be counterproductive

Education scholar Denise Pope has found that too much homework has negative effects on student well-being and behavioral engagement.

#### New analyses verify the use of fire by Peking Man

Zhoukoudian Locality 1 in northern China has been widely known for the discovery of the Middle Pleistocene human ancestor Homo erectus pekinensis ( known as Peking Man ) since the 1920s. By 1931, the suggestion ...

When it comes to shopping for gifts, we try to select things we think people both want and need. According to a new study in the Journal of Consumer Research, focusing too much on the gift recipient can lead to giving the gi ...

#### World's first 3-D acoustic cloaking device hides objects from sound

(Phys.org) —Using little more than a few perforated sheets of plastic and a staggering amount of number crunching, Duke engineers have demonstrated the world's first three-dimensional acoustic cloak. The ...

#### Long-term warming likely to be significant despite recent slowdown

A new NASA study shows Earth's climate likely will continue to warm during this century on track with previous estimates, despite the recent slowdown in the rate of global warming.

#### London launches hi-tech trial for pedestrian safety

(Phys.org) —London is trying out intelligent pedestrian technology to make crossing the road easier and safer. Announced earlier this month, the technology is said to be the first scheme of its kind in ...

#### Africa to spew half world's particle pollution by 2030, study says

With its exploding urban population burning ever more coal and wood, Africa could contribute as much as 55 percent of the world's particle pollutants by 2030, a study said Tuesday.

#### Malaysia Airlines mystery revives black-box debate

The search for Malaysia Airlines Flight 370 has rekindled a debate over the iconic "black box" flight recorder and whether it's time for aircraft to start live-streaming in-flight data in real time.