# NCAA Tournament Pool: Leveling The Brackets

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

## Related Stories

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

March 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, ignore a team's ...

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

March 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 Sweet Sixteen round ...

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

March 4, 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 pool.

#### Web bookies not worried by NCAA underdogs

March 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

December 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, called the ...

#### Behavior Changes Linked to March Madness

March 9, 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 appears to, at ...

## Recommended for you

#### Study sheds new light on ancient human-turkey relationship

January 17, 2018

For the first time, research has uncovered the origins of the earliest domestic turkeys in ancient Mexico. The study also suggests turkeys weren't only prized for their meat—with demand for the birds soaring with the Mayans ...

#### Ancient DNA results end 4,000-year-old Egyptian mummy mystery

January 16, 2018

Using 'next generation' DNA sequencing scientists have found that the famous 'Two Brothers' mummies of the Manchester Museum have different fathers so are, in fact, half-brothers.

#### Want people to work together? Familiarity, ability to pick partners could be key

January 16, 2018

The key to getting people to work together effectively could be giving them the flexibility to choose their collaborators and the comfort of working with established contacts, new research suggests.

#### Communication methods do not work equally across diverse teams

January 16, 2018

More recent thought on how to reach consensus among members of diverse teams for the best outcome has been to use text rather than face-to-face communication, but new research from the University of Michigan shows it's not ...

#### Lifting barriers to citizenship for low-income immigrants

January 15, 2018

Taking the Oath of Allegiance at a naturalization ceremony is an emotional moment for many immigrants, and for good reason: it is the culmination of an often arduous process and many years of striving. Citizenship also opens ...

#### Tiny dinosaur may have dazzled mates with rainbow ruff and a bony crest

January 15, 2018

Ancient dinosaurs were adorned in some amazing ways, from the horns of the triceratops to the plates and spikes of the stegosaurus. A newly discovered, bird-like dinosaur fossil from China contains evidence that could add ...