# Sports Leagues Not Efficiently Structured, Scientists Say

##### August 30, 2007 By Laura Mgrdichian feature

According to a pair of statistical physicists, sports leagues as they are typically set up – with each team playing an equal number of games and the one with the most wins declared league champion – too often allow a weak team to come out on top.

In the August 13 online edition of Physical Review E, Eli Ben-Naim and Nick Hengartner of Los Alamos National Laboratory suggest an alternate structure for league competition in which teams play in preliminary rounds consisting of a small number of games and then a final round played according to standard league format. As the rounds progress, the weaker teams are weeded out and the winner of the championship round is far more likely to actually be the strongest team.

“Current league format is an ineffective way of determining the best team,” Ben-Naim said to PhysOrg.com. “A more efficient and fair way to play leagues is to sequentially eliminate teams from the bottom up.”

The foundation underlying the inefficiency of leagues is that the outcome of a single competition is not predictable. For example, as Ben-Naim and Hengartner note in their paper, over the last 100 years in baseball lower-seeded teams have had an “astounding” 44 percent chance of defeating their better-ranked opponents.

“This inherent randomness has profound consequences in sports,” Ben-Naim said.

To understand how randomness affects the outcome of multiple competitions, he and Hengartner studied an idealized system with an arbitrary number of teams, denoted N, ranked from best to worst so that in each game there is a clear favorite and underdog. They calculate that in a standard league, the number of games needed to reach an efficiency of 70 percent – the best team winning the championship 70 percent of the time – can be approximated by N3. That means, for example, that a league with 20 teams would need to play about 203, or 8,000, games to reach 70 percent efficiency.

As this is obviously not practical, the scientists investigated the use of rounds to increase the likelihood that the most worthy team wins the league over a reasonable number of games.

Based on the rules of competition probability and randomness, they crafted a formula to determine the least number of games that would need to be played in the rounds structure to allow the best team to win as often as in the N3 case. The variables in their formula are the number of teams, N, and the number of rounds played, denoted k.

The formula predicts that in a league containing 10 teams, the N3 scenario of 1,000 games could be reduced more than 10-fold, down to about 63 games, by playing just one preliminary round before the championship playoffs. If two preliminary rounds were played, only about 26 games would be needed.

Ben-Naim and Hengartner ran three simulations based on their formula, corresponding to league sizes of 10, 100, and 1000 teams. The best team won 70 percent of the time and was among the top three 98 percent of the time. The rounds structure yields the same outcome but with far fewer games.

Citation: E. Ben-Naim and N. Hengartner, “Efficiency of competitions” Phys. Rev. E 76, 026106 (2007)

All rights reserved. This material may not be published, broadcast, rewritten or redistributed in whole or part without the express written permission of PhysOrg.com.

Explore further: Researcher finds sports events are surprisingly predictable

## Related Stories

#### Researcher finds sports events are surprisingly predictable

November 3, 2015

November 1 marked the end of Major League Baseball in 2015, as NBA basketball launched its 2015-2016 regular season on October 27. If you're following the games this year, you may want to watch for patterns predicted by recent ...

#### Smart helmets save lives, improve rides

November 6, 2015

As technological advancements enable people to run faster, ride farther and hit harder, experts are using sensors to collect data that could reduce head trauma incidents for football, hockey, cycling and other sports.

#### US startup challenges Japan to giant robot battle

November 16, 2015

They've been popularized in movies, television and video games, but giant fighting robots still haven't left the realm of science fiction. That will soon change.

#### Five awesome uses for drone technology

November 17, 2015

Interest in flying robot technology is skyrocketing, bringing a thrilling wave of novel uses for drones from saving lives to creating new entertainment.

#### Whatever your game, EverSport wants to stream it to you

October 16, 2015

USC football fans in London, Japanese soccer followers in Los Angeles and kickboxing enthusiasts around the globe: Despair no more!

#### Researchers reveal how NFL game outcomes affect stock returns of stadium sponsors

September 10, 2015

An examination of NFL stadium sponsorships and sponsors' stock returns finds that immediately following high-interest games, the stadium sponsoring companies celebrate or suffer their own financial wins or losses, depending ...

## Recommended for you

#### CERN collides heavy nuclei at new record high energy

November 25, 2015

The world's most powerful accelerator, the 27 km long Large Hadron Collider (LHC) operating at CERN in Geneva established collisions between lead nuclei, this morning, at the highest energies ever. The LHC has been colliding ...

#### Physicists set quantum record by using photons to carry messages from electrons almost 2 kilometers apart

November 25, 2015

Researchers from Stanford have advanced a long-standing problem in quantum physics – how to send "entangled" particles over long distances.

#### 'Material universe' yields surprising new particle

November 25, 2015

An international team of researchers has predicted the existence of a new type of particle called the type-II Weyl fermion in metallic materials. When subjected to a magnetic field, the materials containing the particle act ...

#### Exploring the physics of a chocolate fountain

November 24, 2015

A mathematics student has worked out the secrets of how chocolate behaves in a chocolate fountain, answering the age-old question of why the falling 'curtain' of chocolate surprisingly pulls inwards rather than going straight ...

#### Phenomenon could lead to more compact, tunable X-ray devices made of graphene

November 24, 2015

The most widely used technology for producing X-rays – used in everything from medical and dental imaging, to testing for cracks in industrial materials – has remained essentially the same for more than a century. But ...

#### Experiment suggests friction at root of shear force thickening

November 26, 2015

(Phys.org)—A combined team of researchers from Cornell University in the U.S. and the University of Edinburgh in the U.K. believes they may have settled the debate on the cause of shear force thickening in colloidal products. ...