# Sports Leagues Not Efficiently Structured, Scientists Say

##### Aug 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.

## Related Stories

#### Review: Can you really save money by cutting the cord?

Mar 18, 2015

There are more ways to watch television online than ever. Even HBO and ESPN—two channels often cited as reasons people keep expensive cable or satellite TV packages—will be available for streaming on ...

#### Refs cheer new high-def replay system for NCAA tournaments

Mar 17, 2015

The NCAA is going all in on high-def video reviews during March Madness.

#### Coming to a theater near you: esports

Mar 17, 2015

Competitive gaming is ready for its close-up.

Mar 10, 2015

Each year, millions of people lose billions of dollars in NCAA March Madness basketball pools. Still, most return the following year for another pummeling.

#### Being at the big game—from the comfort of your own home

Mar 06, 2015

Imagine sitting on Centre Court at Wimbledon, ringside at a Las Vegas heavyweight boxing title fight, or amongst the VIPs at an NBA game—all from the comfort of your own home.

#### Professor takes madness out of the month

Mar 05, 2015

With the NCAA Men's and Women's Basketballl Tournaments tipping off soon, brackets and bubble-busters are reaching a fever pitch. Dr. Jay Coleman, the Richard deRaismes Kip Professor of Operations Management and Quantitative ...

## Recommended for you

#### Femto-snapshots of reaction kinetics: Bonding behavior of iron pentacarbonyl experimentally decoded

10 hours ago

Using quantum chemical calculations, they were successful in interpreting the data and obtaining a detailed picture of the intermediates and reaction kinetics. The work, which has now been published in Nature, could ...

#### Detailed experiments reveal the operational parameters for a promising thermo-magnetic data-storage technology

13 hours ago

The mechanics and dynamics of heat-assisted magnetic recording (HAMR) are now better understood thanks to work by A*STAR and the National University of Singapore. The experimental study will help scientists ...

#### CERN researchers confirm existence of the Force

16 hours ago

Researchers at the Large Hadron Collider just recently started testing the accelerator for running at the higher energy of 13 TeV, and already they have found new insights into the fundamental structure ...

#### World's largest particle collider ready to restart in 'days'

16 hours ago

Physicists have fixed a short-circuit at the world's largest proton smasher, making the particle-hunting machine ready for a restart "within days' time" after a two-year shutdown.

#### Soft, energy-efficient robotic wings

Mar 31, 2015

Dielectric elastomers are novel materials for making actuators or motors with soft and lightweight properties that can undergo large active deformations with high-energy conversion efficiencies. This has ...

#### Mist-collecting plants may bioinspire technology to help alleviate global water shortages

Mar 30, 2015

Plants living in arid, mountainous and humid regions of the planet often rely on their leaves to obtain the moisture they need for survival by pulling mist out of the air. But how exactly they manage this ...