30.03.2004

**Mathematicians test simplified formula to predict winning baseball percentages**

Is your local Major League Baseball team better than its record suggests? Math researchers are considering alternatives to the Pythagorean Theorem of Baseball, devised by baseball statistician Bill James. Introduced in the 1980s, the "theorem" predicts the winning percentage of a baseball team based on how many runs the team scores--and how many runs it allows.

Websites, including ESPN’s, often include the Pythagorean prediction of the winning percentage of a team during the season. Fans compare the Pythagorean Theorem to the actual winning percentage, in an effort to determine if a team is under- or over-achieving.

When a team scores fewer runs than it allows, the Pythagorean model predicts that the team should have a losing record. For the 2001 season, the New York Mets allowed more runs than they scored and had a winning record; they did much better than the Pythagorean model predicted. So they can be considered an overachieving team. Because the Colorado Rockies scored more runs than they allowed but had a losing record, they were possibly an underachieving team.

Now, Michael Jones and Linda Tappin of Montclair State University in New Jersey have devised mathematically simpler alternatives to the Pythagorean Theorem of Baseball.

To predict the winning percentage of a team, one new model simply uses a little addition, subtraction, and multiplication. It starts with the total runs scored by the team in all its games (Rs), and subtracts the runs it allows (Ra), and then multiplies it by a number called "beta" (B) which is chosen to produce the best results. For the 1969-2003 seasons, the optimal values of B range from 0.00053 to 0.00078, with an average of 0.00065.

Adding 0.5 to the result gives the predicted winning percentage of the team. The resulting formula looks like this:

The estimated winning percentage, P = 0.5 + B*(Rs-Ra)

Because they only use addition, multiplication, and subtraction, these formulas are known as "linear functions"-the simplest kind of equations in mathematics.

In contrast, the original Pythagorean Theorem of Baseball is more complex. It uses exponents: Runs scored and runs allowed are squared-raised to the second power. The resulting formula is: P=[Rs2/(Ra2+Rs2)]

The equation gets its name because of its similarity to the Pythagorean Theorem in geometry, which relates the lengths of the sides in a right triangle as a2 + b2=c2, where a and b are the shorter sides and c is the longest side (the hypotenuse).

Because the Pythagorean theorems use exponents, these formulas are "nonlinear" equations, which are generally more complex than linear formulas.

So was the original Pythagorean Equation of Baseball needlessly complicated? Does the linear equation do just as good a job?

For the baseball seasons between 1969-2003 the linear formula works almost as well in its predictions as the original Pythagorean theorem, Jones and Tappin reported at this winter’s Joint Mathematics Meetings in Phoenix. The one real exception is the 1981 season when there was a baseball strike.

While Tappin and Jones have only analyzed whole seasons with their new formula, they are exploring how well it works for seasons-in-progress. If their formula meets with continued success, you may soon find it on your favorite sports website.

Ben Stein | EurekAlert!

Further information:

http://www.aip.org/

New NASA study improves search for habitable worlds

20.10.2017 | NASA/Goddard Space Flight Center

Physics boosts artificial intelligence methods

19.10.2017 | California Institute of Technology

University of Maryland researchers contribute to historic detection of gravitational waves and light created by event

On August 17, 2017, at 12:41:04 UTC, scientists made the first direct observation of a merger between two neutron stars--the dense, collapsed cores that remain...

Seven new papers describe the first-ever detection of light from a gravitational wave source. The event, caused by two neutron stars colliding and merging together, was dubbed GW170817 because it sent ripples through space-time that reached Earth on 2017 August 17. Around the world, hundreds of excited astronomers mobilized quickly and were able to observe the event using numerous telescopes, providing a wealth of new data.

Previous detections of gravitational waves have all involved the merger of two black holes, a feat that won the 2017 Nobel Prize in Physics earlier this month....

Material defects in end products can quickly result in failures in many areas of industry, and have a massive impact on the safe use of their products. This is why, in the field of quality assurance, intelligent, nondestructive sensor systems play a key role. They allow testing components and parts in a rapid and cost-efficient manner without destroying the actual product or changing its surface. Experts from the Fraunhofer IZFP in Saarbrücken will be presenting two exhibits at the Blechexpo in Stuttgart from 7–10 November 2017 that allow fast, reliable, and automated characterization of materials and detection of defects (Hall 5, Booth 5306).

When quality testing uses time-consuming destructive test methods, it can result in enormous costs due to damaging or destroying the products. And given that...

Using a new cooling technique MPQ scientists succeed at observing collisions in a dense beam of cold and slow dipolar molecules.

How do chemical reactions proceed at extremely low temperatures? The answer requires the investigation of molecular samples that are cold, dense, and slow at...

Scientists from the Max Planck Institute of Quantum Optics, using high precision laser spectroscopy of atomic hydrogen, confirm the surprisingly small value of the proton radius determined from muonic hydrogen.

It was one of the breakthroughs of the year 2010: Laser spectroscopy of muonic hydrogen resulted in a value for the proton charge radius that was significantly...

Anzeige

Anzeige

Event News

ASEAN Member States discuss the future role of renewable energy

17.10.2017 | Event News

World Health Summit 2017: International experts set the course for the future of Global Health

10.10.2017 | Event News

Climate Engineering Conference 2017 Opens in Berlin

10.10.2017 | Event News

Latest News

Terahertz spectroscopy goes nano

20.10.2017 | Information Technology

Strange but true: Turning a material upside down can sometimes make it softer

20.10.2017 | Materials Sciences

NRL clarifies valley polarization for electronic and optoelectronic technologies

20.10.2017 | Interdisciplinary Research

VideoLinks

NASA | A Year in the Life of Earth's CO2

NASA Computer Model Provides a New Portrait of Carbon Dioxide

Black Holes Come to the Big Screen

The new movie "Interstellar" explores a longstanding fascination, but UA astrophysicists are using cutting-edge technology to go one better.

NASA's Swift Mission Observes Mega Flares from a Mini Star

NASA's Swift satellite detected the strongest, hottest, and longest-lasting sequence of stellar flares ever seen from a nearby red dwarf star.

NASA | Global Hawks Soar into Storms

NASA's airborne Hurricane and Severe Storm Sentinel or HS3 mission, will revisit the Atlantic Ocean for the third year in a row.

Baffin Island - Disappearing ice caps

Giff Miller, geologist and paleoclima-tologist, is walking the margins of melting glaciers on Baffin Island, Nunavut, Canada.

The Infrasound Network and how it works

The CTBTO uses infrasound stations to monitor the Earth mainly for atmospheric explosions.

B2B-VideoLinks

Special emitters for optimal energy efficiency

Heraeus special emitters promote both: energy production and energy saving

Gascatalytical infrared heat ...

... can save time, space and money by drying coatings with infrared heat

Efficient reduction of odour and grease with Heraeus UV solutions

Kitchen exhaust air cleaning with UV in gastronomy

Drying and curing of paints on glass and ceramics

Bright and brilliant paints on glass and ceramics require safe solutions for drying and curing.

JULABO World of Temperature

Explore the World of Temperature with JULABO - Superior Temperature Technology for a Better Life.

Acoustic Wave Separation: How It Works

In this animated video, see how Acoustic Wave Separation technology works in full detail.

Infrared Heat for printed electronics

Drying and sintering of printed electronics by specialty light sources from Heraeus

All about Data Logger, how to use

Wolfgang Rudolph explains: all information worth knowing about the data logger and the practical test by means of a drone