Forum for Science, Industry and Business

Sponsored by:     3M 
Search our Site:

 

Streamlining the ’pythagorean theorem of baseball’

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/

More articles from Physics and Astronomy:

nachricht UNLV study unlocks clues to how planets form
13.12.2018 | University of Nevada, Las Vegas

nachricht Unprecedented Views of the Birth of Planets
13.12.2018 | Universität Heidelberg

All articles from Physics and Astronomy >>>

The most recent press releases about innovation >>>

Die letzten 5 Focus-News des innovations-reports im Überblick:

Im Focus: An energy-efficient way to stay warm: Sew high-tech heating patches to your clothes

Personal patches could reduce energy waste in buildings, Rutgers-led study says

What if, instead of turning up the thermostat, you could warm up with high-tech, flexible patches sewn into your clothes - while significantly reducing your...

Im Focus: Lethal combination: Drug cocktail turns off the juice to cancer cells

A widely used diabetes medication combined with an antihypertensive drug specifically inhibits tumor growth – this was discovered by researchers from the University of Basel’s Biozentrum two years ago. In a follow-up study, recently published in “Cell Reports”, the scientists report that this drug cocktail induces cancer cell death by switching off their energy supply.

The widely used anti-diabetes drug metformin not only reduces blood sugar but also has an anti-cancer effect. However, the metformin dose commonly used in the...

Im Focus: New Foldable Drone Flies through Narrow Holes in Rescue Missions

A research team from the University of Zurich has developed a new drone that can retract its propeller arms in flight and make itself small to fit through narrow gaps and holes. This is particularly useful when searching for victims of natural disasters.

Inspecting a damaged building after an earthquake or during a fire is exactly the kind of job that human rescuers would like drones to do for them. A flying...

Im Focus: Topological material switched off and on for the first time

Key advance for future topological transistors

Over the last decade, there has been much excitement about the discovery, recognised by the Nobel Prize in Physics only two years ago, that there are two types...

Im Focus: Researchers develop method to transfer entire 2D circuits to any smooth surface

What if a sensor sensing a thing could be part of the thing itself? Rice University engineers believe they have a two-dimensional solution to do just that.

Rice engineers led by materials scientists Pulickel Ajayan and Jun Lou have developed a method to make atom-flat sensors that seamlessly integrate with devices...

All Focus news of the innovation-report >>>

Anzeige

Anzeige

VideoLinks
Industry & Economy
Event News

ICTM Conference 2019: Digitization emerges as an engineering trend for turbomachinery construction

12.12.2018 | Event News

New Plastics Economy Investor Forum - Meeting Point for Innovations

10.12.2018 | Event News

EGU 2019 meeting: Media registration now open

06.12.2018 | Event News

 
Latest News

Magic number colloidal clusters

13.12.2018 | Life Sciences

UNLV study unlocks clues to how planets form

13.12.2018 | Physics and Astronomy

Live from the ocean research vessel Atlantis

13.12.2018 | Earth Sciences

VideoLinks
Science & Research
Overview of more VideoLinks >>>