Featured Research

from universities, journals, and other organizations

Streamlining The 'Pythagorean Theorem Of Baseball'

Date:
March 30, 2004
Source:
American Institute Of Physics
Summary:
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.

College Park, MD (March 29, 2004) -- 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.

Related Articles


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.


Story Source:

The above story is based on materials provided by American Institute Of Physics. Note: Materials may be edited for content and length.


Cite This Page:

American Institute Of Physics. "Streamlining The 'Pythagorean Theorem Of Baseball'." ScienceDaily. ScienceDaily, 30 March 2004. <www.sciencedaily.com/releases/2004/03/040330090259.htm>.
American Institute Of Physics. (2004, March 30). Streamlining The 'Pythagorean Theorem Of Baseball'. ScienceDaily. Retrieved March 6, 2015 from www.sciencedaily.com/releases/2004/03/040330090259.htm
American Institute Of Physics. "Streamlining The 'Pythagorean Theorem Of Baseball'." ScienceDaily. www.sciencedaily.com/releases/2004/03/040330090259.htm (accessed March 6, 2015).

Share This


More From ScienceDaily



More Computers & Math News

Friday, March 6, 2015

Featured Research

from universities, journals, and other organizations


Featured Videos

from AP, Reuters, AFP, and other news services

Star Wars Inspires Mobile Holograms

Star Wars Inspires Mobile Holograms

Reuters - Business Video Online (Mar. 6, 2015) 3D holograms could soon be coming to your mobile phone. Inspired by the famous Princess Leia hologram from Star Wars, a U.S. company is showcasing a prototype display at the Mobile World Congress at Barcelona and says it could be used for real-time video calls. Ivor Bennett reports Video provided by Reuters
Powered by NewsLook.com
Game Makers Lured Into Virtual Worlds

Game Makers Lured Into Virtual Worlds

AFP (Mar. 6, 2015) Some 25,000 people have descended upon San Francisco to show off the latest technologies and video games at the Game Developers Conference. Developers here discuss the future of the industry. Duration: 02:20. Video provided by AFP
Powered by NewsLook.com
Star Wars-Inspired Prototype Creates Holographic Display

Star Wars-Inspired Prototype Creates Holographic Display

Reuters - Innovations Video Online (Mar. 5, 2015) A prototype holographic display named Leia - after the Star Wars princess who appeared in holographic form asking Obi-Wan Kenobu for help - is demonstrated at the Mobile World Congress in Barcelona. Matthew Stock reports. Video provided by Reuters
Powered by NewsLook.com
IKEA and Samsung Launch Embedded Wireless Charging Range

IKEA and Samsung Launch Embedded Wireless Charging Range

Reuters - Innovations Video Online (Mar. 5, 2015) Samsung and IKEA hope their new embedded wireless charging products, launched at Barcelona&apos;s Mobile World Congress, will tempt consumers eager for plugless power. Jim Drury reports. Video provided by Reuters
Powered by NewsLook.com

Search ScienceDaily

Number of stories in archives: 140,361

Find with keyword(s):
Enter a keyword or phrase to search ScienceDaily for related topics and research stories.

Save/Print:
Share:

Breaking News:

Strange & Offbeat Stories


Space & Time

Matter & Energy

Computers & Math

In Other News

... from NewsDaily.com

Science News

Health News

Environment News

Technology News



Save/Print:
Share:

Free Subscriptions


Get the latest science news with ScienceDaily's free email newsletters, updated daily and weekly. Or view hourly updated newsfeeds in your RSS reader:

Get Social & Mobile


Keep up to date with the latest news from ScienceDaily via social networks and mobile apps:

Have Feedback?


Tell us what you think of ScienceDaily -- we welcome both positive and negative comments. Have any problems using the site? Questions?
Mobile: iPhone Android Web
Follow: Facebook Twitter Google+
Subscribe: RSS Feeds Email Newsletters
Latest Headlines Health & Medicine Mind & Brain Space & Time Matter & Energy Computers & Math Plants & Animals Earth & Climate Fossils & Ruins