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 A tale of two pulsars' tails: Plumes offer geometry lessons to astronomers
18.01.2017 | Penn State

nachricht Studying fundamental particles in materials
17.01.2017 | Max-Planck-Institut für Struktur und Dynamik der Materie

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: How gut bacteria can make us ill

HZI researchers decipher infection mechanisms of Yersinia and immune responses of the host

Yersiniae cause severe intestinal infections. Studies using Yersinia pseudotuberculosis as a model organism aim to elucidate the infection mechanisms of these...

Im Focus: Interfacial Superconductivity: Magnetic and superconducting order revealed simultaneously

Researchers from the University of Hamburg in Germany, in collaboration with colleagues from the University of Aarhus in Denmark, have synthesized a new superconducting material by growing a few layers of an antiferromagnetic transition-metal chalcogenide on a bismuth-based topological insulator, both being non-superconducting materials.

While superconductivity and magnetism are generally believed to be mutually exclusive, surprisingly, in this new material, superconducting correlations...

Im Focus: Studying fundamental particles in materials

Laser-driving of semimetals allows creating novel quasiparticle states within condensed matter systems and switching between different states on ultrafast time scales

Studying properties of fundamental particles in condensed matter systems is a promising approach to quantum field theory. Quasiparticles offer the opportunity...

Im Focus: Designing Architecture with Solar Building Envelopes

Among the general public, solar thermal energy is currently associated with dark blue, rectangular collectors on building roofs. Technologies are needed for aesthetically high quality architecture which offer the architect more room for manoeuvre when it comes to low- and plus-energy buildings. With the “ArKol” project, researchers at Fraunhofer ISE together with partners are currently developing two façade collectors for solar thermal energy generation, which permit a high degree of design flexibility: a strip collector for opaque façade sections and a solar thermal blind for transparent sections. The current state of the two developments will be presented at the BAU 2017 trade fair.

As part of the “ArKol – development of architecturally highly integrated façade collectors with heat pipes” project, Fraunhofer ISE together with its partners...

Im Focus: How to inflate a hardened concrete shell with a weight of 80 t

At TU Wien, an alternative for resource intensive formwork for the construction of concrete domes was developed. It is now used in a test dome for the Austrian Federal Railways Infrastructure (ÖBB Infrastruktur).

Concrete shells are efficient structures, but not very resource efficient. The formwork for the construction of concrete domes alone requires a high amount of...

All Focus news of the innovation-report >>>

Anzeige

Anzeige

Event News

12V, 48V, high-voltage – trends in E/E automotive architecture

10.01.2017 | Event News

2nd Conference on Non-Textual Information on 10 and 11 May 2017 in Hannover

09.01.2017 | Event News

Nothing will happen without batteries making it happen!

05.01.2017 | Event News

 
Latest News

A big nano boost for solar cells

18.01.2017 | Power and Electrical Engineering

Glass's off-kilter harmonies

18.01.2017 | Materials Sciences

Toward a 'smart' patch that automatically delivers insulin when needed

18.01.2017 | Life Sciences

VideoLinks
B2B-VideoLinks
More VideoLinks >>>