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Collegiate Pythagorean Expectation

Bill James invented the Pythagorean expectation formula as a means to estimate the number of games a baseball team “should” have won in a given season or stretch of games as a function of their runs scored and runs allowed in that span.  While the formula only offers a small degree of predictive value, it can be used to calculate by how much a team is “over or under producing” in wins based on the runs that their runs scored and runs allowed.

The original formula produced by Bill James was derived empirically and based on Major League Baseball data.  The formula James produced was as follows:

Win ratio=(Runs Scored)2/((Runs Scored)2+(Runs Allowed)2)

The calculation for expected wins is then simply:

Expected Wins=Win Ratio x Games Played

Following James’s initial production and presentation of his formula to the sabermetrics community fellow sabermetrians questioned the use of 2 as the exponent.  Two formulas produced to determine the ‘ideal’ exponent were the Pythagenport formula and Pythagenpat formula.  The latter is both simpler and believed to be more accurate.  The Pythagenpat formula, originally created by David Smyth, is as follows:

Exponent=(Runs per Game).287

Using this formula and the 2010 runs per game data for each of the 292 Division 1 Men’s NCAA Baseball teams the ideal exponent for college baseball was found.  This exponent was determined to be approximately 2.131.  This produced the expectancy formula of :

Win ratio=(Runs Scored)2.131/((Runs Scored)2.131+(Runs Allowed)2.131)

Using this formula it was calculated that over the past five seasons, the Virginia Tech Baseball team underperformed by approximately 1.60 wins in the 138 games played in those five seasons. This formula can also be used in conjunction with a run expectancy table and play-by-play data in order to hypothesize regarding how many wins a team “should” have gotten had it employed a different strategy, i.e., made different bunt decisions, steal decisions, etc.

It is also worth nothing that the 2.131 exponent is higher than more commonly used exponents. A widely accepted value for the MLB is 1.82. The higher exponent reflects the fact that many more runs are scored in the college game.

Beyond Batting Average — Lee Panas [Review]

Lee Panas generously donated a copy of his book Beyond Batting Average to the Sabermetric Society at Virginia Tech. What follows is a review by me, Bryce.

Brandeis University researcher Lee Panas has written the primer on advanced baseball statistics that I so badly needed when I began studying the sport seriously this summer. As many readers will know, websites such as FanGraphs and Baseball Prospectus do have glossaries but they often lack adequate explanations or are incomplete. There are extraordinarily useful websites such as Sabermetrics Library but these are difficult for the Sabermetrics Newbie to find. Even popular books such as Baseball Between the Numbers and The New Historical Baseball Abstract either lack lucid explanations of sabermetric ratings or do not treat them deeply enough or are not organized in a useful manner. Others, such as The Book, are too specialized for the casual fan.

Panas’s book, on the other hand, does an excellent job treading the territory between superficial and deep treatment of the major sabermetric topics of the day, and it arranges those treatments in quite a clever way. Beginning with a brief history of the development of sabermetrics, starting with Alexander Cartwright and Henry Chadwick and ending with Bill James and Moneyball, Panas then reminds us that the goal of baseball is to score more runs than the other team, something that is easily forgotten by many amateur analysts. After giving us the Big Picture, Panas slowly moves from basic hitting to advanced hitting statistics, repeating the process for pitching, then for defense, wrapping things up with contextual considerations and total player contribution metrics (so you can finally understand what that WAR row on ESPN means). In clearly expressed language, Panas reminds shows us the many ways in which baseball players contribute to helping their teams win. The result is an accessible and insightful read.

There are, however, some shortcomings. I would have preferred a “mathematical” appendix including explicit formulas for the metrics mentioned and some relevant explanation. I would have also liked a comprehensive glossary with definitions for easy reference. The book also has the appearance of a children’s coloring book and the title sounds a bit too much like Baseball Between the Numbers for my taste. A small paperback with slick cover design and a title like Sabermetrics for the Practical Man would make this book instantly more attractive, as would removing Curtis Granderson from the cover and replacing him with someone a bit more relevant—Kevin Youkilis, perhaps?

That said, what is in the book deserves to be there. What Panas does best is explaining the meaning of the various statistics, showing how they relate to one another, and defending the older, more mainstream statistics such as ERA and batting average on the grounds that they do tell us something. Over and over again he emphasizes that the reader understand what a statistic means and that, nearly always, there is not one single stat that tells the whole story, not even WAR; evaluating players is a complicated and evolving task. The completeness of the book, however, is its primary strength: if you patiently read this Beyond Batting Average—which, at 142 pages filled with graphs and tables, should not take long—you will be up to speed on the modern analysis of the game. As Panas writes in the introduction, “My goal is to explain the new world of baseball statistics in a way that any knowledgeable and curious baseball fan will comprehend.” Beyond Batting Average accomplishes that goal.

Final Meeting Tonight!

In Squires 217 at 6 p.m. We will be starting some serious work for the Tech baseball team. Please stop by if you want to help.


Article on Adam Dunn Featured on Baseball Think Factory

I wrote an article on Adam Dunn for The Nats Blog today that was featured on Baseball Think Factory, one of the best sabermetrics sites on the web. (Someone even called me a “jackass” in the comments section!)

The article discusses Adam Dunn’s new swing-happy approach to the plate in ’10 as well as lots of other boring things like batting average, walk rates, strikeout rates, regression, and sample sizes.

Anyway, the point of this post is to encourage you to get writing. If it’s quality stuff, it will get noticed.

(Also, my post was listed just above an article by Dave Cameron on the Baseball Think Factory list–Dave Cameron being the guy from FanGraphs who came to speak two weeks ago. Take that, Dave Cameron.)

FanGraphs Talk: Write-Up and Video

This week, David Appelman, founder of FanGraphs, and Dave Cameron, full-time writer for FanGraphs, visited Virginia Tech for a panel discussion on careers in baseball. The guys themselves were awesome—very friendly and laid back. They also were quite encouraging as far as the various projects the Sabermetrics Society at Virginia Tech was working on and they did a great job fielding the questions I offered in my impromptu role as panel facilitator for our careers in baseball event.

Despite my glowing introduction, however, the event took on somewhat of a pessimistic tone. Again and again it was emphasized that a job in an MLB front office is not exactly ideal. It requires a huge amount of work and commands a low level of pay. More attractive are jobs writing about baseball, but here the guys were also pessimistic. Essentially, they argued, there are not that many jobs available for writing about the game, so getting paid to do so is difficult. Even on the issue of press passes, which teams are making more available to bloggers than ever before, the guys were downers, stating that sitting in the press box isn’t as fun as you might think.

But, even with all the negativity, the talk was ultimately very positive. It seems that if you possess skills such as computer programming, good statistical chops, a penchant for hard work, strong writing abilities, and, perhaps most important, creativity in terms of getting a team interested, landing an MLB job is very possible, even in the face of tough competition. And there are enough success stories, of guys landing jobs or getting rapidly promoted, to balance out the bad ones. There are also many jobs in baseball outside of the MLB front office: in marketing—ticket sales seem particularly important these days— as a lawyer, or at a variety of positions throughout the minors leagues. And once you are within the MLB system, getting a top job becomes a lot easier.

As for writing about baseball, there are actually a surprising amount of jobs for baseball writers out there; FanGraphs employs many part-time writers, SB Nation is a great starting place for potential writers, ESPN and others are constantly looking for help, and there are certainly a number of traditional writing positions out there at newspapers and other media outlets. Perhaps more relevant, however, is the changing face of baseball writing. It is no secret that newspapers are rapidly losing their importance in the world of media. It would not be surprising to see bloggers take a bigger and more legitimate role in covering baseball in the very near future.

Indeed, the dynamism of the baseball writing industry seems to be part of a larger trend in the baseball world. Though at the moment working for an MLB team may not seem particularly attractive, it is likely with the increasing importance of statistics and the proliferation of computer skills amongst young people, that teams may not be able to afford paying their employees so little for much longer; the most talented workers can simply begin contracting their skills out like people such as Tom Tango already do. It will be interesting to see how dramatic the changes in the near future will be—if they’re anything like the extreme changes in the seven years since Moneyball came out, then things should be looking up.

Below is a link to a video of the talk:

David Appelman and Dave Cameron at Virginia Tech from Bryce Wilson Stucki on Vimeo.

Interested in Writing About the Nationals?

Are you interested in writing about the Nationals for a well-known Nationals blog? Can you produce regular content with a statistical bent? Are you intrigued by the idea of getting press passes for Nationals games next year?

If you are interested in writing for The Nats Blog, send Will an e-mail at

Mathematica Sabermetrics Notebook

I’ve added a link to a Mathematica notebook under the “Member Work” and “Educational” sections. The notebook contains various sabermetric formulas, a dynamic interface for computing the Bill James Pythagorean Theorem, and short explanations.

I want the notebook to contain as much sabermetrics knowledge as possible, so I encourage you to download it, add to it, and make it available for free to all who are interested in it.

Mathematica is great software, is fairly easy to learn, and is available for free to all Virginia Tech students (which saves you several hundred dollars). You can download Mathematica and activate it by visiting this page and clicking on the “Network Software” link under the “Ordering Information” header.

FanGraphs is Hiring

FanGraphs is looking for part-time, paid writers.

David Appelman and Dave Cameron (two full-time employees of FanGraphs) were here on Tuesday and gave a great talk about careers in baseball. It seems like working for FanGraphs would be a great start.


David Appelman and Dave Cameron to Speak at Virginia Tech

On November 9th, David Appelman and Dave Cameron–both of–will be coming to Virginia Tech. The event will be held in Squires 345 from 7:00-8:30 p.m. The event will feature brief talks on careers in/making money from baseball. After the talks there will be a panel discussion of baseball-related questions. The tone will be informal, so please come relaxed and ready to enjoy yourself!

There will also be a trip downtown after the event.


See you then! (For questions contact Bryce at


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