If you have any ideas for topics, please email me. Thanks,Stan!
Posted By Dr. Stan, the Stats Man

For the fifth consecutive year, I attended the Joint Mathematical Meeting of the Mathematics Association of America (the MAA) and the American Mathematical Society (the AMS). This year the meeting was in San Diego from January 7 through January 10. This meeting is the most important meeting for both these organizations. At this joint meeting, universities and industries hire new PH.D Mathematicians. In addition, at this joint meeting, mathematicians present their new research under specific topics. My presentation was under the topic “Sports and Math.” The title of my presentation was New Theorems to Predict Winning Percentages and Compare Parity in the MLB, NBA, and NFL. You can read about my research by Googling “Stanley Rothman and the Pythagorean Theorem of Baseball.” This research is described on the website www.baseball-reference.com.

Other sample presentations on Sports and Math included:

Predictive Modeling and Analysis of Golf and Softball Teams Using Linear Algebra.

Statistical Modeling of a Mercy Rule in College Football to Reduce Major Injuries,

,A Search for Champion Boxers,

Modeling and simulation of a bicycle race,

What can a jump tell us about a pitcher? 

The convention is also a time for reconnecting with former students, graduate school friends, colleagues, and family.

For convention pictures, check out my Facebook Page: 





Posted By Dr. Stan, the Stats Man

Bill James, the Father of Sabermetrics,  introduced his ”Pythagorean Theorem of Baseball”.  His theorem provides a formula to predict a team’s winning percentage (W%)  using the runs scored (RS) and runs allowed (RA) by the team for a season.  Sabermetrics uses mathematics (especially Statistics) to make objective baseball decisions. The Pythagorean Theorem of Baseball states: W% = (RS)2 / [(RS)2 + (RA)2]. Like most baseball statistics the more games a team plays the closer the predicted W% comes to the actual season’s winning percentage. For those of you who have my book “Sandlot Stats: Learning Statistics with Baseball” pages 164-168 discusses this theorem.

My latest research done with a junior math major Alex Everett introduces what I call the “Linear Theorem of Baseball.” The Linear Theorem states W% =.000683*(RS – RA) + .50. In a paper to be published, I show that my Linear Theorem and James’ Pythagorean Theorem are both successful predictors of a team’s season winning percentage for the years 1901 to 2013.

The data in the table below provides the actual standings and standings calculated by my Linear Theorem for all games played on or before August 30th, 2014.

Assuming the season ended on Aug 30, these would be the playoff results. In the AL, Baltimore wins the East by either of the two standings. Detroit and Kansas City would be tied by the actual standings and Detroit would win by the Linear Theorem standings. The LA Angels and Oakland would change places with LA winning by the actual standings. The two wild card teams by the actual standings would be Oakland and either Detroit or Kansas City (which ever lost the tie-breaker). By the Linear Theorem the two wild card teams would be the LA Angels and Seattle.

In the NL, the same three teams would be the divisional winners by both standings. In either case San Francisco would be one of the two wild card teams. St Louis would be the second wild card team by the actual standings and Atlanta would be the second wild card team by the Linear Theorem.

Of the two standings, I would choose the standings given by the Linear Theorem to predict the final playoff teams. Looking at the AL East we see that the Yankees had an actual PCT of 0.522 but dropped to a PCT of 0.482 by the Linear Theorem. What can account for this change? This tells me the Yankees have done very well in close games and part of their success can be attributed to their manager. The same argument can be given for Baltimore.  The other New York team had a different result. For the Mets the actual PCT of 0.463 increased to 0.490 when applying the Linear Theorem. This reflects negatively on the Mets manager.  It turns out in 1-run games the Yankees were 21-18, Baltimore was 27-19, the Mets were 21-26. Miami has the best 1-run record at 32-20 which helps to explain its better PCT by the actual standings. 

Predicting MLB Standings

Posted By Dr. Stan, the Stats Man

Bill James introduced his formula for predicting a team’s expected winning percentage (Expected W%) for a season. The formula is Expected W% = (Runs Scored)2 / [(Runs Scored)2 + (Runs Allowed)2] and is called the Pythagorean Theorem of Baseball.  Bill James’s rationale for his theorem was that the number of runs a team scored (RS) compared to the number of runs allowed (RA) is a better indication of a team’s performance than their actual win-loss record. Of course, this reasoning is the antithesis of Bill Parcells’ quotation “You are what your win-loss record says you are.” Let’s say a team is 45-37 at midseason but based on James’ formula their Expected W% was at or below .500. It might be predicted that as the season moves toward the end their win-loss record will also move in the wrong direction.

My current research done with the help of Kevin Faggella, a math major at QU, introduces a new alternative formula to Bill James’ formula to accomplish the same goal. My formula is Expected W% = .000683*(RS – RA) + .500 and is called the Linear Theorem of Baseball. This formula is developed by applying the statistical techniques of linear regression and correlation analysis to the sample of MLB years 1998-2012. For those interested in learning these important mathematical tools and seeing the derivation of these theorems go to Chapter 5 of Sandlot Stats. In fact, my Expected W% formula would have correctly predicted the fate of the 2005 Washington Nationals. On July 5, 2005 the Washington Nationals were in first place with a record of 51-32 having RS = 340 and RA = 340. According to my formula their Expected W% = .000683*(RS – RA) + .500 = .500. This clearly sent a message about how their season would end. In fact, their final record for 2005 was 81-81 with RS = 639 and RA = 673.

Let us now look at the midpoint of the 2013 season and use my formula to make predictions on which teams will make the playoffs. Using 90 wins as the milestone for a team to either win their division or become a wild card, this equates to a final record of 90-72 and a winning percentage of (90/162) = .556. Using my formula, we have .556 = .000683*(RS – RA) + .5000. Solving we get (RS – RA) = 82 (rounded). Of course, one might choose 95 wins or some other amount instead of 90. Based on the closing records before the 2013 All-Star game and using my formula, I created a table of all the teams whose Expected W% = .000683*(RS – RA) + .500 is now greater than .500. I also included the Dodgers because they finished the first half winning 18 of their last 23 games.A New Sabermetrics Formula to Predict Postseason Teams

Using this table along with other data, these are my playoff predictions for 2013. First, the division winners are for the AL-East Boston, for the AL-Central Detroit, for the AL-West Oakland, for the NL-East Atlanta, for the NL-Central St Louis, and for NL-West the Dodgers. My two wild-card choices are for the AL Tampa Bay and Baltimore or Texas (a tossup) and for the NL Pittsburgh and Cincinnati. I pick Detroit for the AL-Conference winner and St. Louis for the NL-Conference winner. The last time Detroit won a World Series was in 1984 under the leadership of Sparky Anderson. Detroit’s current manager Jim Leyland managed the 2013 All-Star game to win and the AL won. Yes, with the help of home field advantage the Detroit Tigers will win the 2013 World Series. Sadly, I predict my beloved Yankees will be on vacation during the playoffs.




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