MA331 Mathematical Modeling: The Mathematics and Physics of Baseball

ex3MTRF 6 G

John Rickert
Associate Professor of Mathematics

Office: G-215A, Crapo Hall
Phone: (812) 877-8473

Address:
Department of Mathematics
Rose-Hulman Institute of Technology
Terre Haute, IN 47803

e-mail: john.rickert@rose-hulman.edu

The Oral presentation schedule for the 10th week oral presentations is now available online. The schedule was modified Wednesday, Feb. 6.

At the beginning of class Tuesday, you should turn in a pitching rotation using the following rules:

You are putting together a pitching rotation that will be pitching in the Whirled Series. You want to put together a rotation that has the most expected wins in the seven games. Your four pitchers, labeled A,B,C,D, will pitch in this order: ABCDABC.

You are selecting the ability levels of your pitchers (are you going to try to have a consistent rotation or a star or two?). You will select the quality of each pitcher by listing the expected runs allowed for the pitchers subject to the following limitations:
I The cost of a pitcher expected to allow R runs per game is 10/(R-1) million dollars.
II You can spend no more that \$20 million
III No pitcher can have a runs total less than 1.

Examples of valid rotations: 3,3,3,3 (cost = 4 times (10/2)=20)
2,4,3.5,4.75 (cost =10 + (3 + 1/ 3) + 4+ (2+2/ 3)=20)

I’ll then run them off each other and see how well they do.
The summary is at pitrot.html. I am using the logistic equation with exponent 2, (the pythagorean projection) to calculate the expected winning probabilities. Some Maple code is also available at pitrot.html.

Several people have asked about the effect of a tailwind on the equations of motion. I’ve written a page which I hope will clarify some of the material discussed in class. If you still have questions, e-mail me.

In 2001, the Colorado Rockies earned run average at home was 6.12. On the road, their earned run average was 4.42.
I’ve made a small table showing the Rockies Runs per game at home and on the road.
The homework passed out Friday is online now. The homework is due Monday, February 4.
Your interim report is due Thursday, January 31.

The flyball file used in class Thursday, is now available online. On Friday, we’ll add some wind, and move to Denver.
On Tuesday, January 22, the class met at the wind tunnel. We generated voltage readings corresponding to drag at several different velocities. Your homework for Friday, January 25 is to use these to

  1. estimate the force on the baseball at the velocities tested
  2. estimate the drag coefficient at the velocities tested

The conversion factors discussed in class Monday and Tuesday are available at windtunnel.html.

The final revised project proposals were due by Tuesday, January 22.
Regarding a question asked in class on Monday: There is a website that has a video of a knuckleball, though it’s pretty difficult to see the unusual motion of the ball.
A cleaned up version of the Maple flyball.mws file is now online.

The final revised project proposals were due by Tuesday, January 22.
Typed preliminary project proposals were due Thursday, January 17.
The questions asked at the end of class Tuesday, January 15:
1. If the baseball is hit when it is three feet above the ground, how far away does it land if it lands uncaught?
2. Determine the angle of elevation, alpha, as seen be an outfielder. alpha will be a function of time.
We are assuming that we are playing in a vacuum. g is approximmately 32 ft/s/s. A typical velocity for a batted ball is 150 ft/s.

Statistical analysis homework problems will be in the file hwstat1.doc. These problems will be due by Thursday, January 17.
Data for the statistical analysis homework will be in the file hwstat.xls.
The binomial distribution example problems passed out Friday are avaialble on-line. Several of the “basic” statistics functions are defined in the Maple worksheet statintro.mws. An updated file containing the cumulative distribution functions as well: statintro2.mws.
An introduction to statistics.

Further Markov chain commands are available in the file batterup2.mws.

Excel commands that we have used:

=AVERAGE(B2:B31)
=STDEV(B2:B31)
=CORREL(B2:B31,C2:C31)
=LINEST(C2:C31,B2:B31,TRUE,TRUE)
=LINEST(E2:E31,B2:D31,TRUE,TRUE)

In Winter 2001-2, the mathematical modeling course will follow the theme “The Mathematics and Physics of Baseball”. The game of baseball provides a wide variety of questions answerable through use of standard mathematical techniques ,while the easy availability of data will allow us to design and test models related to these questions.
To attempt to answer some of these questions, we will study multiple regression, Markov chains, and elementary dynamics.

Among the questions that we will look at are:

  • Who was the “most valuable player” and did he win the MVP award?
  • Is it better to bunt or try for a hit with a runner on first, no outs and the team trailing by a run?
  • What is the best batting order?
  • What the difference between a game in Coors field and a game in Comerica Park?
  • What trajectory is followed by a baseball?
  • How easy is it to hit a 500 foot home run?
  • What happens when the bat meets the ball?
  • How much does a curve ball curve?

Other questions studied will include student generated questions raised in class. Students will be expected to complete a project studying some topic of interest to them.

The will be no required texts. Optional texts are

  • The Physics of Baseball, by Adair
  • Curve Ball: Baseball, Statistics, and the Role of Chance in the Game, Albert&Bennett

Other helpful resources include:

  • Total Baseball, Thorn &Palmer
  • Baseball Encyclopedia, Neht&Cohen
  • Sean Lahman’s Baseball archive
  • Project Retrosheet
  • John Skilton’s baseball links
  • Baseball-Reference.com
  • Clifford Blau’s baseball research page
  • Jim Furtado’s baseballstuff
  • American Statistical Association Sports Statistics page

    Grades weights will be
    Homework and quizzes: 60%
    Project : 40%

    The revised project schedule:

    
Preliminary proposal       Thursday, January 17        Week 6
Final Proposal             Tuesday, January 22        Week 7
Interim Report             Thursday, January 31       Week 8 
Oral Reports                                         Week 10
Final Written Report       Friday, February 15       Week 10

    A list of project ideas is on-line. Project Oral Presentation Schedule:

    Time Period Tuesday, Feb 12 Thursday, Feb 14 Friday, Feb 15
    12:40 – 12:52 Run prediction with Markov
    chains and Linear Regression
    Bye    		 “Close to Home” field advantage
    Huster, Barton, Balasundaram, Albert    		 Statistical Analysis of Run Distribution
    Brosmer, Kissel
    12:56-1:08 How the height of the Pitching Mound affects the play of baseball
    Whitaker, Shields, Forsyth, Bradley    		 MLB Attendance Trends
    Wells, McCue    		 Sweet spot of a baseball bat
    Sullivan, Schwarzmann, Laser, Chaille
    1:12-1:24 Fill out Course Evalautions Effect of Wind upon Runs Scored and Home Runs
    Self, Freihaut, Beverlin    		 Economic models
    Young, Stuchel, Birchall, Berglund

    Notes and Handouts from Dr. Broughton’s weeks:
    Notes

    Worksheets, Quizzes, and Projects

    Scripts

    Script Name Demo/Template/Utility/Review Purpose
    binom.mws demo/template binomial probabilities
    gambruin.mws demo/template script for “show and tell” on gamblers ruin problem
    gambruin.m demo/template Matlab version of the above
    eigplot.m utility Matlab script for plotting the eigenvalues of a matrix
    batterup.mws demo/template script for “show and tell” on batting Markov chain
    batterup.m demo/template Matlab version of the above
    recurrentandtrans.mws demo/template recurrent and transient states expected number of transitions from transient states

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