{"id":1121,"date":"2016-09-27T20:04:08","date_gmt":"2016-09-27T20:04:08","guid":{"rendered":"http:\/\/wordpress.rose-hulman.edu\/rickert\/?page_id=1121"},"modified":"2017-03-27T18:37:32","modified_gmt":"2017-03-27T18:37:32","slug":"ma331-mathematical-modeling-the-mathematics-and-physics-of-baseball","status":"publish","type":"page","link":"https:\/\/wordpress.rose-hulman.edu\/rickert\/ma331-mathematical-modeling-the-mathematics-and-physics-of-baseball\/","title":{"rendered":"MA331 Mathematical Modeling: The Mathematics and Physics of Baseball"},"content":{"rendered":"

ex3<\/a>MTRF 6 G
\n<\/span><\/p>\n

John Rickert
\nAssociate Professor of Mathematics<\/h2>\n

Office:<\/b> G-215A, Crapo Hall
\nPhone:<\/b> (812) 877-8473<\/p>\n

Address:<\/b>
\nDepartment of Mathematics
\nRose-Hulman Institute of Technology<\/span><\/u><\/a>
\nTerre Haute, IN 47803<\/p>\n

e-mail:<\/b> john.rickert@rose-hulman.edu<\/span><\/u><\/a>
\n<\/u><\/p>\n

\n

<\/u>The Oral presentation schedule<\/span><\/u><\/a> for the 10th week oral presentations is now available online. The schedule was modified Wednesday, Feb. 6.<\/p>\n

At the beginning of class Tuesday, you should turn in a pitching rotation using the following rules:<\/p>\n

\n

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.<\/p>\n

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:
\nI<\/b> The cost of a pitcher expected to allow R<\/i> runs per game is 10\/(R<\/i>-1) million dollars.
\nII<\/b> You can spend no more that \\$20 million
\n III<\/b> No pitcher can have a runs total less than 1.<\/p>\n

Examples of valid rotations: 3,3,3,3 (cost = 4 times (10\/2)=20)
\n2,4,3.5,4.75 (cost =10 + (3 + 1\/ 3) + 4+ (2+2\/ 3)=20)<\/p>\n

I’ll then run them off each other and see how well they do.
\nThe summary is at pitrot.html<\/span><\/u><\/a>. I am using the logistic equation with exponent 2, (the pythagorean projection) to calculate the expected winning probabilities. Some Maple<\/i> code is also available at pitrot.html.<\/p>\n

\n

Several people have asked about the effect of a tailwind<\/span><\/u><\/a> 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<\/span><\/u><\/a>.<\/p>\n

In 2001, the Colorado Rockies earned run average at home was 6.12. On the road, their earned run average was 4.42.
\nI’ve made a small table showing the Rockies Runs per game at home and on the road<\/span><\/u><\/a>.
\nThe\u00a0homework<\/span><\/a><\/span> passed out Friday is online now. The homework is due Monday, February 4<\/span>.
\nYour interim report is due Thursday, January 31<\/span>.<\/p>\n

The flyball<\/span><\/u><\/a> file used in class Thursday, is now available online. On Friday, we’ll add some wind, and move to Denver.
\nOn 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<\/span> is to use these to<\/p>\n

    \n
  1. estimate the force on the baseball at the velocities tested<\/li>\n
  2. estimate the drag coefficient at the velocities tested<\/li>\n<\/ol>\n

    The conversion factors discussed in class Monday and Tuesday are available at windtunnel.<\/span>html<\/span><\/a><\/span>.<\/p>\n

    The final revised project proposals were due by Tuesday, January 22<\/span>.
    \nRegarding a question asked in class on Monday: There is a     website that has a video of a knuckleball<\/span><\/u><\/a>, though it’s pretty difficult to see the unusual motion of the ball.
    \nA cleaned up version of the Maple<\/i>     flyball.mws<\/span><\/u><\/a> file is now online.<\/p>\n

    \n

    The final revised project proposals were due by Tuesday, January 22.<\/span>
    \nTyped preliminary project proposals were due Thursday, January 17<\/span>.
    \nThe questions asked at the end of class Tuesday, January 15:
    \n1. If the baseball is hit when it is three feet above the ground, how far away does it land if it lands uncaught?
    \n2. Determine the angle of elevation, alpha<\/i>, as seen be an outfielder. alpha<\/i> will be a function of time.
    \nWe 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.<\/p>\n

    Statistical analysis homework problems will be in the file hwstat1.doc<\/a><\/span>. These problems will be due by Thursday, January 17<\/span>.
    \nData for the statistical analysis homework will be in the file     hwstat.xls<\/a><\/span>.
    \nThe\u00a0    binomial distribution example problems<\/a><\/span> passed out Friday are avaialble on-line. Several of the “basic” statistics functions are defined in the Maple<\/i> worksheet statintro.mws<\/span><\/u><\/a>. An updated file containing the cumulative distribution functions as well: statintro2.mws<\/span><\/u><\/a>.
    \nAn     introduction to statistics<\/a><\/span>.<\/p>\n

    Further Markov chain commands are available in the file batterup2.mws<\/span><\/u>.<\/span><\/p>\n

    \n

    Excel<\/i> commands that we have used:<\/p>\n

    =AVERAGE(B2:B31)\r\n=STDEV(B2:B31)\r\n=CORREL(B2:B31,C2:C31)\r\n=LINEST(C2:C31,B2:B31,TRUE,TRUE)\r\n=LINEST(E2:E31,B2:D31,TRUE,TRUE)<\/pre>\n
    \n
    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.
    \nTo attempt to answer some of these questions, we will study multiple regression, Markov chains, and elementary dynamics.<\/p>\n
    Among the questions that we will look at are:<\/p>\n