SIAM News Blog

Voting Vectors and Major League Baseball’s Most Valuable Players

Baseball has been called America’s past time and each Major League Baseball team routinely draws over 2 million fans to their ballparks. Major League Baseball is divided into two leagues, the American and National Leagues, which consist of 14 and 16 teams, respectively.   At the end of the baseball season, the Baseball Writers Association of America uses a voting vector to choose a winner for the most valuable player (MVP) awards for each league.  In this case, a writer only gives positive scores to his or her top-ten candidates using the voting vector (14, 9, 8, 7, 6, 5, 4, 3, 2, 1).  Not only do the fans care about which player is name MVP, but the decision affects players’ salaries, television contracts, advanced ticket sales, and attendance.  Vote tallies for the 2006 MVP elections demonstrate the election procedure, but also highlight a concern for apparent arbitrariness of the numbers 14, 9, 8, etc. used in the vector.

For the American League in 2006, first baseman Justin Morneau of the Minnesota Twins won the MVP, narrowly defeating New York Yankee shortshop Derek Jeter, 320 to 306.  It was the 10th-closest AL-MVP election in history.  The closest decision was in 1947, in which Yankee outfielder Joe DiMaggio with 202 points edged out outfielder Ted Williams of the Boston Red Sox with 201 points.  In 2005, Yankee third baseman Alex Rodriguez defeated Red Sox designated hitter David Ortiz by 331 to 307 points.  

In 2006, the National League Philadelphia Phillies first baseman Ryan Howard received 388 points to St. Louis Cardinals first baseman Albert Pujols' 347 points.  Howard is the second player to follow up the Rookie of the Year award by winning the MVP the next year.  Two players, Fred Lynn of the Boston Red Sox in 1975 and Ichiro Suzuki of the Seattle Mariners in 2001, won both awards in their first seasons.

The complete voting data for the 2006 MVP elections for both the American League and the National League appear below.  To demonstrate how the point totals are calculated, Justin Morneau received 15 first-place votes (at 14 points each), 8 second-place votes (at 9 points each), 3 third-place votes (at 8 points each), and 2 fourth-place votes (at 7 points each) for a total of:

(15 x 14) + (8 x 9) + (3 x 8) + (2 x 7) = 320 points.

For comparison, Derek Jeter received 12 first-place votes, 14 second-place votes, 1 fourth-place vote, and 1 sixth-place vote (at 5 points) for a total of:

(12 x 14) + (15 x 9) + (1 x 7) + (1 x 5) = 306 points.

Information from The Official Site of Major League Baseball.

As with any election procedure, the use of voting vectors to determine a winner of an election has its champions and its detractors.  Detractors complain that it may not be possible to rank as many candidates as there are numbers.  For the election of an MVP, a writer may only be confident in his or her ability to rank the top five players, instead of the 10 required.  Examining the data, all 28 writers (two writers that follow each of the 14 teams in the American League) for the American League MVP election and all 32 writers (two writers that follow each of the 16 teams in the National League) for the National League MVP election turned in complete ballots for 2006.  A more significant complaint is that voters can misrepresent how they rank a candidate to help their top-ranked candidate win. For example, suppose that two voters who had Derek Jeter top-ranked had Justin Morneau in second-place.  By not voting for Morneau in the top 10, they could have conspired to decrease Morneau’s point total by 18 points, giving Jeter a 306 to 302 victory. 

Champions of voting vectors cite the ease of computation and how voters’ preferences for more than just a first-place candidate are used to determine the election outcome.  In response to the critique that voting vectors can be manipulated by voters who vote insincerely, Don Saari of the Universirty of California, Irvine, showed that the Borda count voting vector (n-1, n-2, …, 2, 1, 0) for an n-candidate election minimizes the likelihood of being manipulated.

Saari’s work suggests that if a voting vector is to be used, then it should be the Borda count voting vector.  One could ask, why does Major League Baseball use the voting vector (14, 9, 8, 7, 6, 5, 4, 3, 2, 1)?  Would another vector suffice?  There is vast literature on the consistency of election outcomes under different election procedures, including different voting vectors.  For the 2006 MVP elections, a voting vector that gave more points for being in second-place would have elected Derek Jeter the American League MVP.  For example, Derek Jeter would have defeated Justin Morneau 362-352 if the voting vector used by the writers was (14,13,8,7,6,5,4,3,2,1) instead.  For comparison, no voting vector (w1, w2, …, w10) in which w1 > w2 > … > w10 would change the outcome of the 2006 National League MVP.

blog comments powered by Disqus