Scott M. Berry

A Statistician Reads the Sports Pages: My Triple Crown

In writing this column four times a year I find too many“smal1 article” topics; topics that are interesting but not substantial enough for a whole column. This issue is an attempt to address three of these smaller, yet interesting, topics. It is my attempt at a . . . triple cravn! In the first leg of the triple crown I address the all-or-nothing strategy in hockey of pulling the goalie when you are down by a goal late in the game. Losing by two goals is no different from losing by one goal-and the chance to have six “skaters” against the opponent’s five increases the chances of tying the game. If you pull the goalie too early you may give up an empty net goal, which essentially ends your chances of tying the game. Should the goalie be pulled, and if yes, when is the optimal time to do so? In the second part of this article I present a neat little model for predicting the results of the NCAA basketball tournament. There have been several great articles on this subject-I do not dispute anything written in those; 1 just present a neat little model for the quality of the seeds and address the expected number of upsets. 1 found it very interesting that there were several Internet sites offering

Gold Medals, Protests, and Trading Ratings: The 2002 Winter Olympics Figure Skating

1,000,000 to anyone who could correctly predict all 63 games of the 2000 tournament . . . how likely is it that someone will win? In the last section of the article I try to address a nasty, yet important, question in sports and statistics. In my second Chance column (Vol. 12, No. 2, Spring 1999) I predicted the 1999 season home-run totals for McCwire and Sosa, as well as 25 other players. Well, the season is over, and I frequently get asked the very simple question, “Were you correct?” Well, of course, I did not get each player‘s season total exactly correct, but I do not think that is the question. In the final leg of my triple crown I try to interpret and answer this simple but nasty question.

A Statistician Reads the Sports Pages: Hired to be Fired

Figure skating is probably the most popular Winter Olympics event. The names of Peggy Fleming, Dorothy Hamill, and Scott Hamilton still evoke thoughts of wonderful all-American champions. Perhaps the popularity of figure skating derives from its blend of athleticism and artistry. The competitors are supreme athletes that spend childhood perfecting their mastery and presentation. Winning in their sport is not simply jumping highest, skating fastest, or directly scoring against an opponent. The winners of figure-skating events are determined entirely by pleasingjudges, Other sports, such as gymnastics, ski jumping, and snow boarding are determined, at least in part, byjudges, yet there is much less controversy surrounding the judging of those events. Figure skating has a history of judging controversies and a general mistrust of the judging methodology. In the 2002 Winter Olympics the judging of figure skating took center stage when a judge admitted striking a deal to grade the Canadian skating pair lower. Later, the Russians protested the judging of the ladies individual event, claiming that their skater was unfairly judged.

Bayesian Smoothing for Measurement Error Problems

I enjoy sports for many reasons. The strength and ability of the athletes doing amazing feats with such grace. The passion of the fans and the finality of a playoff scenario are all thrilling. The endings are unscripted. If you turn on a television drama you are going to get an interesting story, which comes together in a neat little package at the end of an hour. In a sporting event you could get a blowout which is uninteresting after the game is half over. You could get a tight game which comes down to the last minute-and then could be extended to an even longer game. Sports is one of the ultimate random processes. You see the little pieces of variability being combined together to form a simple win-loss result. After games, you can discuss how individual pieces (plays, outs, shots) and decisions shaped the final outcome. As a statistician, I love the variability that comes with sport. As a statistician, I also like to address how certain plays and outs-how the little pieces-contributed to the final win-loss result. There have been many of these plays in sports recently. The 2003 Major League Baseball (MLB) playoffswere extremely exciting.Twoof the famouslyjinxed ballclubs, the Boston Red Sox and the Chicago Cubs, were two of the final four teams competing for the World Series. They each had the lead with five outs remaining, with their best pitchers in the game, in games that would have sent them to the World Series, and lost. Both of these losses involved controversial managerial decisions. Mark Prior and Pedro Martinez, two of the best pitchers in baseball were left in to pitch their eighth inning and both lost their leads. Neither the Red Sox nor the Cubs advanced to the World Series. For the first time, all four divisional playoffgames (round of eight) in the National FootballLeague (NFL) were decided by seven points or less. Each game had pivotal decisions and plays.The Philadelphia Eaglesconverted a fourth down

A Statistician Reads the Sports Pages: Modeling Acceptance to the Major League Baseball Hall of Fame

In the presence of covariate measurement error, estimating a regression function nonparametrically is extremely difficult, the problem being related to deconvolution. In this paper we describe Bayesian approaches to modeling a flexible regression function when the predictor variable is measured with error. The regression function is modeled with smoothing splines.. We provide simulations with several nonlinear regression functions. Our simulations indicate that the frequentist mean squared error properties of the fully Bayesian method are better than those of previously proposed frequentist methods, at least in the examples we have studied.

A Statistician Reads the Sports Pages: Statistical Fallacies in Sports

Growingup in Minnesota, I loved the factthat the Minnesota Twins were a bad baseball team. I could go to their games with very little inconvenience. There were no parking troubles, tickets were easyto get, and you neverhad to wait in linefora Cokeand hotdog. Muchofthat changedMay8th, 1984. That night, Kirby Puckett made his debut for the Twins. He lashedout fourhits in his five at-batsand wasan instantMinnesotahero.Duetohisgreatattitude,teddy-bear physique, and extraordinary ability, he becamea fanfavorite in Minnesotaand throughout baseball. He always seemed to be having fun-truly playing a game. He wasa boyhood hero to me; maybe it is the impressionability ofyouthor the nature of the game, but boyhood baseball heros can do no wrong. Despite the fact that he madegoing to gamesmore hectic, I felt this way about Kirby. Kirby was also loved by the media. He embodiedwhat manypeoplewanted to think baseball was all about. Kirby was on his wayto a sure-thingHall of Fame career. In the middleof his 12thseason, 1995,he washit in the facewith a pitch. He neverplayed again. The nextpre-season he had problemswithhisvision, causedbyglaucoma, andwasforced to retire.Doesthis hurt his Hallof Famechances?In base-

A Statistician Reads the Sports Pages: Does Defense Win Championships?

Scientists like to poke fun at sports experts for their lack of understanding of simple scientific concepts. We nerds take some satisfaction in knowing something or doing something better than the tremendously gifted athletes who play sports. While we can’t field a ground ball in the hole, we know ground balls don’t pick up speed as they travel on artificial turf. We also know that, despite the talents of some pitchers, they can’t increase the mass of a baseball by throwing a “heavy ball.” We yell at the television when an announcer quotes a turnover ratio of +7 or a winning percentage of 0.500. We know Michael Jordan cannot float an extra instant in the air and that a baseball hitting a fence 400 feet away actually would have traveled farther than 400 feet. We snicker at reports such as the following from the Associated Press (St. Louis Cardinals vs. Pittsburgh Pirates, April 26): “Luna, who went 2-for-5 and raised his average to .432, had his fourth straight multi-hit game for the Cardinals, who have won six of seven overall.” These mistakes run from mathematical to physical. There is not a lack of statistical mistakes in sports. They may not be as blatantly obvious as the examples above, but they can be more harmful. Here, I present my top five list of misunderstood statistical concepts in the sports world—I’ll call them fallacies. Interestingly, the fallacies are the same A STATISTICIAN READS THE SPORTS PAGES

A Statistician Reads the Sports Pages: Nature, Nurture, or Culture

During the National Football League (NFL) playoffs there is a two-week break between the semi-finals and the finals (Super Bowl). This break is known as a very difficult time for the players because the media scrutiny is overwhelming. I have my own two-week scrutiny every year. Nonstatisticians who know I dabble in sports statistics and have various “computer” models for predicting games ask me “so, who is going to win?” Typically they want to know who they should bet on. They are typically unsatisfied when I explain to them that by modeling these games I understand the huge amount of variability and either team can win—statisticians never have to say they are certain! I do have a simple little model that ranks teams throughout the season. This model is described in a previous column (Chance, Vol. 16, 4649) in which I investigate the “normality” of football games (actually in college football games). The normal assumption is very reasonable. One thing has always bothered me a bit about my model. It models the difference in each game using one strength parameter for each team. The model tends to predict very well, but there is a cliché in the NFL that “defense wins championships.” This mantra is repeated by many and believed by many. I am never one to believe in “effects” that I am told over and over again, but this makes sense. Could my model be naive in not modeling both offense and defense? I have always wanted to investigate further this theory—with the expectation that I would show that offense and defense don’t matter, that football teams can be characterized by one strength parameter. In the next section I present the NFL data available for this investigation as well as the models used to characterize NFL teams.

A Statistician Reads the Sports Pages: The Great One

About five years ago I was interviewed by a sports talk radio station in Winnipeg. They were interested in an analysis I had done about hockey players. At the time of the interview I was living in Texas. After several questions the interviewer asked me, “So, what does a guy in Texas know about hockey?” After the initial shock of the question, I explained that I grew up in Minnesota playing hockey for much of my childhood. His response was (I’m paraphrasing), “Oh, Minnesota, that’s okay, eh.” I was given instant hockey credibility because I was from Minnesota. We recently spent two years in Illinois, from Texas, and there were whispers of this “Texas” kid who was a baseball and football player. My son had some instant baseball and football credibility because he was from Texas. I understand some of this regional bias. The ability in and knowledge of hockey of Minnesota residents is clearly better than that of Texas. In Minnesota hockey is the cultural “thing to do.” Most athletic young kids in Minnesota give hockey a try. In Texas there are very few who play hockey. We played travel baseball in Illinois from mid-April until the end of August. In Texas, baseball is played nearly year-round. There are impressions that different regions produce different types of athletes in different numbers. For example, in Major League Baseball (MLB) there are currently 1,429 players from the United States, of which 319 (22%) are from California. In the National Hockey League (NHL) there are 94 current players from the U.S., of which three (3.1%) are from California. In this article I investigate the current professional athletes and the distribution of their home states. I am interested in the general distribution of the athletes from professional sports, investigating the effect of weather and cultural bias. I collected home state information for professional athletes in hockey, baseball, football, basketball, and golf. The home state for an individual may not be well defined or may be difficult to determine; for players in many sports, finding the place of birth is the easiest. For golf, baseball, basketball, and hockey this was the approach I took, considering the state of birth for U.S. players as their home state. At ESPN.com, I accessed each of the current NHL players and recorded the place of birth. I included the 94 U.S.-born players in my sample. Minnesota and Massachusetts totaled 15 each, the most home state players. ESPN.com has a feature with which you can sort MLB players by state of birth. There were 1,429 players born in the U.S., with California the most populated (319). At www.basketball-reference.com I accessed each of the National Basketball Association (NBA) rosters and recorded the state of birth for each U.S. player on the roster. There are 405 NBA U.S.-born players, of A STATISTICIAN READS THE SPORTS PAGES

A Statistician Reads the Sports Pages: Turn! Turn! Turn!

As with many statisticians my initial interests in numbers, math, and statistics were through sports. As a kid I would scour the daily sports page box scores, standings, and league biders. I memorized the statistics on the back of bubble gum cards. As a 10-year-old I followed the Major League Baseball home run leader, George Foster. At the midpoint of the season he had 32 home runs. I was sophisticated enough to be able to double that total and predict that he would hit 64 home runs, which would break the record of 61. I made a small wager with my dad that he would break the record. He finished the season with 52 home runs. After losing this bet, and several others like it, I became interested in the phenomenon that players would be on pace to break records at the midpoint of the season and would invariably fall short. I now understand the phenomenon. The reason is simple the players on pace for records arc not as good as their pace. They were the extreme observation in a population of players. When their numbers are removed from the context of their population and sport they are misleading. By their nature records are extreme observations in very few cases are players truly as good as their record numbers. One such extreme athlete was Wayne Gretzky. The 1979-80 National Hockey League (NHL) season was his first. As an 18-yearold, he tied for the league lead in points scored (137). The following season he broke the record for the most points in a single season, with 164 (152 was the old record set by Phil Esposito in 1970-71). He went on to lead the league in scoringand win the leagues Most Valuable Player award for those first eight years. He was the first extreme athlete I had ever seen. He posted numbers that were thought impossible. He was one of the special athletes who set records with performances that were normal for him. His average performance was good enough to be better than the best performance of