Teaching Statistical Thinking Using the Baseball Hall of Fame Steve C. Wang

Statistics can be more salient to students when used in a real context. One professor at Swarthmore College used The Hall of Fame to teach statistical thinking.

aseball is a natural context in which to learn about statistics. BOur national pastime is replete with averages and percentages, counts and amounts, and totals of all kind. To the fan, these are not mere numbers, but condensed stories, instantly intel- ligible as the true literature of the game. Compared to more fluid sports such as football, basketball, hockey, and soccer, baseball especially lends itself to data collection: It is inherently sequential and discrete, with players taking turns at the plate and stopping at fixed places on the field. Such characteristics make baseball a superlative source of examples for teaching statistical principles. In 1999, I designed and taught a course on the Baseball Hall of Fame, Museum patrons view plaques of recent inductees into the National Baseball Hall of Fame titled “Baseball’s Highest Honor,” dur- and Museum in Cooperstown, N.Y. (AP Photo/Tim Roske) ing winter study session at Williams College. Winter study is a month-long term during January, with courses on subjects not part of the traditional aca- Course Catalog Description demic canon. Students take one course Math 013: Baseball’s Highest Honor during the winter study period, with classes typically meeting for 5–10 hours Baseball’s Highest Honor is election to the Hall of Fame. The history of the per week. Class sizes are kept small to election process, however, has been fraught with controversy, confusion, and encourage discussion. accusations of “favoritism.” A sticking point is that there is no clear definition of The goal of my course was to use what a Hall of Famer should be, other than a player of the caliber usually elected the Baseball Hall of Fame, particularly to the Hall of Fame. But with diverse standards applied by a myriad of commit- the process of voting for players to tees, the Hall of Fame is a self-defining institution that has failed to define itself, be enshrined, as a subject for teach- to paraphrase author Bill James. What should the criteria be, and what, in fact, ing statistical and scientific principles. have the criteria been? How should one define “greatness”? The course was not intended to teach In this course, we will discuss the history of the Hall of Fame, methods of students how to carry out statistical rating players, and election criteria. Two focuses of the course will be (1) to techniques, but rather to discuss what review modern statistical methods for evaluating players (sometimes referred to constitutes a good or bad statistical as “sabermetrics”), including models for run production and comparisons across argument, and thus was in the spirit of eras, and (2) to contrast systematic, “scientific” methods for player evaluation a quantitative literacy course. Although with the ad hoc campaigning typical of Hall of Fame arguments seen today. We the course was ostensibly about base- may also discuss the improvement or decline in quality of play over time, the ball, my underlying goal was to demon- relative importance of pitching and hitting, and other related issues. strate the value of sound statistical and

CHANCE 25 scientific thinking. Essentially, this was Fame, it’s easy to see why this distrust Here is another example of stat-pick- to be a science course whose subject arises. In baseball (and in many other ing from a letter to Baseball Digest (quoted happened to be baseball. contexts), statistics too often is used by James) that we discussed in class: The class enrolled 31 students, most as a rhetorical bludgeon to end argu- “He played in 1,552 games, had of who were nonscience majors, and we ments and prove points, rather than as 5,603 at-bats, 882 runs, 1,818 hits, met two hours per day for three after- a means of discovering knowledge. This a .324 lifetime batting average, 181 noons every week. For each class, there provides an ideal opportunity to con- home runs, and 997 RBI. I think he were assigned readings, which included trast such arguments with proper uses belongs in the Hall of Fame. most of Bill James’ 1995 book Whatever of statistics in scientific (“sabermetric”) arguments. Bill James, in his 1981 Base- Happened to the Hall of Fame?, articles from “Here is a man who from 1926 ball Abstract, uses an elegant analogy: various annual editions of the Bill James through 1931 knocked in 90 or Baseball Abstract, and articles from main- “Sportswriting ‘analysis’ is largely an more runs four times and reached stream media. Evaluation was on a High adversarial process, with the most double figures in home runs every Pass/Pass/Not Pass basis and was based successful sportswriter being the year. So you tell me. Why hasn’t on class attendance and participation, a one who is the most effective advo- Babe Herman been elected to the presentation, a group project, and occa- cate of his position... Sabermet- Hall of Fame?” sional short-writing or research assign- rics, by its nature, is unemotional, ments. Finally, we ended the course by noncommittal. The sportswriter Here again, statistics are provided going on a class trip to Cooperstown to attempts to be a good lawyer, the without a context for understanding visit the Hall of Fame. sabermetrician, a fair judge.” them. How do Herman’s numbers com- In baseball, the term “statistics” usu- pare with his peers? The author rattles ally is used to refer to what academic off these statistics as if they are evi- statisticians would call “data,” rather Misuses of Statistics dence for Herman’s greatness, but are than formal inferential methods, such as they? Herman led the league in any cat- One of the most common misuses of egory only once, in triples in 1932. He hypothesis tests or confidence intervals. statistics is what I’ll call “stat-picking”: I retain this colloquial usage here. I also knocked in 90 or more runs four times? choosing only those numbers that sup- The truly great hitters of his day were have updated all statistics through the port the writer’s position and ignoring all end of the 2005 season. driving in upwards of 150 runs a year; others, while leaving out any semblance the NL record of 191 RBI and the AL of context. In class, my students and I dis- record of 184 RBI were both set during cussed this example from a letter to The Statistics in Baseball: a Sense this period. Similarly, reaching double Sporting News (quoted in James’s Whatever of Distrust figures in home runs is hardly a Hall of Happened to the Hall of Fame?): Statistical arguments often are viewed Fame–caliber achievement. with suspicion in popular culture in gen- “I often encounter the opinion Herman was a very good player, but eral and in baseball specifically. “Figures that the Veterans Committee of as James points out, Herman often is the don’t lie, but liars figure,” people say, and the Baseball Hall of Fame should subject of fallacious arguments because who among us has not heard the old saw be disbanded because of a ‘lack of his candidacy is a stretch. Another writer about “Lies, damned lies, and statistics”? worthy candidates.’ quoted by James argues that Herman In a 2005 article on www.espn.com, for “finished his 13-year major league career instance, television personality Jimmy “It doesn’t take much homework with a .971 fielding average, a dozen Kimmel expressed his resentment of sta- to find a number of players worth points ahead of Ty Cobb’s mark.” This tistics in an article about Steve Garvey’s considering. A prime example is is a remarkable statement. First of all, Hall of Fame qualifications: Tony Mullane. A 30-game win- it’s factually incorrect: Herman’s fielding ner for five consecutive seasons, he average was actually 10 points ahead of “We have computers now that won 285 games overall. He belongs Cobb’s, not “a dozen,” but that’s a quibble. ‘revalue’ baseball players of the in the Cooperstown shrine.” Second, even if the statistic was correct, past. They travel back in time with this would be evidence that Herman new and frequently nonsensical At first, the quoted numbers seem should not be in the Hall, not that he formulas designed to quantify impressive—for nearly four decades no should. Fielding average has increased greatness—or, more often, to pitcher has won 30 games in a single steadily over time as playing conditions make a case against it... These are season, let alone in five consecutive sea- and equipment have improved. The the ‘facts’ pointed to most often sons. But in the 1880s, when Mullane’s league average outfielder during Cobb’s when Garvey’s Hall of Fame quali- streak took place, starting pitchers rou- time fielded .961, and Cobb was exactly fications are discussed: random, tinely pitched in more games than they do now, recording more wins. During average in this respect. During Herman’s machine-generated equations. his five-year streak, Mullane never led career, the league average had increased His on-base percentage wasn’t the league in wins; the leaders in those to .981, so Herman’s mark was actually good enough. His OPS (whatever seasons had 40, 43, 52, 41, and 46 wins. 10 points below average. Third, and that is) doesn’t compare to some But these additional statistics—essential most importantly, no one thinks Cobb of the other guys.” for understanding the value of Mullane’s belongs in the Hall of Fame because of If we look at how people often use accomplishments—are omitted from his fielding average, so the entire argu- statistics in arguments about the Hall of the argument. ment is specious. Clearly, the writer is

26 VOL. 20, NO. 1, 2007 trying to be an advocate for Herman: ray is a legitimately comparable player, “in the middle of the group.” One way His goal is to marshal those statistics and Schmuck does later acknowledge to select groups that are legitimately that bolster Herman’s case, not to learn that Palmeiro is not in the same class similar is to use upper and lower cut- from statistics. as Mays or Aaron.) offs, rather than just minimums. Rafael A related fallacy is what James labels People instinctively distrust such Palmeiro, for example, has 3,020 hits the “in a group” argument, in which a arguments because they know Her- and 569 home runs; his comparison player is compared to other players man was no Cobb and they know Pal- group might be defined by players with with similar statistics. The catch is that meiro was no Mays. They too often 2,700–3,300 hits and 450–650 home “similar” is defined only by minimum conclude that all statistical analysis is runs, rather than those with 3,000+ cutoffs, so the player is grouped with unreliable and dishonest. And who can hits and 500+ home runs. This idea of players at least as good as (and likely blame them? If you can “prove” Herman selecting similar subjects by controlling better than) he was. For example, when was better than Cobb, then you really for covariates often arises in academic Rafael Palmeiro got his 3,000th hit in can prove anything with statistics. But statistics—in case-control studies and 2005, it was widely reported that he that’s not the fault of statistics; it’s the matched-pairs designs, for instance. was only the fourth player with 3,000 fault of an approach that uses statistics Another key principle of good statisti- hits and 500 home runs, the others selectively to end an argument, rather cal arguments in baseball is that statistics being Hank Aaron, Willie Mays, and than to inform an argument. Of course, must include a context in which to judge Eddie Murray. In a 2005 Baltimore Sun there are better ways to use statistics, them. How do we know whether “30 article, titled “For Palmeiro, 3,000 Hits, and comparing and contrasting these wins” or “90 RBI” are impressive numbers? 500 HRs Add Up to a Spot in Hall approaches is an effective way of illus- We must ask, “relative to what?” How of Fame,” sportswriter Peter Schmuck trating how proper scientific method- many games were other pitchers in the argues that membership in this exclu- ology works. As baseball is one of the league winning at the time? How many sive club should seal Palmeiro’s Hall of most visible contexts in which statistics runs were other batters driving in? Did Fame chances: is applied, recognizing the strengths of either figure lead the league, or come “Rafael Palmeiro could get his a statistical approach in baseball can go close? The idea of comparison is a key 3,000th career hit at Seattle’s a long way toward demonstrating the principle in academic statistics as well: Safeco Field tonight, and there value of statistics in a variety of fields. By itself, a treatment group is of limited actually is talk show debate over An additional fallacy, albeit one not use unless there is a control group with whether he should be a first-ballot strictly statistical in nature, is the belief which to compare it. As Edward Tufte Hall of Famer. that arguing something is plausible writes in Visual Explanations, “The deep, establishes it as true. For instance, peo- fundamental question in statistical analy- “Please. ple argue that Roger Maris was aided by sis is ‘Compared with what?’” Yankee Stadium’s short right field line Many traditional statistics, such as “...I can’t see how anyone could in 1961, when his 61 home runs broke pitchers’ wins and RBI, are strongly question whether he should be Babe Ruth’s long-standing record. Right dependent on factors other than the inducted at Cooperstown in his field in Yankee Stadium was indeed player’s abilities, such as the quality of first year of eligibility. short by major league standards at 296 his teammates or the characteristics of feet, so it is plausible this would have his home park. Thus, arguments using “Tonight, maybe tomorrow, he’ll helped Maris, a left-handed pull hitter. these statistics are of limited value. In become only the fourth player in But not everything plausible is true. In recent years, however, increasingly baseball history to amass both 500 fact, Maris hit more home runs on the sophisticated metrics have been devel- home runs and 3,000 hits. The road (31) than at home (30) that year. oped that better quantify or isolate a other guys are Hank Aaron, Willie While this is more of a logical, rather player’s value to his team and adjust for Mays, and Eddie Murray. End of than statistical, fallacy, it does establish extraneous effects. We discussed several conversation.” that, in good science, we always need of these in class, including on-base plus Note that this was written before to look at data, and that conclusion is slugging, runs created, linear weights, Palmeiro’s late-2005 steroid revelations. certainly a statistically valuable one. support-neutral won-lost record, and It is literally true that only Aaron, Mays, zone rating. Academic statistics may Murray, and Palmeiro have this combi- Principles of Sound Statistical not have direct analogues of these met- rics, but the idea of isolating the effect nation of accomplishments. But these Arguments arguments are often misleading because of a factor by accounting for the effects they invariably group the player in What, then, makes a statistical argument of covariates is familiar. question with others who were better sound? In class, we discussed principles These are just some of the principles than he was. This occurs because the of good quantitative arguments and for making valid arguments in baseball groups are defined by a lower bound how these reflected principles of formal that have analogues in formal academic on the number of hits or home runs, but academic statistics. For instance, the “in statistics. What is most important, how- not an upper bound. Thus, Aaron, who a group” argument involves selecting ever, is not any particular principle, but has 751 more hits and nearly 200 more subjects similar to the player in ques- rather a general attitude toward using home runs than Palmeiro, is “in the tion. This argument can be made valid if statistics. It is said that people most often group,” as is Mays with 263 more hits the player is legitimately similar to those use statistics the way a drunk uses a lamp- and nearly 100 more home runs. (Mur- in the group—if, as James writes, he is post—for support, not for illumination.

CHANCE 27 Table 1—Comparison of Chuck Klein and Larry Walker’s Seasons How many MVP-type seasons did he have? AB HR RBI AVG OBP SLG Was he a good enough player that Klein 1932 650 38 137 .348 .404 .646 he could continue to play regu- Walker 2001 497 38 123 .350 .449 .662 larly after passing his prime?

Klein 1933 606 28 120 .368 .422 .602 Did he have an impact on a num- ber of pennant races? Walker 2002 477 26 104 .338 .421 .602 Is he the very best player in base- ball history who is not in the Hall of Fame? In contrast, the key step in formulating a home park—like, say, Sammy Sosa—or valid statistical argument is to use statis- was he merely a good player whose num- Are most players who have com- tics to not just prop up a teetering claim, bers were inflated by time and place, parable career statistics in the Hall but to shed light on the issue. such as Dante Bichette? As it turns out, of Fame? Klein was comparable to Larry Walker, What impact did the player have a legitimately very good player who also Class Assignments for on baseball history? Developing Sound Statistical played in a high-offense park and era. Arguments As of 2005, both Klein and Walker had In their presentations, students used played 17 seasons, and both were pri- the Keltner List to assess the credentials Because there is no self-contained defini- marily right fielders. Walker’s counting of modern players of their choosing, tion of a Hall of Famer, two key steps in statistics are somewhat better, but his such as Darryl Strawberry, Kirby Puck- any sound Hall of Fame argument are career park-adjusted OPS (on-base plus ett, and Don Mattingly. Taken together, to identify similar players who have and slugging) is close to Klein’s (Walker was the goal of Our Generation and the have not been enshrined and to com- 40% over the league average; Klein was Keltner List was to help students evalu- pare a player to his contemporaries. Two 37% over.). At least, superficially, Klein’s ate players’ statistics in context—the exercises designed to clarify these tasks 1932–33 seasons are a good match for former by comparing selected older are Our Generation and the Keltner List. players to modern ones and the latter So the class would gain experience in Walker’s 2001–02 seasons (see Table 1). Most fans today have a much better by comparing selected modern players developing sound statistical arguments, to older ones. I assigned students to use these exercises conception of Larry Walker’s place in the game than they do Chuck Klein’s, The course also required a final proj- to research players of their choice and ect, a 10-page paper reporting original present their findings to the class. Pre- so such comparisons to an active player are an effective way of conveying a research carried out in groups of two sentations usually were done in groups of to four students. Any topic relating to three and lasted about 20 minutes. player’s stature. baseball was allowed, even if it was not “Our Generation” is an article writ- The Keltner List is a series of ques- directly related to the Hall of Fame, as ten by James in his 1992 Baseball Book in tions intended to systematically assess long as it could be addressed through which he compares great players of the a candidate’s Hall of Fame qualifica- substantive research, as opposed to last half-century with “similar” modern tions. James created the list in 1984 opinion and conjecture. Some sample counterparts. For example, Tom Seaver is after receiving a letter advocating Ken compared to Roger Clemens, and Ernie Keltner’s enshrinement in Cooperstown topics include: Banks to Cal Ripken. For their presenta- because he had a higher batting average Are there racial or ethnic biases in tions, students repeated this exercise for than Eddie Mathews, more RBI than Hall of Fame voting? some lesser-known Hall of Famers, such Jackie Robinson, and more hits than as Chuck Klein, Rube Marquard, and Ralph Kiner—all three Hall of Famers. How has the role of third basemen Tommy McCarthy. This was a useful Logically, this is the equivalent of argu- changed over the years? What way for students to get a better idea of ing that a Yugo is a great car because it’s ramifications does this have for the stature of players of previous eras. cheaper than a Rolls Royce, gets better HOF voting? For example, students may have been gas mileage than a Ferrari, and is easier vaguely familiar with Klein: They might to parallel park than a Hummer. James What types of players are over- have known he had some notable single- instead proposed a list of 15 questions represented in the Hall of Fame? season marks, with as many as 250 hits that would be more relevant to a player’s Among marginal selections, what and 44 assists. They might have been Hall of Fame qualifications than “Does traits do they have in common aware of his impressive seasons in the he have more hits than Ralph Kiner?” that are not shared by other 1930s in a high-offense era. They might Here are some typical questions from equally worthy players who have have heard his home park during those the list: not (yet) been selected? seasons, Philadelphia’s Baker Bowl, was an extreme hitters’ park. But was he a Was he ever regarded as the best What types of teams exceed their truly great player who benefited from his player in baseball? runs-created estimates?

28 VOL. 20, NO. 1, 2007 determined a straight line would be nonsensical because it could predict that the probability of election exceeds 100% (for players with many home runs) or falls below 0% (for players with few home runs). Moreover, stu- dents intuitively knew that one addi- tional home run is less important for players with many home runs (who are likely to be enshrined anyway) or those with very few home runs (who are unlikely to be enshrined, regard- less), so the curve should flatten out at high and low values of home runs. On the other hand, an additional home run is most important to borderline Hall of Fame candidates, so the curve should be steepest for players on the cusp of Figure 1. Best-fitting S-shaped (logistic) curve for the Baseball Hall of Fame data greatness, which corresponds to about 400 HR. The students were thus able to conclude, with some guidance, that Does good pitching beat good MVP award, five points for getting 200 the curve should be S-shaped. hitting? hits in a season, one point for leading the I then showed them Figure 1, which league in triples, etc.). Players who reach plots P(HOF) as a function of the num- How was the 1919 World Series 100 points are predicted to get into the ber of home runs hit. I collected data viewed at the time? Hall of Fame, with players above 130 from the web on all players who hit at The only topic I did not allow was almost certain to be elected. This sys- least 300 home runs, including whether whether player X deserves to be in the tem, however, is somewhat ad hoc, and they were in the Hall of Fame. I then Hall of Fame. Such arguments have been the optimal parameter estimates (point plotted each player’s home run total (X) rehashed at length for almost any cred- values) are difficult to determine. and HOF status (Y = 1 if in the HOF, 0 ible candidate, and I wanted the students Here was a natural opportunity to otherwise; Y-values have been jittered to do something original. introduce logistic regression and com- to improve legibility). I was not able to pare it to informal methods such as the find systematic data listing players who Career Monitor. I began by asking the hit fewer than 300 home runs, but I told Advanced Topics: Logistic students to imagine making a graph the students to imagine there should be Regression of the probability that a player will be many more points representing such One advantage of having a class of elected to the Hall of Fame (denoted by players in the left side of the graph, most baseball fans is that by taking advan- P(HOF)) as a function of the number of whom are not in the HOF. I pointed tage of this common interest, I was able of home runs he hit. I asked students out that the curve was the “best-fitting” to introduce substantial statistical con- to consider what such a graph would curve determined by a statistics pro- tent at a nontechnical level, including look like. For instance, would the graph gram, and, indeed, it was S-shaped, with advanced topics not typically covered be linear or curved? Students quickly its steepest part around 400 HR. in introductory courses. Since all the stu- dents were familiar with the background and motivation of baseball examples, they could more easily focus on learn- ing the statistical concepts in a context with which they were comfortable. For example, an inevitable topic in a course on the Hall of Fame is to determine the de facto criteria for election to the Hall of Fame. How does hitting 400 or 500 home runs affect a player’s chances of being enshrined? What about having a .300 average, or 1,500 RBI? In Whatever Happened to the Hall of Fame?, students read about a method, the Hall of Fame Career Monitor, invented by James to answer such questions. This system involves awarding points for various achieve- ments (e.g., eight points for winning an Figure 2. Poorly fitting S-shaped curve for the Baseball Hall of Fame data

CHANCE 29 I then asked the class to think about odds for the first player would be .00123 e( 6.7 .0175HR) what makes this curve the “best-fitting” e.0175(369) = .784, whereas the odds for the P(HOF)  ( 6.7 .0175HR) curve, and how one might define “best- 1 e second player would be .00123 e.0175(359) fitting.” This is not an easy question for Some students, particularly those with = .658. The ratio of these two odds students with little or no formal statistics less math background, found this equa- is .784/.658 = 1.19. In other words, a background. It often is helpful to give tion intimidating, so I rewrote the equa- player with 369 HR has 19% better odds counterexamples when introducing a tion in a “simpler” form as of election than a player with 359 HR. new topic, so I displayed a “poorly fit- What about the odds of election for P(HOF) ting” curve as well (Figure 2). This curve  .00123e.0175HR a player with 475 HR vs. the odds for clearly is shifted too far to the right; per- 1 P(HOF) a player with 465 HR? (These happen haps less obviously, it also is too steep. to be the figures for Willie Stargell and Students clearly could see this I then asked students what the fraction Dave Winfield.) We calculated the odds curve did not match their intuition. For on the left side represents. Sports fans using the equation and found their ratio instance, it predicts that players hit- typically have had enough familiarity was again 1.19—that is, a player with 475 ting 500 HR have a miniscule chance with wagering to recognize this fraction HR has 19% better odds of election than of being enshrined when, in fact, such is the odds of being elected. What this a player with 465 HR. By now, students players are virtually guaranteed to be equation says, then, is that the odds of were wondering if this was a coincidence, Hall of Famers. In other words, in light being elected is related to a player’s home or if the ratio of the odds was always going of the players who actually are or are not run total through the expression on the to be 1.19 for any two players separated in the Hall of Fame, the curve in Figure 2 right side. by 10 HR. I asked the class how we could seems unlikely to reflect the voters’ true Students initially found the form of prove the ratio will always be 1.19? We criteria. On the other hand, the curve in the right-hand expression to be cryptic. could keep trying pairs of players sepa- Figure 1 seems much more likely in light I asked them to compare the odds of rated by 10 HR—perhaps 252 and 242 of the actual voting. In fact, it is the most election for two players who are 10 HR HR (the figures for Bobby Murcer and likely such curve, which is why statisti- apart—say, 369 HR vs. 359 HR. (As it Dusty Baker). If we tried enough pairs and cians call it the “best-fitting” curve. happens, these are the career HR for each time found a ratio of 1.19, we might I then gave the students the equation Ralph Kiner and Johnny Mize, respec- be fairly confident that this relationship of the curve in the form tively). The curve would predict the would always hold for any two players separated by 10 HR. But would that be proof? Is it possible, in fact, to prove this Assessment conjecture with certainty? To answer this question, I wrote Overall, the class was a success. By the end of the course, the students were bet- the odds ratio as (.00123e.0175 (HR+10))/ ter able to critically evaluate statistical arguments. At the end, students filled out (.00123e.0175 HR). After I cancelled anonymous course evaluations in which they were encouraged to give honest terms (and briefly reviewed properties feedback. Here are some of their comments: of exponents), students could see the odds ratio always would be e.0175(10), Excellent. I really learned a lot. It was extremely interesting and worthwhile. which equals 1.19. In other words, each 10 additional HR is associated with a I loved it. Best winter study course I’ve taken in my four years. Format of class and 19% increase in the odds of election, readings was perfect. regardless of the “baseline” number of HR, so we have thus proved the con- Can I major in this? Just kidding, it was a great experience. jecture to be true. I asked the students whether this kind of statement sounded It was a good way to analyze baseball in a kind of scientific way and fun to learn familiar; had they ever heard something about some of the new stats, how stats can be skewed, and to learn to distinguish good along these lines? With some prompt- arguments from bad arguments. ing, someone offered that it reminded him of medical reports: each additional It opened up a lot of doors to understanding baseball and statistics that I wasn’t aware pack of cigarettes you smoke increases existed. your odds of cancer by some percent. And that, I replied, is exactly how medi- I think [the student presentations] were good, as they made us focus on a couple of specific cal researchers come up with those esti- players in order to appreciate their overall standing in the history of baseball. In doing mates; we’ve just rediscovered it in the so, we learned about the subtleties of comparing and analyzing players. context of baseball. At this point, there are many options I thoroughly enjoyed the class. It gave me the means to defend my arguments with for what to cover next, depending on the statistical evidence. mathematical level of the students. If data are available, one could apply logistic I knew enough about baseball to know I wouldn’t get lost, but it taught me many new regression to a large set of predictors and ways of looking at things and, in a very interesting way, taught me more about the compare the resulting model to James’ intricacies of the game. Career Monitor. Or, one could present

30 VOL. 20, NO. 1, 2007 the formal statistical model underlying today’s controversies. For instance, the existing group. That process may be tak- logistic regression, or explore concepts Hall of Fame originally was conceived ing place in baseball today, as a new breed such as subset selection for model build- as a museum to draw tourists to Coo- of general managers—Paul DePodesta in ing. One could even discuss, at a nontech- perstown, which had been devastated Los Angeles, J. P. Ricciardi in Toronto, nical level, classification methods such as by Prohibition and the Great Depres- Theo Epstein in Boston—finds statistical discriminant analysis, classification trees, sion. Designing a selection process to analysis a natural part of baseball. This and neural networks. Regardless of what honor the game’s greatest players was an so-called Moneyball revolution provides one covers next, it is clearly possible to afterthought, and the many committees an excellent discussion topic: In what introduce important statistical concepts responsible for the voting have never ways does it follow a Kuhnian scientific (conditional probability, the logistic agreed on what constitutes a Hall of paradigm shift? How does it differ? And curve, maximum likelihood estimation, Famer. (James points out that in the early how far will the revolution go? (As I write odds ratios, and the nature of mathemati- years, it was not even clear what type of this, DePodesta has been fired, but other cal proof)—even for an audience with no player should be elected—some advo- young executives are making inroads.) formal statistics background—by taking cated the enshrinement of Eddie Grant, a advantage of the shared knowledge and marginal player but a war hero who died Conclusion intuition about baseball students bring in World War I—let alone which players Statistical arguments about who should to the course. should be elected.) As a result, there is no be in the Hall of Fame are ubiquitous. clear definition of a Hall of Famer, except A primary goal of the course, then, was Additional Topics a player of the caliber usually elected to to learn to critically evaluate such argu- the Hall of Fame. This has led to today’s ments. What constitutes a good statisti- In addition to learning about statistical state of controversy, in which a multi- cal argument or a poor one? How does and scientific reasoning, we used the Hall tude of candidates is debated by writers a statistical or scientific argument differ of Fame and baseball in general to provide and fans using a variety of standards and from other kinds of arguments? a context for discussing other sociologi- agendas. Since earlier selections justify By the end of the course, students cal, historical, and scientific issues. later ones, thereby compounding old were able to construct sound statisti- errors, a different initial selection process cal arguments and to critically think Cities and Demographics could have led to a vastly different Hall about data. In addition, they were able In discussing the effects of parks on play- of Fame. Such a role for contingency in to identify common misuses of statistics ers’ statistics, we looked at photos of sev- history is analogous to that proposed in quantitative arguments. eral old stadiums. Philadelphia’s Baker by paleontologist Stephen Jay Gould to Not all the students in the course Bowl, for instance, was known for inflat- explain the history of life. Small changes were initially interested in statistics, but ing the batting statistics of Chuck Klein in an ecosystem long ago, argues Gould because students took the course by and others who played there, as noted in his book, Wonderful Life, have led to choice, all were interested in baseball— above. The reason for Baker Bowl’s gener- far-reaching evolutionary consequences and some rabidly interested in a way not osity to hitters is clear from aerial photos: millions of years later. commonly encountered by teachers of the right field line was only 281 feet deep. introductory statistics service courses. Indeed, the stadium looked as if a large Scientific Revolutions The Baseball Hall of Fame thus provides strip of right and center fields had been In the past few years, Michael Lewis’s an ideal opportunity to discuss statistical lopped off. When I showed a photo of 2003 book, Moneyball, has been the sub- principles in a context in which many Baker Bowl, a student immediately asked ject of much controversy among base- students are passionate, making statisti- why the stadium was built that way. That ball fans. The book describes how Billy cal thinking accessible to an audience led to a discussion of how early 20th-cen- Beane, general manager of the Oakland that might not otherwise take an elective tury stadiums were located in cities and A’s, turned to statistical analysis to build course in statistics. often had their dimensions constrained a successful team on a tight budget. Mon- by the size and shape of the city blocks in eyball had not yet appeared when I was Further Reading which they were situated. Baker Bowl, for teaching my course, but if I were teach- Gould, S.J. (1990). instance, had a rail yard behind the right Wonderful Life: the ing the course today, I would certainly . field fence, clearly visible in aerial photos Burgess Shale and the Nature of History address it. In many ways, the process of New York: W. W. Norton. (see www.ballparks.com). During the 1950s de-emphasizing traditional scouting in James, B. (2001). The New Bill James His- and 1960s, however, stadiums often were favor of statistical analysis, as described built in the suburbs in the midst of huge torical Baseball Abstract. New York: in Moneyball, parallels the process outlined Free Press. parking lots, so their dimensions were by Thomas Kuhn in his classic 1970 work unconstrained and could be made sym- on the history of science, The Structure of James, B. (1995). Whatever Happened to the metrical. That led to a discussion of the Scientific Revolutions. Kuhn argues that in Hall of Fame? Baseball, Cooperstown, and the American population shift from the cities scientific revolutions, such as the quan- Politics of Glory. New York: Fireside. to the suburbs and the ways in which tum mechanics revolution in 20th-cen- Kuhn, T.S. (1970). The Structure of Scien- baseball mirrors demographic trends. tury physics, people rarely convert from tific Revolutions, 2nd Ed. Chicago: The an existing paradigm (classical mechan- University of Chicago Press. History and Contingency ics) to a new paradigm (quantum mechan- Lewis, M. (2003). Moneyball: the Art of We also discussed the history of the Hall ics). Instead, the revolution is completed Winning an Unfair Game. New York: of Fame and traced the historical roots of when a new group of scientists replaces the W. W. Norton.

CHANCE 31 R. Todd Ogden earned a PhD ups. He now works on statistical problems in paleontology. in statistics from Texas A&M in 1994 Before joining Swarthmore, he taught at Williams College and has worked in a variety of applica- and Harvard University. He became interested in statistics tion areas since then. He is an associate as a result of being a baseball fan while growing up. professor in the biostatistics department of Columbia University, with a joint appointment in psychiatry. As part of Samuel S. Wu is assistant professor this position, he works as the statistician in the Division of Biostatistics, Col- in the Brain Imaging Division of the New York State Psychi- lege of Medicine, at the University of atric Institute, a multidisciplinary group dedicated to using Florida. He is also a biostatistician at the imaging technology to study mood disorders. VA Rehabilitation Outcome Research Center and the VA Brain Rehabilitation Research Center in Gainesville, Florida, Suzanne Switzer recently earned and a specially appointed professor in a BA in mathematics and statistics from the Department of Statistics at the Tianjin University of Smi College. Curren ly, s e a ends th t h tt Finance and Economics in China. [email protected]. the Indiana University School of Library and Information Science, but when she finishes being a student, she hopes to explore the applications of statistical Andrew Yang is assistant professor methods in library and information of Biology and Liberal Arts at the School science. Until then, she’s content playing both classical and of the Art Institute of Chicago (SAIC). Irish flute and, of course, studying. [email protected]. His interests in biological categoriza- tion and the concept of race in genetics stems from his primary research areas Steve Wang is an assistant professor of evolutionary biology and the phi- of statistics at Swarthmore College. He losophy of biology. At SAIC, he teaches earned his BS from Cornell University various courses on biology and the interfaces between art, and his MS and PhD from the University design, and science, including the role of visual represen- of Chicago, where he wrote his MS thesis tation in biology. He earned his PhD in biology from Duke on Markov chain models of baseball line- University. ACCESS PROFESSIONAL RESOURCES with the American Statistical Association

MEMBERS ENJOY: A SUBSCRIPTION to Amstat News, the ASA’s monthly membership magazine, full of upcoming events and job opportunities

NETWORKING through the ASA’s regional Chapters and special-interest Sections

MEMBERS-ONLY FEATURES of the ASA JobWeb at http://jobs.amstat.org, including “Post Your Resume” and “Notify Me!”

OPPORTUNITIES to expand career horizons with the ASA’s Career Placement Service at the Joint Statistical Meetings

DISCOUNTED registration fees for the annual Joint Statistical Meetings and Continuing Education courses

ONLINE ACCESS to the Current Index to Statistics (CIS), a bibliographic index to publications in statistics and related fields

Visit us at Become a MEMBER of the ASA. Join at www.amstat.org/join. www.amstat.org, or call customer Most membership categories include a subscription to Amstat News. Student members also receive STATS: The Magazine for Students of Statistics. All members receive discounts on ASA publications, meetings, and educational service at programs. For information regarding your benefits, including how to subscribe to additional publications or register (888) 231-3473. for ASA meetings, contact customer service at (888) 231-3473 or visit our web site, www.amstat.org/join.

4 VOL. 20, NO. 1, 2007