Revisiting the Ex-Cub Factor
This article was published in the Fall 2014 Baseball Research Journal.
Baseball is a superstitious sport. Players skip over foul lines on the way to the dugout, refuse to change their socks during a hitting streak, and avoid talking to a pitcher while he is hurling a no-hitter. Some superstitions have as their subject not only an individual player but an entire team. For instance, the Curse of the Bambino supposedly befell the Boston Red Sox after they sold Babe Ruth to the New York Yankees, and resulted in their failing to win any of the next 83 World Series.1 (The Red Sox ended the Curse by defeating the St. Louis Cardinals in the 2004 World Series.)
Another such superstition involves the Curse of the Billy Goat, which supposedly explains why the Chicago Cubs have not played in a World Series since 1945.2 The story goes that William Sianis, the owner of the Billy Goat Tavern in Chicago, bought two tickets to Game Four of the 1945 World Series, which pitted the Cubs against the Detroit Tigers. One of the tickets was for Sianis; the other was for his goat, whose name has been variously given in different references as either Murphy or Sonovia.3 The goat was refused admission to Wrigley Field and, to add insult to injury, Sianis was told that the reason the goat would not be allowed into the park was “the goat smells.” Sianis put a hex on the Cubs, stating that they would never again play in the World Series.
THE EX-CUB FACTOR IS BORN
In 1981, Ron Berler, then a columnist for the Boston Herald American, invented and popularized another superstition that is also related to the Chicago Cubs: the Ex-Cub Factor (ECF). From his review of baseball statistics dating back to 1946 (the first season of baseball following the Cubs’ final World Series appearance and the pronunciation of the Billy Goat Curse), Berler determined that,
According to the Ex-Cub Factor, it is utterly impossible for a team with three or more ex-Cubs to win the [World] series.4
Berler explained that the ECF was the result of the “Cubness” inherent in ex-Cubs:
“Cubness” is a term one encounters again and again when speaking with ex-Cubs. It is synonymous with the rankest sort of abject failure, and is a condition chronic among all Cubs, past and present.5
THE FACTOR IS MODIFIED
Pulitzer Prize-winning Chicago columnist Mike Royko also believed in the relationship between “Cubness” and the Ex-Cub Factor. He likened the ECF to a virus that infected a baseball team:
And when there are three [ex-Cubs], this horrible virus comes together and multiplies and becomes so powerful it makes the other players weak, nearsighted, addle-brained, slow-footed and lacking in hand-eye coordination.6
In 1986, Royko expanded the idea of the ECF into what he called his “Modified Cub Factor”: “A team with no ex-Cubs probably has the edge on a team that has even one.”7
Royko stated that, beginning in 1946, only one of twelve teams with three or more ex-Cubs on their World Series rosters had won (the 1960 Pittsburgh Pirates). Other, more recent, authors have made similar claims about the consistency of the ECF, mentioning the 2008 Philadelphia Phillies and 2001 Arizona Diamondbacks as the only other teams to defy the ECF.8, 9
Van Santen, a lifelong Chicagoan, grew up knowing of the ECF. During a visit to the Hall of Fame in 2013, he proposed to May that the two study and write about the Factor. May suggested that the study include both Berler’s and Royko’s takes on the ECF. Thus began our research into the dual Ex-Cub factors.
STUDYING THE EX-CUB FACTORS
May, a mathematician, suggested that the examination begin with precise definitions of the important terms.
Ex-Cub: An ex-Cub is a current or former player in Major League Baseball in whose career statistics the name Chicago Cubs (or some abbreviation of that name) appears at least once as a team on whose roster he was included.
Ex-Cub Total: This is the number of ex-Cubs on the roster of a given team.
Ex-Cub Factor: A team possesses—some would say, “is smitten with”—this if its roster contains at least three ex-Cubs.
We were then able to state the Berler and Royko conjectures precisely.
The Berler Conjecture: In the World Series, if only one of the two competing teams possesses the Ex-Cub Factor, that team will lose the Series.
The Royko Conjecture: In a World Series between two teams with different numbers of ex-Cubs on their rosters, the team with the larger Ex-Cub Total will lose the Series.10
THE EX-CUBS ARE OUTED
To make our analyses comparable to those of Berler and Royko, we used their time frame of 1946 through 2013. Our first task was to track down each man who had appeared on a World Series roster in some year during that 68-year period. We drew our data from a variety of sources. The two most helpful were the tome authored by David S. Neft and Richard M. Cohen: The World Series: Complete Play-By-Play of Every Game 1903–1989, and the 2011 edition of The Elias Book of Baseball Records, by Seymour Siwoff.11, 12
These invaluable works include, among their many useful features, the complete roster—that is to say, the list of all 25 men who were eligible to play, not just those who actually set foot onto the playing field as batters, fielders, pitchers, or runners—of each team in every World Series from 1903 on. The 1979 Pirates provide a perfect example of the value of these books to our study. Box scores from other sources told us about 24 of the 25 men on the Pirates’ Series-winning roster; however, they excluded late pitcher Dave Roberts, who was indeed a Pirate but was the only member of the pitching staff, and the team, not to play in the Series.13 Roberts was a member of the Cubs 1977–78, signed with the San Francisco Giants as a free agent in February 1979, and was traded to the Pirates that June.
Thus, his name should be added to those of Matt Alexander and Bill Madlock, giving the Pirates three ex-Cubs on their World Series roster and adding one to the number of World Series in which the Ex-Cub Factor figured and Berler’s Conjecture was in play. Roberts’s name appears in The World Series and The Elias Book. Every other source that we consulted mentioned only the Pirates whose names appeared in a box score, and thus omitted him.
To obtain the full rosters of the 2011–13 Series, we consulted the hometown newspapers of the participating teams. The most helpful online source that we used in our work was Baseball-Reference.com.14 Others were Baseball Almanac and Retrosheet.15, 16
The players’ strike of 1994 and the resulting cancellation of that Series reduced from 68 to 67 the number of Series we needed to study (and the number of teams to 134). Each of those Series involved two 25-man rosters; so we needed to fill 67 x 2 x 25, or 3,350, roster slots. (Since, however, many players found themselves on more than one World Series roster, we ended up needing to comb fewer than 3,350 career records.) Because of the completeness of our combined sources, we were able to fill all the slots.
Next, we searched the 134 rosters for ex-Cubs. This involved looking up the career statistics of each of our World Series roster-occupants. As an example, Mark Grace was a playing member of the 25-man roster of the Arizona Diamondbacks team that won the 2001 World Series. Records (and our personal knowledge of baseball) indicated that Grace had played for the Cubs from 1988 through 2000. Thus, Grace was an ex-Cub.
As our definition of ex-Cub implies, we considered a player to be an ex-Cub regardless of how briefly he had been under contract to the Cubs, so long as he had been with the Cubs before playing on the World Series team under consideration. The number of ex-Cubs on each of the 134 teams was recorded using a Microsoft Excel spreadsheet. Excel was also used to determine the number of instances in which at least one team had at least three ex-Cubs on its roster (i.e., satisfied the Berler Conjecture) and the number of instances in which one team had more ex-Cubs than the other (i.e., met the Royko Conjecture).
THE FACTOR'S DAMAGE IS ASSESSED
A study of the table accompanying this article (see below) reveals that the Berler Conjecture has experienced remarkable success, albeit in a small sample. Twenty-two times since the pronouncement of the Curse of the Billy Goat, it has been “in play”—that is, has had its hypothesis, that exactly one of the two teams possesses the Ex-Cub Factor, satisfied.17 In 17 of those Series, the team smitten with the Ex-Cub Factor has lost. The Berler Conjecture thus has had a success rate of 17/22, or approximately 77 percent, from 1946 through 2013.
The record of the Royko Conjecture is less impressive but nevertheless positive. It has been in play for 56 of the 67 World Series held since 1945, and it has been correct in 32 of those 56. This is a rate of success of 57 percent. Although bettors were not so safe in using the Royko Conjecture from 1946 through 2013 as they were with the Berler, they still won more than half the time.18 There is one further observation worthy of note about the Royko Conjecture. In the 34 World Series in which it was in play and the Berler Conjecture was not, the Royko proved true 15 times. This is a success rate of 44%.
IS EITHER CONJECTURE OF USE GOING FORWARD?
So much for the past. What about the future? Is either conjecture a good predictor of the winners of World Series yet to come? Since the Royko Conjecture has a longer track record than the Berler, in the sense that it has been in play for a larger number of Series than the latter, let us look at it first. A standard technique of statistical inference allows us to say, with 95% confidence, that the Royko Conjecture will correctly predict the World Series winner between 44% and 70% of the time, whether or not the Berler Conjecture is in play.19
Although the success rate of 70% looks encouraging, the 44% figure is much less so. In light of these mixed results, we ran a hypothesis test to determine whether the success rate of the Royko Conjecture was greater than 50%.20 The test allowed us to infer that, at the .05 level of significance–as a matter of fact, at any level up to .14—the data from the World Series of 1946 through 2013 fail to provide evidence sufficient to conclude that the Royko Conjecture will correctly predict the winner of the Series more than 50% of the time.
When the Berler Conjecture fails to be in play and the prognosticator is forced to rely on the Royko, he or she can be 95% certain that it will correctly predict the Series winner between 27% and 61% of the time. A hypothesis test similar to the one described in the paragraph immediately above says that the 1946-through-2013 World Series data provide even less evidence that the Royko Conjecture will correctly predict the Series winner more than 50% of the time.
Let us infer about the long-term prospects of the Berler Conjecture. The size of our Berler sample required us to employ a technique different from the one we applied to the Royko sample. The method, Wilson’s Adjustment for estimating a proportion of success21, yields a 95%-confidence interval of approximately (0.560,0.901). In other words, according to the Wilson Adjustment, we can say, with 95% confidence, that the Berler Conjecture will be correct between 56% and 90% of the time. Although the Berler Conjecture has come into play less often than the Royko (22?67, or 33% of the time, as opposed to 56?67, or 84%, of the time for the Royko), it appears that when it is in play it is more likely to yield a correct prediction than the Royko.22 In addition, it is almost certainly a better predictor than a coin-flip.
WHAT HAVE WE LEARNED?
Our work shows that, when the Berler Conjecture is in play, it is a fairly reliable guide to predicting the World Series winner. When it is not in play and the Royko Conjecture is, should one use the latter as guide? Almost certainly not, for the World Series from 1946 through 2013 provide evidence glaringly insufficient to conclude that the Royko Conjecture works any better than a coin-flip in picking the winner when the Berler Conjecture fails to be in play. (We are unaware of any method that has experienced a success-rate of more than 77% in predicting World Series winners during that period of time. We would appreciate any information on the existence of such a method.)
WHERE DO WE GO FROM HERE?
An answer often leads to more questions, and our work with the Ex-Cub Factor is no exception to this rule. A reasonable next task would be the replicating of our work for, say, an ex-Yankee, ex-Cardinal, or ex-White Sox factor. Doing so would provide a way to test whether the Ex-Cub Factor has any significance. If, for example, there turned out to be an ex-Yankee factor that was similar to the Ex-Cub Factor in the damage it wrought on a World Series team, the credibility and significance of the Ex-Cub Factor would pale, possibly into oblivion. If, however, no ex-non-Cub factor were discovered, evidence would mount that Ron Berler and Mike Royko have discovered and elucidated a significant tool for predicting the winner of the World Series.
Finally, critics might argue that the amount of time spent as a member of the Cubs would play a significant role in whether or not a player has acquired enough “Cubness” to affect the play of his post-Cub teammates. As a result, it might also be helpful to assess the Ex-Cub Factor when the amount of time on the Cubs roster is taken into consideration.
LEE MAY, Ph.D. (no relation, so far as he knows, to the former major-league slugger), is a professor of mathematics and computer science at Salisbury University in Maryland. He earned his bachelor’s degree at—and played some first base for—Wake Forest University, and he received his doctorate from Emory University. He is probably best known at Salisbury for his course “Statistics through Baseball,” which he designed and has taught since 2006. He has been a member of SABR since 2002.
FRANK VAN SANTEN, Ph.D., is a member of the faculty in the Speech, Language, and Learning Program in the Roxelyn and Richard Pepper Department of Communication Sciences and Disorders at Northwestern University in Evanston, Illinois. He grew up in Chicagoland and has been a lifelong Cubs fan. His mother was a Mike Royko fan, and his grandfather was recruited as a pitcher for the White Sox (He turned them down because he would make more money working at the local steel plant).
World Series Teams, Ex-Cub Players, and Fulfillment of Berler or Royko Conjecture by Year
|Year||Winning Team||ECT||Ex-Cubs||Losing Team||ECT||Ex-Cubs|| Berier true?
|1946||Cards||0||Red Sox||1||Rip Russell||NO||YES|
|1959||Dodgers||0||White Sox||1||Turk Lown||NO||YES|
|1967||Cards||1||Lou Brock||Red Sox||0||NO||NO|
|1970||Orioles||1||Moe Drabowsky||Reds||2||Ty Cline,
|1975||Reds||1||Bill Plummer||Red Sox||0||NO||NO|
|1977||Yankees||1||Ken Holtzman||Dodgers||3||Mike Garman,
|1985||Royals||1||Larry Gura||Cards||2||Bill Campbell,
|1986||Mets||0||Red Sox||1||Bill Buckner||NO||YES|
|1988||Dodgers||1||Jay Howell||A's||2||Dennis Eckersley,
|1992||Blue Jays||2||Joe Carter,
|1993||Blue Jays||1||Joe Carter||Phillies||2||Danny Jackson,
|1994||No World Series|
|1996||Yankees||1||Joe Girardi||Braves||3||Mike Bielecki,
|1997||Marlins||1||Alex Arias||Indians||1||Paul Assenmacher||NO||NO|
|1998||Yankees||1||Joe Girardi||Padres||1||Randy Myers||NO||NO|
|1999||Yankees||1||Joe Girardi||Braves||3||Jose Hernandez,
|2002||Angels||1||Jose Molena||Giants||3||Benito Santiago,
|2003||Marlins||1||Lenny Harris||Yankees||2||Felix Heredia,
Jon Lieber (DL)
|2004||Red Sox||2||Bill Mueller,
|2005||White Sox||1||Ross Gload||Astros||1||Jose Vizcaino||NO||NO|
|2006||Cards||1||Jose Vizcaino||Tigers||1||Neifi Perez||NO||NO|
|2007||Red Sox||0||Rockies||1||LaTroy Hawkins||NO||YES|
Jerry Hairston Jr.,
|2010||Giants||1||Mike Fontenot||Rangers||1||Andres Blanco||NO||NO|
|2013||Red Sox||1||Ryan Dempster||Cards||0||NO||NO|
- 1. “The Curse of the Bambino,” CNN/Sports Illustrated, 2001 (http://sportsillustrated.cnn.com/baseball/mlb/news/2000/03/22/the_curse_timeline).
- 2. John Snyder, Cubs Journal: Year by Year & Day by Day with the Chicago Cubs Since 1876 (Cincinnati, Ohio: Emmis Books, 2005), 343.
- 3. The Billy Goat Tavern’s own website names the goat Murphy [www.billygoattavern.com/legend/curse/] while the name Sonovia appears in John Snyder, Cubs Journal: Year by Year & Day by Day with the Chicago Cubs Since 1876 (Cincinnati, Ohio: Emmis Books, 2005) 343.
- 4. Ron Berler, “The Ex-Cub Factor: Theory will Decide World Series Winner,” Boston Herald American, October 15, 1981.
- 5. Ibid.
- 6. Mike Royko, “The Ex-Cub Factor Will Destroy A’s in the Series,” Chicago Tribune, October 19, 1990.
- 7. Ibid., “The Cubs World Series Legacy Has Traveled Well Beyond Wrigley Field,” Chicago Tribune, October 20, 1986.
- 8. Al Yellon, “Is the Ex-Cub Factor Dead?” Baseball Nation, October 19, 2011 (www.baseballnation.com/2011/10/19/2500278/2011-world-series-ex-cub-factor).
- 9. Dave Wischnowsky, “Wisch: Behold, The ‘Ex-Cubs Factor’ is Alive and Well,” October 19, 2011 (http://chicago.cbslocal.com/2011/10/19/wisch-behold-the-‘ex-cubs-factor’-is-alive-and-well/).
- 10. Royko dubbed this “the Modified Cub Factor” in the Chicago Tribune of October 17, 1986.
- 11. The World Series: Complete Play-By-Play of Every Game 1903–1989. New York: St. Martin’s Press, 1990.
- 12. The Elias Record Book, New York, NY: Elias Sports Bureau, Inc., 2011. We were pointed to this reference by one of the reviewers of our manuscript. We thank both reviewers for their helpful comments and suggestions.
- 13. Jenifer Langosch, “Former Hurler Roberts Passes Away,” mlb.com, January 9, 2009. (http://mlb.mlb.com/news/article.jsp?ymd= 20090109&content_id=3738241&vkey=news_mlb&fext=.jsp&c_id=mlb). Teammate and pitcher Kent Tekulve described Roberts as being integral to the Pirates’ World Series victory. Prior to pitching a scoreless ninth inning in game two against the Baltimore Orioles, Tekulve had eaten strawberry shortcake at a Baltimore restaurant. With the Pirates down three games to two and returning to Baltimore, Roberts encouraged Tekulve to go back to the same restaurant and have strawberry shortcake before he pitched again. Subsequently, Tekulve pitched four 2?3 innings of one-hit shutout baseball, securing the final two wins for Pittsburgh. Once again, superstition had manifested itself in baseball.
- 14. http://www.baseball-reference.com
- 15. http://www.baseball-almanac.com
- 16. http://www.retrosheet.org
- 17. In the 2009 Series, between the Yankees and the Philadelphia Phillies, each team had exactly three ex-Cubs on its roster. This violated the hypothesis of both the Berler and Royko conjectures.
- 18. A brief review of the numbers also suggests that there is some support for three ex-Cubs on a World Series team (as opposed to two or four or five ex-Cubs) being a “tipping point” or critical mass for activating the Ex-Cub Factor. Among the 67 World Series teams reviewed, the only one that had five ex-Cubs lost its only Series (0–1). Those with four ex-Cubs won 33 percent of the time (1–2), and those teams with three ex-Cubs won only 22 percent of the time (4–14). In contrast, teams with only two ex-Cubs won 63 percent of the time (17–10).
- 19. See, for example, James T. McClave and Terry Sincich, A First Course in Statistics, 11th edition (New York: Pearson Education, 2013), 265
- 20. Ibid., 365.
- 21. Ibid., 267.
- 22. We can say only that the Berler Conjecture “appears” to be a better predictor than the Royko because of the fact that the two confidence intervals, (0.44, 0.70) for the Royko and (0.56, 0.90) for the Berler, overlap.