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September 10, 2003

Lies, Damned Lies

Loopy in the Loop

by Nate Silver

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It was a good Monday morning in Chicago. The Bears' embarrassing loss in San Francisco was hardly noticed; the looming prospect of six months of gloomy weather dampened no one's spirits. The start-of-the-workweek blahs were tempered, and 30% fewer cups of coffee were consumed, except by those who, toasting their heroes, reveled late into the night in the pubs of Bridgeport and Wrigleyville, 8 a.m. conference calls be damned. It was the 8th of September, and the Cubs and the White Sox were in first place. But for a few old-timers who spoke in frenzied hushes of billy goats and black stockings, nobody could remember such a thing happening before.

---

You'll need to excuse me for indulging my poetic license; there's a reason why I stick to non-fiction. But it is an awfully good time to be a baseball fan in Chicago, with teams on both sides of town good bets to reach the post-season, something that hasn't happened since the Cubs and Sox met in the World Series of Base Ball in 1906. In their honor, let's take look at the dynamics of the two-team market in Chicago.

It's a well-established fact that teams that have a rival in their own market compete for scarce resources like television and radio contracts, media exposure, and fan loyalty. For those reasons, it's safe to assume that a club in a two-team market will not make as much money, or draw as many fans, as if it had the market all to itself. But we want to get at a somewhat more specific question here: How much does the success or failure (as opposed to the mere presence) of the crosstown rival affect the success of the other club?

The Cubs have not always been the box office juggernaut that we've seen in the Sammy Sosa Era. The team limped through much of the '70s in the bottom half of the league in attendance, averaging around 15,000 per for the decade. The Cubbies' big attendance turnaround came in 1984. Prior to that Orwellian year, they'd never averaged 25,000 fans per game; since then, they've only had one season in which they failed to meet that threshold.

The increase in attendance was the result of the confluence of several, rather unrelated events:

  1. The 1984 team won the NL East, ending a nearly 40-year post-season drought for the Cubs.
  2. Cable television penetration had expanded rapidly in the previous decade, and WGN was beamed into tens of millions of homes. Rather smartly, the Cubs recognized that their broadcasts could be used as advertisements for the ballpark itself, thus improving its profile.
  3. The Wrigleyville neighborhood was at the start of a long transformation from working class to yuppie heaven.

Meanwhile, across town, the White Sox were struggling. Old Comiskey Park and the neighborhood surrounding it were decaying, and so was the team on the field. After winning 99 games and drawing 2.1 million to Comiskey in 1983, the White Sox watched as their attendance dropped to dead last in the American League by 1989 amidst threats that the team would be moved to Florida. The opening of New Comiskey in 1991 helped matters, especially in the early going. But as a box office draw, the Sox now play second fiddle to the Cubs, whose attendance has continued to increase through good times and bad:

Let's try and develop a simple model for predicting Cubs per-game attendance. We will take into account three factors: the Cubs' winning percentage in the current season, the Cubs' winning percentage in the previous season, and an estimate of the Gross Metropolitan Product for the City of Chicago for the year in question. The latter factor is the tricky bit: it is estimated by U.S. per capita GDP in 1996 dollars, times Chicago population as provided by the census bureau. For example, Chicago's GMP for the year 1960 is estimated at $46.7 billion (3.55 million people at $13K each). In 2000, the GMP was $94.3 billion (2.89 million people at $33K each). While that approach is more complicated than using a linear variable to represent the year, it's important to account for the fact that baseball attendance has continued to increase with the country's expanding wealth, and using the GMP estimator is considerably more accurate than looking at time alone.

In any event, our little model is pretty good at estimating Cubs attendance. Looking at all seasons since 1946, the model explains about 78% of the variance in Cubs attendance, and all three variables are statistically significant. I'll present the key terms from the regression here for those who are interested:


Variable                        Coef.   t       P>(t)
Chicago GMP (billions of 1996$) 411.8   11.65   0.000
Cubs Winning Percentage (n)     25416   2.53    0.014
Cubs Winning Percentage (n-1)   20492   2.21    0.032
Constant                       -28041  -4.90    0.000
                                        R^2:    0.775

To translate that into something that's easier to understand, each additional win is estimated to boost Cubs attendance by 23,000 people, spread out between the current season and the season following. The long-standing proposition that Cubs attendance is insensitive to the quality of the team on the field doesn't hold up very well here; it's only been very recently that there's enough excess demand for Cubs tickets that they draw well even when they aren't playing well.

But what if we introduce another factor: White Sox winning percentage. As it turns out, while there is little discernable effect stemming from White Sox winning percentage in the current season, there is a statistically significant effect (at the 90% confidence level) related to Sox % in the previous season. It seems that the two teams are competing to some degree for season-ticket sales, which are driven largely by success in the previous season, and which are more of an either-or proposition than are single-game tickets. Here are the results of the new model:


Variable                        Coef.   t       P>(t)
Chicago GMP (billions of 1996$) 415.4   12.05   0.000
Cubs Winning Percentage (n)     25163   2.57    0.013
Cubs Winning Percentage (n-1)   17554   1.92    0.061
Sox Winning Percentage (n-1)   -15542  -1.97    0.055
Constant                       -18900  -2.60    0.012
                                        R^2:    0.791

Does the same thing hold on the other side of town? Interestingly, it doesn't: White Sox attendance appears to be relatively insensitive to Cubs winning percentage. Curiously, White Sox attendance is also rather insensitive to Sox winning percentage in the year previous, which suggests just how dependant the Sox are (and have always been) on walk-up sales.

The White Sox attendance model is specified below. (Note that we've included an additional term to account for the "honeymoon effect" associated with the opening of New Comiskey. It's a dummy variable that takes on the value of five in 1991, the first year that the new park was open, and decreases by one every year until the effect is presumed to run out in 1995).


Variable                        Coef.   t       P>(t)
Chicago GMP (billions of 1996$) 162.5   5.81    0.000
Sox Winning Percentage (n)      35551   5.52    0.000
New Comiskey dummy              3562    7.49    0.000
Constant                       -11903  -3.17    0.003
                                        R^2:    0.759

Confused? Good; I'm a little confused, too. But what I think is happening is as follows:

  • The Cubs have a fan base full of Cubs fans (including many tourists), who will come out to Cubs games regardless and don't care so much about the quality of the team on the field. Though I've tried to refute the notion that Cubs attendance is insensitive to team quality, they have their share of loyalists.

  • The White Sox also have a fan base, but they're a more demanding breed and want to see their team play well before turning out.

  • Next, you've got plain old baseball fans like me, who will go to more games if both teams are playing well

  • Finally, you've got a set of potential season-ticket buyers, presumably from the corporate sector, who need to pick and choose between the two teams, but tend to default to the Cubs, all else being equal.

Nothing like linear regression to take all the joy out of a pennant race, huh?

I ran a similar analysis for the other two-team markets--Los Angeles, New York, and the San Francisco Bay--but no city except for Chicago exhibited attendance patterns that were interdependent in this way. That may have to do with the relative ease of transport between the two parks--Wrigley is about 20 minutes away from U.S. Cellular Field on the Red Line, with the Loop stuck halfway in between--so Chicagoans can afford to discriminate based on team quality in a way that residents of other two-team cities can't.

In any event, it's going to be a fun September in Chicago. Check that: a fun October.

Nate Silver is an author of Baseball Prospectus. 
Click here to see Nate's other articles. You can contact Nate by clicking here

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