Do chicks dig the long ball?

The scene opens on a baseball field. The stands are mostly empty, save for the first few rows, and Mark McGwire is in batting practice, hitting home run after home run. Two women, quite attractive, watch in awe, giving off pleasurable moans as the ball travels 400 feet over the outfield wall.

Off a ways stand Tom Glavine and Greg Maddux, the latter of whom yells to the seemingly unresponsive women, “Hey, we’ve got Cy Young winners over here!” It doesn’t seem to help. Suddenly, an idea strikes the pitchers. They go shoe shopping and pick up McGwire’s preferred Nike sneakers. They take batting practice. They study hitting. They lift weights. They run stairs. They pummel each other in the stomach with baseball bats. They hit off tees. And then they take batting practice again.

Every pitch flies into the stands. At last, the women acknowledge them: “Hi, Tom,” the blonde calls out. They have reached their goal—the ladies love them. And finally Maddux puts into words what the viewer has long realized: “Chicks dig the long ball.”

Such was the famous late-90s Nike commercial. It epitomized an era that had seen a huge drop-off in attendance after the 1994 strike and then a bounce-back driven in large part by ever-increasing home run totals and challenges to Roger Maris’ single-season record. As home runs went up, so did attendance.

Or so the story goes. Today’s article is not about steroids, or why home runs increased so suddenly in the 90s, or anything like that. Rather, the question I want to ask today is, Do fans in general dig the long ball? We assume that McGwire and Sosa helped bring fans back to the ballpark, but is that actually the case? More generally, do home runs increase attendance?

We can try to examine this very basically by looking at a graph of home runs and attendance over the years:

The trend is not totally clear, though generally both home runs and attendance have increased since 1970. Overall, the correlation between the year-to-year change in home run rate and the year-to-year change in attendance per game is 0.37—significant but not particularly strong.

More importantly, that number is rendered meaningless by an old statistical axiom: “Correlation does not imply causation.” What that means is just because two numbers are correlated does not mean that one has caused the other. Just because home runs and attendance have tended to move together does not mean that attendance has gone up because of an increase in home run rate. After all, it could just as easily be the other way around—when more fans show up to the park, hitters hit more home runs—or even simple coincidence. So which is it?

Answering this question requires team-level data. If we can show that teams that hit more home runs draw more fans in a given season than do teams that hit fewer, then we will have established a strong base of evidence that high home run totals actually cause more fans to show up at the park.

But the problem is more complicated than just establishing that teams that hit a lot of home runs draw a lot of fans. First of all, teams that hit a lot of home runs tend to be good teams, so of course they’ll see higher attendance figures than low home run teams will. And secondly, teams that hit a lot of home runs tend to be teams that can afford to sign expensive power hitters, and those teams are often flush with cash because they play to a larger fan base—say, New York or Los Angeles.

This leaves us with a problem: Each team needs to be controlled for itself. If the Yankees hit a lot of home runs and draw a lot of fans, that still isn’t evidence that the fans are coming specifically for the home runs. What we need is to see if Yankee teams that hit more home runs draw more fans than do other Yankee teams that hit fewer home runs, even when we hold the overall quality of the team constant.

So how can we do that? Here’s my method.

First, I adjust all statistics—attendance, home runs, wins—for the league average and translate them into 2007 numbers, so that the average team in any season ends up with a bit under 33,000 fans per game, 160 home runs and 81 wins. Then, I adjust each statistic for the team’s historical (league-adjusted) average, so that again, each team averages around 33,000 fans per game, 160 home runs and 81 wins between 1970 and 2007. What this approach does is place each team on a level playing field. Essentially, we’re correcting for all the biases I raised.

I then ran a regression trying to predict attendance per game for each team-season based on the following factors:

1. Adjusted wins that season.
   
2. Adjusted wins the previous season.
   
3. Whether or not the team made the playoffs the previous season.
   
4. Whether or not the team won the World Series the previous season.
   
5. Whether or not the team was playing in a new stadium that season.
   
6. Whether or not the team was an expansion team the previous season.
   
7. And finally, the number of adjusted home runs hit by the team that season.

If the final variable is positive and significant, then—controlling for all these things—teams do indeed draw more fans when they hit more home runs.

So is that the case? Let’s go to the results:

VARIABLE	           COEFFICIENT     P-VALUE
Constant term        -1,478,097       0.000
Tm_adj_wins              30,707       0.000
Tm_adj_prev_wins         15,714       0.000
Prev_playoffs           254,407       0.000
Prev_WS                 159,319       0.103
New_stadium             701,985       0.000
Prev_expansion          611,264       0.000
Team_adj_HR               2,027       0.001

What the above table tells us is that each win in a season adds almost 31,000 fans in attendance that season and 15,000 the next. Making the playoffs is worth about 250,000 extra fans in attendance the next year, while winning the World Series adds 160,000 on top of that. A new stadium is worth about 700,000 extra fans, while an expansion franchise sees more than 600,000 extra fans in attendance in its second year.

And what of home runs? Well, the data tell us that each home run puts about 2,000 extra fans in the stands, and that number is highly significant. In other words, although Ryan Howard and Todd Helton are roughly equally valuable players, Howard is probably worth an extra 60,000 fans a season in terms of attendance.

That is a very large difference. It’s so large, perhaps, that we may want to examine alternative theories. Maybe fans prefer run scoring in general and not home runs specifically? Well, if we re-run this regression using an adjusted runs measure instead of home runs, we find that the coefficient for runs is insignificant (p = .511), and runs have no discernable effect on attendance. Actually, if we add adjusted home runs back into the equation, we find that on the balance, more run scoring leads to lower attendance once we control for home runs. Perhaps that’s because other ways of scoring runs take up a lot more time (and without the potential of catching a big hit!), and thus make the game less enjoyable.

Either way, Maddux’s theory appears to hold up: Chicks dig the long ball—and so does everyone else.