$1 Hot Dogs in Chicago: the White Sox Wiener's Winnings

Last year, I asked "Are the White Sox Winners or Wieners?" And now, we may be able to answer the question!

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Every Wednesday since August 2, 2017, the White Sox have offered hot dogs (regularly priced $4.50) for just $1 at home games. While I first noticed that attendance was not very responsive to this promo, I also said that since only a handful of games had featured the promo, it was perhaps too early to tell and we would need to ketchup with the Sox later to see how the fans are relishing the experience.

Now, twenty-five $1 Hot Dog Days later and the results are in: everyone and their dog is enjoying the promo. The question remains, just how much money can the White Sox expect to profit from their wieners?

In order to calculate this, I first estimate how many additional tickets are sold on Wednesdays. To do this, I turn to my regular regression that I have used numerous times to predict home-game attendance (e.g., Chicago White Sox, Miami Marlins, Oakland Athletics, San Diego Padres, and, of course, Bobbleheads). This includes controlling for the day of the week, month, year, opponent, and $1 Hot Dog Days. The final result is a model that is able to explain nearly 80% of the variation in attendance.

As for the effect of the promo in question, what I find is that $1 Hot Dog Days bring in about 15% more fans than would otherwise attend - this amounts to nearly 2,500 more tickets!

But what about the cost of selling all those extra wieners? And just how many wieners are actually sold? Just how much profit does a $1 Hot Dog Day provide to the Chicago White Sox???

Unfortunately, they keep those numbers pretty heavily under wraps. But, we can make some educated guess as to what the numbers might actually be.

First, let us define how to calculate profit on a regular day:

where Π is the profit and p_t and p_h are the prices of tickets and hot dogs, respectively, a is the attendance, and q_h is the quantity of hot dogs sold. Note that the subscript H^- denotes a non-$1 Hot Dog Day. Lastly, C_F and c_h denote fixed costs and cost of a hot dog, respectively, both of which are unknown.

The National Hot Dog and Sausage Council suggest that one in four fans buy a hot dog when faced with the full price, so we can simplify the above equation:

Next, we can define a similar equation for the profit on a $1 Hot Dog Day:

Notice the subscript H for $1 Hot Dog Day and that p_h is now equal to one (I remove it entirely from the notation for simplicity).

To understand the marginal profit, we take the difference of the two aforementioned profit equations:

which simplifies down to:

And if we consider the cost of a hot dog, c_h , as a function of the price and margin, m_h , then the equation can be written as:

Since we know the change in the attendance at $1 Hot Dog Days, the average price of a ticket ($28.38), and the price of a hot dog ($4.50), the above equation is now expressed in terms of three unknowns: quantity of hot dogs sold on $1 Hot Dog Days, the margin of a regularly priced hot dog, and the marginal profit.

I can then make some educated guesses at the former two unknowns and calculate the latter. Below is a graphical depiction of the iso-profit lines, or the estimated additional profit due to $1 Hot Dog Days for various scenarios of quantity of hot dogs sold and hot dog margin.

What we see is not only that there is a huge range of possible values for $1 Hot Dog Day profit - anywhere from $30,000 to $65,000 - but also that the range is all above zero! Anyway you slice it, $1 Hot Dog Days appears to be quite the financial success.

But how much of a success depends: if the margin is below 77.8%, each additional hot dog sale has a negative impact on profit (i.e., it costs more to make a hot dog than it sells for). 

If we take an estimate of the margin from online articles, we can imagine some different scenarios:

This article suggests that Costco uses its $1.50 hot dogs as a loss-leader to entertain their members. That would imply the cost of supplying a hot dog would be greater than $1.50, and therefore the White Sox would face a upper bound margin of 67%. According to the figure above, the $1 Hot Dog Day profit would be right around the $55,000 range, almost regardless of how many additional hot dogs were consumed.

Instead, if we consider this article, the cost of supply hot dogs in bulk is stated to be 40 cents per wiener, implying a margin of +90%. Now consider that a colleague of mine just attended a $1 Hot Dog Day game bought three hot dogs: 200% more than she would have otherwise purchased! Together, these two estimates suggest the White Sox could be making a profit in that elusive $60,000+ range!

All-in-all, we can say $1 Hot Dog Days are no dog-and-pony shows, and maybe, just maybe, the top dogs running the White Sox may just know what their doing.

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$1 Hot Dogs in Chicago: Are the White Sox Winners or Wieners?

TLDR: With two months remaining in the 2017 MLB season, the Chicago White Sox found themselves playing in front of an ever-dwindling number of spectators. In an effort which was purported to reward fans, the Chicago White Sox began to offer a new type of promotional event: $1 Hot Dogs!

Ever since August 2, 2017, fans in attendance at every Wednesday game hosted by the White Sox can purchase a hot dog for $1.00 (regularly priced $4.50).

I find that there is no evidence that to suggest that $1 Hot Dog games actually see an increase in attendance. Therefore the White Sox need each fan to eat an average of 1.44 hot dogs or over 21,000 hot dogs in total in order to for the promotion to be revenue-neutral!

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With two months remaining in the 2017 MLB season, and with zero chance of reaching the post-season, the Chicago White Sox found themselves playing in front of an ever-dwindling number of spectators. Other than the two games against their cross-town rivals, the Chicago Cubs, games in which even half of the 40,000+ seats were occupied were few and far between.

In an effort which was purported to reward fans, the Chicago White Sox began to offer a new type of promotional event: $1 Hot Dogs!

Ever since August 2, 2017, fans in attendance at every Wednesday game hosted by the White Sox can purchase a hot dog for $1.00 (regularly priced $4.50). I want to investigate if this type of promotion actually makes economic sense, at least in the short-run. I begin by collecting all the attendance data for Chicago White Sox home games since 2016 from my favourite source, Baseball-Reference.com. I run a simple regression controlling for the day of the week, month, year, and opponent, and then predict the attendance for the $1 Hot Dog games.

Since the inception of the idea, there have been 11 Wednesday home games, all featuring the $1 Hot Dog promotion. There does exist a bit of an issue wherein the promotions are held on each and every Wednesday home game, however, I attempt to correct for this by using 2016 data, as well as 2017 data from before the first $1 Hot Dog game. This assumes that, aside from potential impacts from the $1 Hot Dog promotion, the day of week effect on attendance has been unchanged over the years, e.g. I assume Wednesday's have not become more popular for Sox fans since August 2017 therefore any changes to a Wednesday's attendance may be the result of the $1 Hot Dog promotion.

Below is a graphical depiction of the results of the aforementioned regression:

On average, the model predicts the attendance would be a little bit lower than it actually was for the $1 Hot Dog games. However, this result is not statistically significant: there is no evidence that to suggest that $1 Hot Dog games actually see an increase in attendance! The actual average $1 Hot Dog game attendance of 15,633 lies within the 95% confidence interval of the predicted $1 Hot Dog attendance, visually depicted by the hot dog on the left sitting within the interval of mustard on the right.

We may then ask ourselves, if the attendance is unchanged for $1 Hot Dog games, how many $1 hot dogs would the White Sox need to sell in order to be revenue-neutral? To answer this question, imagine a simple formula for calculating the revenue of a baseball team:

where TR is total revenue, p_t and p_h are the prices of tickets and hot dogs, respectively, and a is the attendance. In a publication released by the National Hot Dog and Sausage Council, I find that one in four fans purchase a hot dog at a baseball game, therefore ^a⁄₄ denotes the number of hot dogs sold during the course of a game.

Now consider the revenue equation for a regular non-$1 Hot Dog game:

where a_H- is the attendance for a non-$1 Hot Dog game. Similarly, we can form a revenue equation for a $1 Hot Dog game as follows:

where gamma represents the new hot-dog-to-fan ratio (I am - probably safely - assuming that there is an increase in demand for hot dogs when the price decreases by approximately 75%).

If we set these two equations to equal each other, we can substitute in values and solve for the value  of gamma required for the White Sox to be revenue-neutral. I use Forbes' suggested average ticket price for a White Sox game of $30. Recall that since there is no statistical evidence that a_H > a_H-, I eventually substitute a_H = a_H-.

Therefore, if the $1 Hot Dog promotion does not increase attendance, we would need each fan to eat an average of 1.125 hot dogs in order for the White Sox to just bring in the same level of revenue!

But, there does exist another potential issue, known as cannibalization. While I do not expect the fans to eat one another, I would expect some sales of nachos, burgers, and sausages to decline in favour of hot dog sales. For example, I would expect that most (if not all) the individuals who would normally purchase a $6.25 brat would now purchase $1 hot dog(s). According to the National Hot Dog and Sausage Council, one in twenty fans purchase a sausage or bratwurst, in some form or another. Therefore, we can modify the non-$1 Hot Dog game revenue and solve for a new break-even gamma.

This implies that if the $1 Hot Dog games do not impact attendance, each fan would need to eat 1.44 hot dogs on average. This is equivalent to over 21,000 hot dogs!

In the end, perhaps this promotion is not seen as too risky for the team: the White Sox need only increase attendance by 4.8% in order for the promotion to be revenue-neutral without a single additional hot dog sale. And as more promotional days pass, we will ketchup later to see if the fans are truly relishing the $1 Hot Dog games.