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!
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, pt and ph 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 aH- 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 aH > aH-, I eventually substitute aH = aH-.
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.