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

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.

**If I had a dollar for every reader ...**

Turns out I actually can! (or at least fractions of a dollar).

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