Maybe it was all the resistant starch beforehand, or a ton of time in the ice tub, but I just had the craziest dream the other night.
I dreamed I was with my friends, and the "Birthday Problem" came up. That is the one that many quant-y folks have run into in a statistics class. It goes like this:
There are 23 people in a classroom. What is the probability that at least one of them has the same birthday?
The probability is astoundingly high by most people, because the natural inclination is to think that this is very very rare. My students mouths always dropped open when the answer was revealed, and it really got them thinking that maybe statistics wasn't so useless after all.
I had one student who was a real go-getter, and in her spare time, she liked to rent roach coaches, create interesting menus and hang around the local sports stadiums for a quick buck. Unfortunately, many other folks in the restaurant biz hadn't run into the problem.
Anyway, where was I?
Oh yeah, the dream.
I decide to explain the birthday problem in great detail to my quant-y friends. We arrange for a short presentation at a hotel we're staying at. Other hotel guests get wind of the presentation, and by the time I am ready to start, the room is full of people with all sorts of interests and levels of understanding. It gets quite comical. I decide to start with some basics, and somehow I get into a discussion of the history of industrial statistics. My new students are enthusiastic, but needy and time-consuming, so I remind myself and them what the talk is really about. As I go back to the technical discussion of the birthday problem, most of the lecture-crashers leave, and I am left with my original presentation and my original friends.
As most dreams go, I never get to the presentation. I wake up to my house-flipping neighbor's construction crew jack-hammering their front porch, and I sit there for awhile with my day-brain, wondering how I could actually describe the birthday problem more easily, and for that matter, why did this dream even come up?
Earlier I was reading about the percentage of celiacs, which is now around 1 out of 100 people if you include the folks who don't know they have it yet. I had also gotten off the phone with a family member. We were planning another mandatory multi-day get-together. I was told I was "on my own" with the food situation, but also that we weren't going to make it a big-deal food-prep week like many of our gatherings. Basically, it was, "You can't eat and you can't cook." I was pretty mad about this. (Said relative has now thought, back-tracked, and decided better accommodation was a good idea.) But it got me thinking about how places like Starbucks and Panda Express pretty much say, "Hey Celiacs! You're on your own here. If you have some sort of problem, then don't eat ANY of our food."
And I thought, they probably think that there isn't much celiac to accommodate, right? Isn't it like they are going to lose around .1% of their customer base by flipping celiacs the bird?
Like the birthday problem, the actual consequences of their decision are much larger. The way to solve the birthday problem is not to look at how many people have the same birthday, it is to look at how many ways the students in the classroom CANNOT have the same birthday divided by the total possible ways that they can all have birthdays. That is pretty easy to do, and then you just subtract that from one to get the answer.
So here's the restaurant problem. It is not that they will lose even 1 percent of business. People usually go to restaurants with other people. So in order to see impact on restaurants, you have to calculate the probability that NONE of the dining party has celiac and then subtract from 1.
I have done the calcs, and put together a little table, showing the reduction in business if a typical table of 4 or 6 decides not to eat there if the restaurant refuses to provide workable gluten-free options. The various percentages of celiac or wheat intolerances are also shown based on estimates by Drs. Fasano and Davis. Of course, this calculations assumes independence, and we all know by now that this is not really the case with dining families, since it is an inherited disease. So if one person has celiac, the others are much more likely to have it as well. But, the table does work for friends.
Percentage C or WI Table of 4 Table of 6
1% 4% 6%
7% (Fasano est.) 25% 35%
37% (Davis est.) 84% 94%
You can see that the lost business starts to get pretty high. Currently, it is pretty easy to ignore the celiacs, either by not offering appropriate menu choices, or improper preparation. But it is getting pretty hard to ignore the gluten-intolerant. This is probably what is going on with Lean Cuisine, bread stores, and even places like Red Lobster.