Single-issue customers – How to count vegetarians

You’ve no doubt heard of single-issue voters. People who vote for a candidate purely based on issues like abortion, capital punishment, gun control and so on. But what about single-issue customers? That is, customers who won’t patronize your business because it’s so unfriendly to smokers, vegetarians, or whatever. How many of those groups can you afford to alienate? Maybe not as many as you think.

I’ve been a vegetarian since 1982 if I remember correctly, which is hard what with my brain fried from malnutrition from not eating dead cows and all. Anyway, back then going to restaurants as a vegetarian was a disappointing affair even in lefty liberal bastions like Burlington, Vermont, where I lived at the time. Burlington was on the verge of electing a socialist mayor and had already made minor local celebrities out of two hippies named Ben and Jerry, but it was still quite a challenge to find a vegetarian meal in a restaurant. When my brother took me out to eat and I had to settle for a baked potatoe for dinner, he declared me a cheap date.

Since then, it’s become much easier to find a vegetarian meal, especially in California, but for about the first time in my twelve years in California, I ran up against the wall. We picked up my hungry in-laws at Fresno airport to whisk them off to Yosemite and decided to eat at the rather fancy, supposedly award-winning Steak and Anchor restaurant at the Piccadilly Airport Hotel.
Once seated, it turned out there was not a single vegetarian item on the menu. I mentioned that to the waiter and he said, unhelpfully, that I could look through the menu for ingredients I liked, and ask the chef for something made from those ingredients. Since there were hardly any vegetarian ingredients mentioned, that didn’t get me very far. In similar situations in the past, the waiter has typically offered to go talk to the chef to get a list of options. Anyway, so what they served me was an attrocious salad.

When the restaurant manager came by to ask how everything was, I said politely that it was "fine" and then thought better of it. He would probably want to know how I really felt, right? So I called him back and said I was actually quite disappointed that there wasn’t a single vegetarian option on the menu. He said they used to have one on the menu, but it sold poorly, and therefore they removed it. At that point I had to explain to him that his math for counting vegetarians was wrong.

How the restaurant counts vegetarians

I’m guessing they figure the value of vegetarians like this:

  • Add up the number of times a customer orders the vegetarian dish.
  • Compare it to the number of times customers order each of the other dishes.
  • If you’re planning to cut the three worst-selling dishes and the vegetarian dish is the second worst-selling, it gets cut from the menu.

How they should count vegetarians

But here’s the problem with that: vegetarians do not typically eat alone and they do not typically dine only with other vegetarians. They will not, however, go to a restaurant that has nothing to offer vegetarians. So if you lose the vegetarian’s order, you lose the whole group. So the proper way for a restaurant manager to count vegetarian meals is like this:

  • Add up the number of times customers order the vegetarian dish.
  • Multiply that number times the size of your average group.
  • Now use that number to rank order the importance of offering a vegetarian meal on your menu, because that’s the true income that vegetarian meal represents.

The best estimates are that in 2008, 3.2 percent of Americans are vegetarians, according to research conducted by Harris Interactive and commissioned by Vegetarian Times. Additionally, 10 percent "say they largely follow a vegetarian-inclined diet." Let’s take the real vegetarians only though. That means that only about one in thirty customers should be a vegetarian. But let’s say that the average groups size is three. That means that the chance of there being one vegetarian in the group is 9.3% (see Notes below). But here’s the killer. Occasionally you have groups of 10, which is presumably a nice, high-profit group.
That group has a roughly 30% chance (30.1% actually) of having a vegetarian who will not want to patronize a restaurant with no veggie items. So you could actually lose out on almost 1/3 of all large groups. As group size increases, the chance of taking the vegetarian menu into account increases and your chance of seeing that group in your restaurant goes down.

Most restaurant managers get it. This one did not (though he was real friendly and nice). So here’s the end result of that: I will never go to that restaurant again. It no longer matters if they add a vegetarian item or not. It’s too late. They’ve lost me as a customer. I’m not being petty or vindictive, it’s just that I will never bother to check. I’ll try the Holiday Inn next time and if they have no veggie meals, I’ll just give up on the airport dining, but why would I take the time to go back on the off chance they’ve added something for me? It’s just not a good investment of my time. They’ve also lost as customers every hungry passenger I will ever pick up at the airport, whether vegetarian or not.

So Who Cares? I Don’t Serve Food

Fine. You can do without vegetarians, but that’s just one example of how a small group can cost you a lot of customers. In a similar vein, my mother-in-law is hearing-impaired. If a restaurant is particularly noisy, we don’t go back. Of course this can apply to any type of business. So you have to ask yourself — who can you afford to alienate and how much would it really cost you to minimally accomodate that group?

Some people assume that you figure cumulative probabilities by adding, so if the chance of any one person begin vegetarian is 3.2%, the chance that a group of ten has at least on vegetarian is 32%. Obviously that doesn’t work, because if you had 100 people the chance would be 320%, which is not possible. Actually, if x is the probability that any one person is a vegetarian and there are n persons in the group:
probability as percentage = 100 * (1 – (1-x)^n)
Got it?

12 Responses to “Single-issue customers – How to count vegetarians”

  1. Thanks Jeff. I just hope one business owner somewhere is helped by it and that I, in the process, benefit as a customer.

  2. Good god, typical vegetarian that goes to a steak house and wonders why all they serve is steak story.

    You’re almost as bad as my sis-in-law that ordered the Steak Au Poivre without the au poivre, which was the only steak on the menu that night that then bitched because it still tasted like pepper even without the sauce.

    What’s wrong with you people, can’t you eat food instead of eating the weeds that food eats? :)

  3. Now Bill,

    As a connoisseur of a good rant, I would have expected more sympathy ;-) Or maybe not.

    Really, though, you should know that I’m not telling them *what* to serve. And I don’t *expect* a steak house to serve a vegetarian meal, I just find that 99% of the ones that I’ve ever been in are happy to come up with something. But of course, a restaurant is welcome to serve whatever they want. If they don’t have vegetarian meals, I want eat there. But that’s their prerogative. That’s not what I’m talking about at all.

    What bothers me is that they don’t know how to *count* for God’s sake. You can substitute anything you want. Celiac-friendly, Kosher, unspicy, single malt Scotch for instance ;-) If you run a restaurant and quit offering single malt because it isn’t a top seller, you have to ask how many customers you have for whom the single malt issue is a really a make or break.

    If you run the numbers correctly and it isn’t worth it, well then it isn’t worth it. But if you just count the number of orders for the one vegetarian, kosher or single-malt enhanced meal you sell, you’re not counting right.

    As for food versus weeds, I won’t say anything about that except this. My aunt used to say I ate “birdseed”. At our wedding, we had everyone served up with real food, and we brought out a special plate for her. Piled high with birdseed! So beware if you should find yourself dining at our house ;-)

    Don’t worry, though, we did serve her “real” food too.

  4. LMAO! Hope your Aunt had a good sense of humor.

    Don’t mind me, I have a few vegetarian friends so I’m familiar with the plight but have never seen them in a situation like yours.

    Likewise, I get all bent at restaurants that don’t have beer on tap and when they do, it’s not real beer, it’s Bud or Millers.

    I don’t want your beer in a can, no thanks, and if I have to suffer through a Bud once in a while, so be it.

    But considering I don’t eat out that much these days the beer on tap is the extra treat for me which dictates where I do and do not go.

    So while you eat your vegetables, I drink mine fermented.

  5. Doug Hemken

    I seldom sit down twice in a restaurant with hard seats, because of my wife’s back, and she seldom sits down twice in a restaurant with nothing on the menu that suits my medical requirements.

    As a result, we don’t have very many restaurants where we eat regularly.

    The poor restaurant manager needs more information, though. He needs: the probability of the key customer, the distribution of group sizes, and the distribution of billing totals for each group size. You have an estimate for the first quantity that is biased on the high side, a point-guess-timate of group size, and nothing about the bill (or profit).

  6. Oh sure, just what I need. A professional statistician. Or maybe I do. But I don’t really agree with your last paragraph.

    My estimate for the first number is from the Harris Poll, so why is that high?

    Then, yes, there’s a guess of group size issue. The first estimate is low. The second is high. I don’t manage a restaurant, so I throw those out there. Maybe they’re high or low. That isn’t really the point. The point is HOW you calculate the effect of not serving that customer base. Now, the manager has these numbers. Presumably, he knows what the group size distribution is and he can run the numbers.

    But as I understood him, they ran the numbers on a per menu-item basis, which does not tell you the effect that item has on total sales. You need to include group sizes (again, he should have that distribution) and probability of having one customer in each group of a given size who is affected by their menu choice.

    For some single-issue customers (celiac, vegetarians, kosher), he also has the probability data, though admittedly it’s not local and national numbers skew things a lot. For some, of course, he can’t really get those numbers (hard-chair haters).

    The point, though, is that if he just counts customers who hate hard chairs and won’t be back, he is WAY undercounting the total number of customers who are being affected.


    Irrelevant. The profit/bill question only becomes relevant if there’s a difference between the profit on a group with a single-issue customer and group without and then only if the restaurant is frequently full and wants to attract only the highest paying customers. In that case, of course, they should market to alcoholics, since the biggest profit is typically in that area.

  7. Very funny post. Kind of reminds me of the Fermi problem of predicting the number of piano tuners in a town.

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