32 dogs

Like most normal people, I’ve been eating hot dogs for a long time. And for the last ~20 years, I’ve put the exact same condiments on my hot dog: ketchup & onions. Sure, there’s been the occasional Chicago-style dog, the cheese dog, the chili cheese dog, the bacon dog, etc. But my go-to dog is always ketchup & onions.

In these last 20 years, across baseball stadiums, picnics, barbecues, cafeterias, and other hot dog meccas, I’ve come across exactly one other person who eats the same condiment combination as I do. Given how many hot dogs I’ve eaten in the last 20 years, that’s crazy, right? You’d think the odds would be better for me finding more hot dog soulmates. Let’s see what the percentages say…

There are five standard hot dog condiments: ketchup, mustard, relish, onions, and sauerkraut. That means there are 2^5 = 32 possible condiment combinations. That also means that if everyone who ate hot dogs had a 50/50 chance of liking each one of the five different condiments, there’s a 1-in-32 chance that a hot dog eater I randomly run into would eat the same combination as I do. However, I know that it’s not 50/50 for each of those five condiments.

Let’s assume that the following percentages of hot dog eaters likes each of the five condiments:

  • ketchup: 50%
  • mustard: 25%
  • relish: 40%
  • onions: 33%
  • sauerkraut: 10%

Let’s also assume that there are no higher-order combination effects going on (e.g., ketchup & onions go really well together, such that the likelihood of someone using both is greater than the individual likelihoods would lead us to assume). At those rates, it turns out that about 1-in-15 hot dog eaters should have my exact ketchup & onions combo. The number of people I’ve observed putting condiments on their dogs is at least an order of magnitude bigger than 15 — and probably closer to two orders of magnitude bigger. So in 20 years, I should have run into 20, 30, 40+ people who eat ketchup & onions on their dogs. Either my “like” percentages above are wrong, my odds calculations are wrong (Jim Merino will correct me if that’s the case), or the distribution of hot dog eaters is not randomly distributed.

I’ll stop this post before it becomes a statistical paper. What do you like on your dog and how many people have you run into who like the exact same thing?

As a Vietnamese guy, I take great risk of ridicule (among other things) in posting the picture above, but I couldn’t help it. Picture courtesy of killahbeez.com.

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9 Comments

Filed under Food, Food & Drink

9 responses to “32 dogs

  1. Erez

    Hi Pete,

    Another cute and entertaining post of yours. I just wonder if there are not 120 possible combinations with 5 optional condiments. Given of course that there is not any hot dog rule that forbids getting more than two condiments…

    Erez

    • Thanks, Erez. I think there are 120 permutations, not combinations. That is, if “ketchup & onions” were distinct from “onions & ketchup”, then there would be 120. However, since I’m considering only combinations, I’m pretty sure it’s 32.

      BTW, you didn’t say what you eat on your hot dogs…

      Happy New Year!

  2. Pete,

    Fun article– I think the issue here is the ketchup %- your hypothesis of 50% may be too high. It’s certainly a regional %. Having lived in Chicago, you are not supposed to put ketchup on hot dogs in Chicago– will even be ridiculed for it by hot dog connoisseurs. That thinking doesn’t hold I’m sure in the Bay Area, but would think ketchup and mustard would be roughly equal. My combination of choice is always mustard and onions.

    • Thanks, Apurva. You know, I hadn’t even thought about regional differences. I just assumed that ketchup was the most common topping. I do love a good Chicago-style dog. I had a great one at the HP Pavilion at a Sharks game.

      peter

  3. Jen G

    My toppings of choice: ketchup, plain mustard, and relish. I googled this topic, thinking that surely someone has done some kind of polling on this before. Apparently, at least as of 2005, the most common topping in the US is mustard, not ketchup. This is somewhat of a surprise to me since I love ketchup on so many food items, including hot dogs. But I guess push comes to shove, if I could only have one topping, I would choose mustard over ketchup. Hmm. Apparently there is a Hot Dog Council for all things hot dog related. Who knew? More info here: http://www.suite101.com/content/how-can-you-top-it-a37145

    • I don’t run across a ketchup, mustard, and relish very often…good for you. You’re right, I’m surprised, as well, that mustard is the most popular.

      “The National Hot Dog and Sausage Council is a project of the American Meat Institute”…awesome.

      Hope your case is almost done…

      peter

  4. I like the Costco hot dogs. Where else can you get that kind of value? It’s onions, ketchup and relish for me. I like tomatoes too, if they’re available. But if I do tomatoes, then forget the relish. 🙂 I love hot dogs! Oh, with mac n cheese – that’s an old favorite. Looks like I’m going to have to hit Costco soon to get a fix for my new craving.

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