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.