Pizza Delivery and the Law of Large Numbers

Random pizza delivery thoughts because that's what I'm thinking today.

Being the "on call" driver hasn't been a big deal most nights because mostly it hasn't been busy enough for the "on call" driver to come in. Both last night and tonight, though, I was called in. Which is a good thing. I like the hours. Tonight was a lot of work. I was on call from 6-9pm. At about 5pm, while Jackson and I were helping an older lady from church carrying her Christmas decorations from her basement upstairs, the manager calls me in. So I hurry up and finish, skipped dinner and got in about 5:45. Tonight was the first major snowstorm of the year. Roads were awful, drivers were sliding all over, it was cold and we were very, very busy. I finally got home about 10:45.

Keeping track of some things while delivering has been a wonderful confirmation of the Law of Large Numbers. That's the law in probability theory that states that if you perform a number of trials, say n trials, for example, the average result as n approaches infinite will approach the calculated expected value. Which basically means things average out over time. The classic example is tossing coins. If you flip a coin 3 times, you may get 3 heads in a row, i.e. 100% heads, 0% tails. In fact, it's likely enough that if you try a bunch of tests of 3 coin flips each, it will eventually happen. However, the longer you flip the coin, the closer you will get to 50% heads and 50% tails. If you could flip the coin forever, you would get exactly 50% heads and 50% tails.

I average 3 deliveries per hour. $2.50 tip per delivery. Just under 4 miles per delivery. I understand how averages work, so I expect that some days vary from those numbers. But over time, that's what I get. And I'm very impressed with how close I get to those numbers pretty much every day. Today for example, in my five hours at work I took 15 deliveries and drove 55 miles. I would have expected to get $35-$40 dollars, but today of all days, weather and driving conditions notwithstanding, I was stiffed five times. I only got $29 in tips. That's what a $.50 drop in the tip average means. It means I got paid about $1.50 per hour less than normal. That's a big deal on low income wages.

Do a little math because, you know, math is fun and all. Assume the other 10 deliveries were normal, which they seemed to be. Recognize that the resulting $2.90 per delivery average occurs only if you exclude all tips of $0. We can calculate that, normally, I could expect to not get tipped about 2 deliveries out of 15. We just need a theorem defining some number, X > 2 that is considered to suck. If 5 > X, we can claim to have mathematically proven that tonight, indeed, did suck. I don't have such a theorem, though, so you're just going to have to take my word for it.

On the upside, it was a beautiful night. The air literally seemed to glow. I assume it has to do with the city lights reflecting off the new fallen snow, or off dense, low hanging clouds, maybe some combination of the two. Or I don't know. Something like that. In any case, it was so bright out that I could see address numbers even when porch lights were left off. That was just kind of a corollary benefit, though. What was really impressive was driving through the city with that new fallen snow radiance. It was very, very pretty.