New York started issuing a new series of license plates in 2001. The standard car plates have three letters, followed by a space, followed by four digits. The first plates issued had letter groups beginning with A; our two cars have ASY and ATT. Later plates had groups beginning with B, C, and D. One gets the impression they started at AAA 0000 and started incrementing from there. They probably skipped ASS and a few other groups, of course.
One group I noticed some time ago they did not skip was DDT. At some point I realized I’d seen not just a few DDT plates — I’d seen a lot. More recently I’ve seen quite a few DNA plates too.
This morning while riding to work — Heather was driving — I decided to start counting license plates, resetting the count at every DDT plate, to get some idea what fraction of cars have DDT plates. I counted only New York plates of the “AAA 0000” form, omitting vanity and commercial plates. The first DDT plate I saw was plate #6!
I started counting from 1 again and got to 47. Five plates later I saw the third DDT plate. Then I counted about 74 plates before seeing the fourth.
Now, the two that were five plates apart were parked on the same side of the same street. Conceivably they were linked in some way, e.g. both were owned by the same family, who moved to New York and got both sets of plates at the same time. In any case, four plates out of about 123 isn’t much of a statistical sample.
But press on. Suppose (and I grant this is an unreasonably simplified model) New York issued plates beginning with AAA 0000, on up through AAA 9999, then AAB 0000 and so on. I don’t know how far they’ve gotten, but I’ve seen DNA plates and haven’t seen any starting with E, so let’s assume they’ve gone through DNA. (Of course they’ve probably gone further.) And let’s assume these sequential plates were distributed with no regard for geography, and that all of them are still in use. Then there would be 262 * 10000 = 6760000 plates starting with A, the same number starting with each of B and C, and, hmm, 1 * 13 * 26 * 10000 starting with DAA through DMZ (I saw a DMZ plate today too: De-Militarized Zone) plus 10000 starting with DNA. Total number of plates issued: 23,670,000. New York’s population is about 19,000,000, so that’s not an entirely crazy number — skipped groups like ASS and plates removed from use would bring the number down somewhat.
In this model there are about 2367 letter groups in use, with 10000 plates in each group. So you’d expect to count, on average, up to 2367 plates before seeing a DDT.
That’s clearly wrong.
Suppose, then, they’re not using all letter groups — not just skipping ASS but using, say, only every nth letter group. Trouble is, as I said above, I’ve seen DMZ and DNA, which are consecutive. There could be some other criterion, of course; they could skip certain letters in the last place, for instance. Why, though?
Or it could be distribution is tied to geography. That is my working hypothesis. For instance, there are 62 counties in New York; suppose each letter group is issued only in one county. Then to the extent that all the cars you see in a given county were registered in that county (another simplification), you’d see either no DDT plates (in 61 counties) or one on every 2367/62 = (about) 40 cars (in the 62nd county). That’s certainly in the right ballpark.
Research continues… while Heather’s driving.