I've read descriptions of DCA as buying more of something when it's cheap, and less when it's expensive. In contrast, if you buy much of that thing all at once, you may be buying the whole load at a peak or trough price, i.e., you're either way worse off or way better off. This means it's more of a gamble due to its uncertainty. In a sense, with DCA, you end up buying at the temporally local average price.
As a conceptual toy problem, I pondered what would be a good frequency at which to make DCA purchases. I haven't been able to see an intuitive answer over the years, but I'm wondering if this next idea might be a good rough guide.
The fluctuations in the price of a thing to buy has a slow and fast variations. You'll never average out the slower fluctuations unless you intend to make DCA purchases forever. Would it be a good idea to look at the autocorrelation of the price function in time, gauge the time interval that it takes to fall "relatively" flat, then choose a DCA purchase interval to be that time? My thinking is that, with purchases made at that interval, the prices are uncorrelated, so you end up averaging out the faster fluctuations.