Dollar cost averaging doesn't have a better expected value than lump sum investing, but it should have a lower variance, no? Also, there's dollar cost averagin

Dollar cost averaging doesn't have a better expected value than lump sum investing, but it should have a lower variance, no? Also, there's dollar cost averaging like "I have a lump sum now, but I will invest it slowly over the next 2 years" and there is dollar cost averaging like "I will invest money as it comes in slowly over the next 2 years instead of saving it up and investing it as a lump sum then". The former is the technical definition, but the latter is what most people mean when they use the term informally...