increase capacity by 1/3
???
It's the magazine tube that governs capacity, not the barrel. Given non-fixed length magazine tubes- that is, a design that will take an extension- it's possible to have a magazine longer than the barrel. Perhaps not wise, and somewhat odd looking, but I have seen 3-gun shooters with scatterguns set up that way.
For designs with fixed length magazines like the Mossberg 500, various High Standard pumps, etc., this might be a consideration with some models. But it can't be generalized quite so broadly, I'm afraid. With guns that have pull-through cleanout magazine tube designs, magazine capacity has nothing to do with barrel length. No shotgun magazine is ever big enough anyway, IMHO it's more important to learn to load the gun than it is to try to get the longest magazine possible.
That said, there's little difference IMHO in practical funtion between an 18", 18.5" or 20" barrel. Personally I like the 18 or 18.5" but I can sure live with a 20" if that's all I can get. Last two spare 870 barrels I got decent deals on were both 20", one CYL bore bead sight and one ImpCyl rifle sight, and I happily paid for both of them.
lpl