If using say a Sanyo NCR18650GA you can look at HKJ’s graphs to see how the battery sag will react to the driver and the vf of the led used. There will also be a small amount of other voltage drop losses too.

It’s a very simple decent efficient solution. I think that’s probably why there’s not that many single cell buck drivers around. The amc7135 linear regulator driver pretty much took the market and is a cheap, good reliable driver.