So I'm trying to formulate a no sparge version of Jamil Zainascheff's English Barleywine recipe and I'm confused. The two methods of calculating no sparge scale factors in Palmers book give very different results. JZ's recipe has 20.4 lbs of grain with an average FGDB congress yield of 36.7 ppg for a total of 748 pts. He says to collect 7.1 gallons with a boil gravity of 1.070 so that’s 497 points which he then boils down to 5 gallons at 1.100. That gives an extract efficiency of 66%. When I do a no sparge mash my extract efficiency is usually about 62% so I obviously need more grain and there are two ways to calculate it. If I do it based on my efficiency I get the following. I want to end the 2 hour boil with 5.5 gallons at 1.100 so that’s 550 pts. I want to start the boil with 7.5 gallons so that’s a boil gravity of 1.073. If I want to collect 550 points and I usually get 62% then I need 887 points in the mash. So if my mash needs 887 points and the recipe has 748 points in it, it seems like I should scale the grain bill by 887/748 which is 1.186. So instead of his 20.4 lbs I'll need 24.2 lbs of grain. That seems fine. But if I use the "long way" calc from palmers book which is based on this derivation: http://home.roadrunner.com/~brewbeer.../nbsparge.html
it tells me I need to scale up the grain bill by 1.52 which is 31 lbs of grain! That’s quite a difference. I've read that derivation and it makes sense to me, but so does the efficiency approach that I described above. Which is right?