Batch sparging confusion

[Warthaug]

I check the actual gravity against the intended pre-boil gravity when I hit the pre-boil volume from the sparge (measure volume of first run-off, add just enough sparge water to hit the pre-boil volume). The efficiency is usually higher than expected so here's an equation for correcting that with brewing water instead of increasing your volume (I'm volume limited and plan for the absolule max that I can boil):

Efficiency Too High

(PBV) Pre-Boil Volume [Gallons]
(PBG) Recipe Pre-Boil Gravity
(AG) Actual Mash Gravity
(RV) Removed Volume to be Replace with Brewing Water [Gallons]

RV = PBV*(1 – PBG/AG)

Example

PBV = 4.125
PBG = 48
AG = 54
RV = 4.125*(1-48/54) = 0.46 gallons

My pre-boil gravity was higher than expected (equivalent to 85% mash efficiency); my planning was for 75%. But, because I didn't sparge enough, my final mash efficiency was more like 79%, and total brewery efficiency was on the low side (I forget the exact numer; perhaps 60%). Funny thing is, I hit my OG pretty much dead-on; would have had a realy boozy beer if I'd spraged better (not like that's an issue!).

Bryan