I was very confused for a long time over efficiency calculations.
The model that I finally settled on ( that made sense for me anyway ) was to work on a point system, multiplied out by the volume.
The theory behind this system is that if we take a quantity of liquid and measure the density of sugars in suspension ( ie gravity ) for example 2 liters at 1.048, then if we dilute the solution with water ( lets say to 4 liters ) the gravity is reduced by the same amount ( ie it will now be 1.024 ). i.e the density is directly related to the amount of sugars and the volume, and this relationship will not change unless you actually take some of the sugars out of the system.
This way you can calculate the expected gravity of all your run-offs ( if you batch sparge like I do ) and also work out your conversion ratio.
This method is actually very simple when it comes down to it (despite me trying my best to make it long winded and complicated), and takes away a lot of the mystery surrounding the efficiency calculations.
Basically you start with the theoretical maximum gravity that you could get if you had an efficiency of 100%. ( So lets say it is 1.068 for example ) and you factor this with the number of liters that you expect ( assuming that there are no loses to trub or dead spaces etc ) lets say 25 liters. To do this take the last 3 digits of the gravity reading ( lets call it "points" for want of a better term ) and multiply it by the number of liters. In this case:
25 x 68 = 1700
Now this figure represents the theoretical maximum amount of "points" what we are able to extract if we could get 100% efficiency and there are absolutely no losses.
So now to determine our actually efficiency we just calculate the number of "points" that where extracted after sparging, by measuring the gravity of the wort in the boiler ( lets say 1.052 or 52 and 23 liters ) which ends up with:
23 x 52 = 1196
So our efficiency is
1196/1700 = 0.70 ( or 70% )
Now the fun part of this method is that we can even work out an approximate conversion % if you are batch sparging, as well as the expected gravity of each of the batches ... yes I know that brewsmith and all those other tools already do this for you ... but this way you may even get to understand it a bit.
I have a horribly rough spreadsheet that I use to do all this if anyone is interested, might even get around to cleaning it up for mass consumption one of these days
Some other points on efficiency calculations:
i) Its only a theoretical model and will never represent the real world exactly. To start with, if the grain that we are mashing varies from the grain that they used to determine the extract potential, then the calculations are not going to match exactly even before you take into account your process, and your equipment ( ie don't get too carried away about it being spot on to what you have calculated, as this rarely happens ).
ii) Low efficiency is not a sign of lack of manliness, and there is much to say that you might end up with a better beer at the end of it. In fact some brewers have reported good results by only taking the first runnings from the grains, and not adding extra sparge water at all ( about 50% efficiency ). I usually aim for around 70%.
iii) The only real benefit of accurately knowing your efficiency is to be able to plan your recipe to give you the gravity that you need for the beer you are making. Once you can consistently predict this, then you don't really need to worry about it.
The "cost" of not getting that extra 10% out of your system is probably only a couple of dollars in grain, and mostly likely will lead you to doing stupid things like over sparing and ruining many potentially fine batches of beer ( and yes I am talking from experience here ).
Cheers
Chris