Originally Posted by lumpher
but that [Ballings's Formula] doesn't take the aggressiveness of the yeast into account at all. with that calc, windsor and wlp001 would be just as effective as nottingham.
Yes, actually, it does, if by the agressiveness of yeast you mean their ability to ferment i.e variability in attained ADF. The Balling formula is
ABW = f*(OG - AE)
but AE = OG*(1-ADF) so
ABW = f*OG*ADF
ADF is expressed as a fraction here rather than a percentage.
I was too lazy to look up the formula for f last night but it is
f = 0.39661 + 0.0017091*OG + 1.0788E-5*OG*OG
with the OG in °P. This is from a curve fit to the Balling Table as published in DeClerck, VolII p 428.
What Ballings formula does not take into account is that different yeast strains produce different amounts of biomass in the course of a fermentation. As the nominal production is 5.5% of extract consumed, and the tables are based on that, it is clear that doubling or halving of the yeast mass relative to the nominal doesn't have that much of an effect. It also relies on Tabarie's principle which, in my brief experiments with it seems a bit iffy. But then as you don't really know what your OG was (evaporation loss in the fermenter, dilution/concentration by the sugar content of the starter etc.) you couldn't really expect to be able to calculate alcohol content accurately from the formula anyway. It is, given this, often the practice that the alcohol content is measured and an effective OG calculated from that by using Balling's formula in reverse. Of course the limitations apply in the reverse direction as well so we seem to have a sort brewing Heisenberg principle: you can take a good OG measurement and calculate approximate alcohol content from that or take a good alcohol measurement and calculate approximate OG but you don't seem to be able to get both accurately.
There is another Balling formula
ABW = g*(OG - TE) where g is another factor depending in OG
g = 0.48394 + 0.0024688*OG + 1.5609E-5*OG*OG
and TE is the true extract. This takes Tabarie out of the picture and so is doubtless more accurate but the variability in biomass produced per unit of extract consumed is still problematical and few homebrewers are willing to go to the trouble to determine TE though it isn't really that difficult to do and requires minimal equipment in addition to a hydrometer i.e. a beaker and a volumetric flask.
The Balling equations may be the best out there because they take OG into account whereas the others don't but there are still limitations. In my experience the OG/AE form of the Balling equation, based on a specific gravity reading in the fermentor just after filling, underestimates the alcohol content of the beer by a few tenths of a percent. With respect to back calculation the effective OG is somewhat higher than the measured OG.