The term efficiency is an often misused and misunderstood. What is being discussed here is combustion efficiency. How well the fuel is burned, compared to it's theoretical maximum. This has nothing to do with overall efficiency, the efficiency of the appliance burning the fuel. For example I could burn fuel at theoretical efficiency in a fireplace and it wouldn't heat my house very well.
All fuels consist mostly of atomic Carbon (C), Hydrogen (H), Oxygen (O), Nitrogen (N), Sulfur (S), minerals (ash) and water (H2O). In fuel combustion the molecular Oxygen (O2) in air react with the combustible components of a fuel. As an example the fuel Carbon (C) reacts with O2 of the air to generate Carbon Dioxide (CO2). If the reaction is incomplete Carbon Monoxide (CO) is produced. The empirically determined formula for Anthracite coal is:
Perfect combustion is simply a mixture of fuel and oxygen, with both being completely consumed in the burning process. The ideal situation would be to provide just enough air in the combustion chamber to insure complete burning of the fuel. This would be true if it were physically possible to bring each atom of fuel in direct contact with the amount of air required to complete its combustion.
If we reduce the amount of oxygen, in a perfect mixture, we would have a fuel-rich condition. However, if we increase the amount of oxygen, in a perfect mixture, we now have excess, which does not contribute to the burning process. Having just the right amount of oxygen (no more, no less) is called the stoichiometric point, or stoichiometric combustion. The stoichiometric point is also called the 100% air point.
Anything above the 100% point is called excess. Excess air just goes out the chimney lower the amount of heat that heats your home.
The excess air is above theoretical is typically, 1.3-1.5 times for mechanical (stoker) firing and 1.5-2.5 times for hand firing.
Use the above Anthracite formula in combination with your amount of excess air to determine where you are operating you coal appliance.
Get out your high school chemistry books and just do it.
If you are up to it, here's the formula you need. Just match up the x's and y's of coal.
In all seriousness it would only be an academic exercise, because you couldn't possible expect your coal, a mineral, to be consistent load to load and the amount of air supplied would vary with the weather. What you can do is understand what changes how much heat goes up your chimney is dependent on excess air amount. This is the only thing you can control. The other is how well your coal appliance extracts the heat out of coal combustion and puts it into your home. This is designed into you coal appliance, and there is nothing you can do about it. That's why it's important to buy the right coal appliance and why for efficiency reasons you don't use your fireplace.