The method of calculation is outlined in the D1 Manual 15.5.3.2, or 15.5.2.2 in the D2 Manual. The D1 Manual has the more recently written rule, and is clearer.
First, we need to understand a "grant in aid". A full grant in aid is the sum of tuition, fees, room/board, and a fixed amount toward books. I know I will sound like a broken record, since I've posted this many times, but a full grant in aid is not the same as the cost of attendance. The COA is a federally defined calculation, and the COA for a given school is usually a few thousand dollars more than a full grant in aid.
A D1 school is allowed up to 11.7 equivalencies. The calculation of a given player's award is done as a ratio (which is usually spoken of as a percentage because 35% sounds better than 0.35
). Each item in the ratio can be the average cost for all students, or the actual cost to the particular player, at the school's option. The only exception is tuition: In-state and out-of-state tuition can not be combined to get an average tuition, and each player's ratio must include the actual tuition he is liable for. The numerator is made up of the award to the player, and the denominator is the value of a a full grant in aid, which depending on the method the college uses (and for sure if out-of-state tuition is involved) may be different among the players.
Let's take a simplified version of JMoff's example:
In state total $20K ($10K tuition, $10K books, fees, room and board)
Out of state total $35K ($25K tuition, $10K books, fees, room and board)
If the coach provides a 50% award to both players, he has used one equivalency. His program budget is charged (probably) $27.5K. The in-state player has to pay $10K, and the out-of-state player pays $17.5K.
If he offers "full tuition" to each, and only that, then the in-state player still uses 0.5 equivalencies, but the out-of-state player uses 0.714. If he offers each room and board, the in-state player uses 0.5 and the out-of-state player uses 0.286.