Batting averages and book awards

Babe Ruth goes 2-for-4 in his first game of the year. Which batting performance in his second game will increase his batting average the most?

a. 2-for-2.

b. 3-for-3.

c. 4-for-4.

d. Doesn't matter because his hits and at bats are the same in each case.

The right answer, of course, is c: 4-for-4.

Game 1

Game 2

Batting average

2/4

2/2

0.667

3/3

0.714

4/4

0.750

Which takes us to Proposal 2010-75 and book awards.

What Proposal 2010-75 does
Two things:

1. Increases the financial aid equivalency figure for calculation purposes for books from $400 to $800 and

2. Eliminates partial book awards. If a student-athlete receives any portion of a book allowance, $800 shall be used in the numerator and denominator of the equivalency calculation. 

So how does this proposal work in practice? We'll see shortly. 

But before we begin, remember that the value of book awards is merely a placeholder in the equivalency calculation. Each student-athlete could have a different cost of books depending on the courses s/he takes.

Room, board, tuition, and fees can often be identical for most students. But books? Nope. That's why the placeholder concept makes sense. It removes a number of accounting and compliance headaches.

The current figure of $400 is artificially lower than the actual cost to outfit a student-athlete with books today. So was the previous placeholder of $200. And so is the proposed figure of $800. We'll see what the future holds.

Now on to the examples.

Full grant student-athletes
This one is easy. A full grant is a full grant is a full grant. In an equivalency sport, a full grant amounts to a 1.0 equivalency, regardless of the value of the books placeholder because all the components of aid in the numerator (including the books placeholder) equal their counterparts in the denominator. Proposal 2010-75 has no effect here.

Equivalency award less than a full grant, without books
In these cases, the equivalency fraction will be smaller under Proposal 2010-75 because the denominator is increasing due to the larger value for the books placeholder while the numerator for the books component remains equal to 0.

To continue the Ruth example from above, if The Sultan of Swat had followed up his 2-for-4 opening day performance with an 0-for-3, his batting average will go down. It'll go down even more if he goes 0-for-4, and more still if he goes 0-for-5.

Equivalency award less than a full grant, with books
In these cases, the equivalency fraction will be higher under Proposal 2010-75.

As we've seen from the Ruth example above, increasing the numerator and denominator of a fraction by the same amount results in a larger number.

Let's go to the blackboard:

blackboard

Keep in mind that because Proposal 2010-75 eliminates partial book awards, student-athletes who receive even one book will have the book placeholder equal the full $800 in the numerator.

So what have we learned from all this?


Grant-in-aid amount

Equivalency under Proposal 2010-75

Full GIA

No change 

Partial GIA with books

Higher

Partial GIA without books

Lower

 
In addition, generally speaking, increases or decreases in an individual student-athlete's equivalency calculation are likely to be negligible. But if you have a team full of student-athletes getting book awards, the sum of negligible individual increases might amount to a significant impact on the team total.

So what's your point?
There may be three categories of student-athletes impacted to varying degrees by Proposal 2010-75. But just because one group is affected positively, another negatively, and the third is not affected at all does not mean that the overall effect of the proposal is neutral.

Before you vote on Proposal 2010-75, take a look at how many of your current student-athletes fit in these categories, particularly those student-athletes who are receiving a partial grant-in-aid. Does your institution give partial book awards? Do you have a lot of student-athletes who don't receive book awards at all? 

Then figure out how this proposal will impact their equivalencies and the team total. Re-run your equivalency calculations substituting $800 for books.

Only then will you know if it's worth tinkering with a placeholder.