In Monty's post, he states APR measures athletes' retention during an academic year, so does it only hurt the APR if the transfer happens during the school year? Also you stated transfers can dilute the APR, how does that differ from lowering the APR? Just trying to understand the APR and how it changes.
There are nuances, but generally speaking...
Transfer timing - no, this would only matter if it's the student-athlete's first year at an institution.
Tying this into your other question, think of it this way:
Each player can potentially earn 2 points per semester (or semester equivalent) - one 'retention' point and one 'eligibility' point. In other words, 4 points per player, per school year. Because the APR is generally looked at on a four-year rolling basis, many schools will have roughly 200 potential points as their denominator (13 players x 4 points x 4 years).
If a transfer leaves your school in good academic standing, it's possible that your school receives 3/3 points (1/1 in the second semester - that being the eligibility point... but if the kid leaves after the school year to go pro, or transfer to another 4 year school and leaves in good academic standing, the 1 possible retention point is disregarded... that is, it's not a 1/2 for the semester.. it's just a 1/1).
So, if you have 13 kids on your team...
8 kids stay academically eligible and come back the following year... you get 32/32 points for that school year (8 * 4 for both the numerator and denominator).
3 kids stay academically eligible and graduate. You get 12/12 points (3 kids * 4).
1 kid transfers after the school year. He leaves in good academic standing. You get 3/3 points.
1 kid leaves early to be a professional. He stays until the end of the semester and finishes up his course work. You get 3/3 points.
So, in this situation, you're looking at 50/50 points. The APR is usually stated as a whole number, but it's simply a percentage. 50/50 = 1,000, a perfect APR.
Now, if of those 8 kids that stay in school... 1 of them screwed up their academics and had to sit out the second semester.. but then was eligible the following year... you would be looking at a 3/4. Or, in total, a 49/50 = 980 APR. If the transfer and the professional had instead stayed at your school, you would have gotten another 2/2.. and the total APR would have been 51/52 = 981 APR. So, the fact that those two left is mathematically dilutive to your APR if you do not have a score of 1000... in this example and in most real life cases, the impact is going to be minimal, especially when you consider the four year average is the key figure (so one transfer is roughly taking away 1/1 from x/~200).
By the way, in the case of a Paul Carter, he graduated and therefore I believe would have added the full 4/4 possible to the team's APR score, despite 'transferring'. Cobbs, I believe a 3/3.
I think I have the particulars of Minnesota's calculation nailed down for 2009-10... i.e., 44/49, with three guys (I won't ruin the fun by saying who and why right now) not obtaining an equal numerator and denominator, and Cobbs receiving a 3/3 due to transfer... but the fact that the school published one figure yesterday and then the NCAA published another one today (backing off an 0/2) is interesting. I have my guesses on what may have happened there, but...