<p>Actually, it seems that I lied.</p>
<p>I have never seen Princeton's average SAT score charts (although they very well may exist). Rather, the "middle 50%" charts seem to be the more prevalent ones, which means that even if Princeton takes applicants with a 2400 SAT, it's not going to help them. </p>
<p>If we take this data for admitted applications (<a href="http://www.princeton.edu/pr/facts/profile/06/08.htm%5B/url%5D">http://www.princeton.edu/pr/facts/profile/06/08.htm</a>)
CR: 690-800
Math: 700-790
Writing: 680-780
SAT II: 710-790</p>
<p>...we can see that the middle 50%'s SAT range is from 2070 to 2370. Of course, this fact is flawed because an admitted person with CR 800, Math 800, and Writing 600 would not be represented in the middle 50% for Writing, so we cannot assume that the low end applicants did have 2070's and that the high end ones had 2370's. Either way, saying that the middle 50% is from 2070 to 2370 gives us an idea of the larger picture.</p>
<p>This is the data that Princeton cares about. Now, in all honesty, I do not see how that SAT average of the bottom one-third of the class is about 2100. However, focusing on the low end of things will only result in rejection letters. It's the high end of the middle 50% which is closer to the average score of your average (non-legacy, non-athlete, non-URM, non-world champion) applicant. Thus, if we consider a target score of be 2300 to 2350 to be average, then we can already see the necessity of a high score if we are average applicants. </p>
<p>However, this is already common knowledge, and the purpose of this brief analysis is to prove why a 2400 score is no better than slightly lower score, in the scope of the admission office, that is (A 2400 still grants bragging rights). After the middle 50%, Princeton simply doesn't care. Who cares if the top 25% is made up purely of 2400-scorers? No one sees that data. Of course, a few 2400's are sure to help shift up the middle 50% statistic, but so would a 2380 or 2390. Actually, any score above the exact middle would move the middle 50% up, and by an equal amount as well (one person's worth). Thus, if someone were to have a score about the exact middle (not the average), they would be increasing Princeton's middle 50% (sounds rather obvious now).</p>
<p>If we look at the middle, I would guess it to be in the mid 2100 range (2140~2160). Thus, a 2200 would indeed statistically help Princeton as much as a 2400.</p>
<p>Does this mean that a 2200 is the same as a 2400? Of course not. Just looking at the low end of things, Princeton seems to not care too much about the numbers, so the impact of either score on the middle 50% is probably a minor consideration. No, what makes the 2400 so much more attractive is the fact that there are only a few hundred applicants with a 2400, where as thousands will be in the 2200 range. The 2400-scores have one more thing to help set themselves aside from the rest of the applicant pool, which is important in the admissions process.</p>
<p>Summary: Statistically, a 2200 is as good as a 2400.
Summary of a summary: a 2400 is still going to help a lot more than will a 2200.</p>
<p>Ok, I just spent my time proving the obvious. kthxbai</p>