<p>As far as the game goes–and a game is exactly what it is–the total number of applications is not the most important factor. You also have to take into account class size and yield rate and admit rate. MIT and Caltech are extremely unpopular and receive very few applications compared with the other schools, but they have small classes so they have a low admit rate. Similarly, Penn, Northwestern and Duke get 31,00 applications–more than Yale and Princeton–but Penn, Duke, Northwestern have a higher admit rate because they have bigger classes (and lower yield).
For the long run, Penn, Duke and Northwestern won’t be able to compete with UChicago because UChicago has a significantly smaller class size and thus will end up with the lower admit rate as its total applications grow. Northwestern and Penn could never overtake Harvard, for instance, because they have larger classes and thus would have to get many more applications than Harvard to be equally or more selective (keeping in mind yield rate.) Stanford Business School overtook Harvard Business School in admit rate (i.e, became harder to get into) by remaining smaller. Thus UChicago will be able to make gains on the top schools in the country (based on admit rate) that are simply impossible for Duke, Penn, or Northwestern.
Also, from the figures below, you will see it is fairly common for schools applications to grow something like 22,000 to 25,000 or 26,000 to 29,000 to 31,000. Which is my guess about what UChicago will do over the next few years.</p>
<p>2016 2015 2014 2013 2012 </p>
<p>Columbia:
31,818 34,929 26,178 25,427 22,585</p>
<p>Penn:
31,127 31,659 26,938 22,808 22,922</p>
<p>Duke:
31,565 29,689 26,784 22,280</p>
<p>UChicago:
25,271 21,774 19,370 13,600</p>
<p>UChicago has plenty of room to grow its application pool (up to 31,000-35,000). That is not the case for Penn, Northwestern, and Duke. Thus, UChicago has more room to lower its admit rate further than the others.</p>
<p>(And this is not just a three year change for UChicago; it’s a 20 year trend)</p>