<p>
The near-ideal student you described would only have a 94% chance of being rejected if Stanford admission selections were done by pure random selection, which is obviously not true. For example, according to the admissions profile at [Applicant</a> Profile : Stanford University](<a href=“http://www.stanford.edu/dept/uga/basics/selection/profile.html]Applicant”>http://www.stanford.edu/dept/uga/basics/selection/profile.html) , last year Stanford apps who had a 800 on verbal SAT had a 14% admit rate, which is 2-3x the admit rate of the overall class. In contrast apps who scored below 600 only had a 1% admit rate. As you add in more information, you can get more accurate estimations. With the few paragraphs of info in the 2017 RD thread posts (no LORs, essays, …), I was able to predict ~90% of the listed admission decisions correctly.</p>