How much does class rank matter for college admissions?

I graduated from essentially the top high school in Singapore with 38 points on the IB Diploma. Due to the nature of high school admissions in Singapore, with upper and lower tier schools, although my score is somewhat decent (equivalent to approximately 3.8 GPA) it puts me in the bottom 20 percentile of my class. My school does not rank, however this will be obvious comparing my grades to the school profile. Will I have to forego applying to the Ivies in this case? The rest of my application is fairly strong, in my opinion at least. Thanks!

Because your school does not provide class rank, most colleges will not go through the trouble of computing it themselves; instead, they're likely to base their admissions decision on other criteria like GPA, standardized test scores, personal statement and other essays, and extracurricular involvement. Part of the reason schools do value standardized test scores is because not all high schools grade their students equally; standardized test scores are a (theoretically) a way to make things more equal.

As this ExpertHub answer points out, your grades are just part of a larger picture. Assuming that you've taken advantage of the opportunities your high school provides (e.g. taking advanced classes like IBs), being in the bottom 20% of your class isn't an instant disqualifier when applying to competitive schools like the Ivy League. For the best advice on how to get into highly selective schools, I highly recommend reading this article.