1. Scaling down in linear colorspace is essential. One example is [1], where [2] is sRGB and [3] is linear. There are some canary images too [4].
2. Plain bicubic filtering is not good anymore. EWA (Elliptical Weighted Averaging) filtering by Nicolas Robidoux produces much better results [5].
3. Using default JPEG quantization tables at quality 75 is not good anymore. That's what people referring as horrible compression. MozJPEG [6] is a much better alternative. With edge detection and quality assessment, it's even better.
4. You have to realize that 8-bit wide-gamut photographs will show noticeable banding on sRGB devices. Here's my attempt [7] to reveal the issue using sRGB as a wider gamut colorspace.
[1] https://unsplash.com/photos/UyUvM0xcqMA
[2] https://cloud.githubusercontent.com/assets/107935/13997633/a...
[3] https://cloud.githubusercontent.com/assets/107935/13997660/b...
[4] https://cloud.githubusercontent.com/assets/72159/11488537/3d...
[5] http://www.imagemagick.org/Usage/filter/nicolas/
This is pretty astonishing to me. I always thought applying smartly designed color filters to pictures was basically Instagram's entire value proposition. In particular, I would have thought that designing filters to emulate the look and feel of various old films would have taken some fairly involved imaging knowledge. How did Instagram get so far without color experts?
Working in a different color space than standard requires a little bit of familiarity and finesse that modifying 8-bit jpegs for consumption on the internet did not require.
Many photographers and printers are familiar with this dilemma in a variety of circumstances, where the cameras create images in a different color space and higher bit depth that can't be perceived at all with any technology or the human eye.
As an analogy, think of the value music theory (i. e. https://en.wikipedia.org/wiki/Scale_(music)#Harmonic_content) for composition.
[0] http://blog.johnnovak.net/2016/09/21/what-every-coder-should...
(I'm a maintainer of pillow)
Vertical Image: 1080px in width by 1350px in height
Horizontal Image: 1080px in width by 566px in height
And you probably overestimate how large Instagram, the app, is.