Why some files compress to almost nothing and others refuse

This works through data compression in the order the parts actually depend on each other.

Compression is prediction

A compressor builds a model of what is likely to come next and spends fewer bits on likely symbols than unlikely ones. Text compresses well because letters and words are highly predictable from what preceded them.

Repetition is the crudest form of predictability, and referring back to an earlier occurrence rather than repeating it is the basis of most general-purpose compressors. The better the model, the smaller the output, which is why stronger compression costs more processing time.

There is a floor and it is provable

Information theory sets a minimum size for representing data given the best possible model of its structure. Data with no structure, such as the output of a good random generator, cannot be compressed at all by any method.

This is why no compressor can shrink every possible input; making some inputs smaller necessarily makes others larger. Any claim of a universal compression ratio on arbitrary data is therefore mathematically impossible rather than merely unproven.

Why some files stubbornly refuse

Photographs, music, video and most archives are already compressed, so their remaining redundancy has been removed. Encrypted data is designed to be statistically indistinguishable from randomness, which makes it incompressible by construction.

In practice, this is why compression must always be applied before encryption, never after, in any system that wants both. Putting a folder of photographs into an archive typically achieves a saving of a few per cent, which is the packaging rather than the pixels.

Lossy compression changes the question

Rather than preserving every bit, lossy methods discard information a human observer is unlikely to perceive. Audio codecs exploit masking, where a loud sound hides a quieter one nearby in frequency or time, and simply do not encode the hidden part. Image and video codecs discard fine colour detail more aggressively than brightness detail, because vision is less sensitive to it.

The savings are enormous compared with lossless methods, and the discarded information is gone permanently.

Video adds the time dimension

Most frames in a video resemble the previous one, so codecs store the differences and the motion of blocks rather than whole images. Only occasional complete frames are stored, which is what allows seeking and what makes those points larger.

In the datasheet, scenes with fast motion or noise break the prediction and consume far more data, which is why grain and confetti destroy quality at a fixed bitrate. Newer codecs achieve similar quality at lower bitrates by predicting better, at a cost in encoding and decoding effort.

This is the general case; a specific device may behave differently by design.

Choosing settings sensibly

For archival storage, choose lossless and a format with published specifications, and accept the size. For distribution, choose the lowest bitrate at which the artefacts are not objectionable for the content in question. Compression level in general-purpose archivers trades time against size with diminishing returns, and the highest settings are rarely worth it.

Never re-encode a lossy file if the original is available, since each generation compounds the loss.

The takeaway

Compression removes predictability. When there is none left, the file has already been compressed.

Understanding the failure mode tells you more than the feature list does.