What compression is actually doing
A lossy image format is, at heart, a very good guesser. It looks at a picture and works out what it can throw away without you noticing — a shade of green that is almost the shade next to it, a texture too fine for the eye to track. It keeps the shape of the thing and discards the parts you were never going to miss.
That trade works brilliantly on a photograph, because a photograph is full of detail nobody is examining closely. It has almost nothing to work with when the picture is a logo: four flat colours and some hard edges. There is no imperceptible detail to remove, and the edges are the one thing you would notice being softened.
Two kinds of picture, opposite results
We ran two files through the converter on this site, at the same settings, and measured the results.
A 1600×1200 photograph went from 501 KB to 29 KB — about 94% smaller. A small flat graphic with transparency went from 1.8 KB to 2.7 KB. Same tool, same quality setting, opposite direction.
Treat those as the shape of the difference and not as numbers to plan around. The ratio moves a long way with the content of the picture: a detailed landscape and a flat studio shot do not compress alike, and neither will your files. The direction is the reliable part — photographs down, flat art often up.
The reason is the guessing. Flat colour is already about as compact as a description can get: "this rectangle is all one green" is a short sentence in any format. A newer format's cleverness has nothing to bite on, and it still has to write its own headers and structures around the image. On a large photograph that overhead disappears into the saving. On a small graphic there is no saving for it to disappear into.
A small file has less to win and more to lose
This is why the effect shows up most on the images you would least expect: the icon, the screenshot of an error message, the chart out of a spreadsheet. They are small to begin with, so the fixed cost of the container is a real fraction of the total, and they are flat, so there is nothing to compress away.
There is a second reason worth knowing. If the original was a PNG, it was lossless — every pixel exactly as drawn. Converting it to a lossy format does not only risk making it bigger; it also permanently discards information, and on hard edges that shows up as faint fringing around the lines. You can pay a cost in both directions at once, which is a poor trade whichever way the file size goes.
What to do about it
Convert one file first and look at what comes back. That is the entire technique, and it takes about ten seconds — the converter here reports the size of what it produced, so you can compare before you commit a folder to it.
If the file grew, keep the original. Nothing is lost by doing that; the format you already had was the better one for that picture. For flat-colour art that needs to stay sharp, PNG is usually the right destination, not a lossy format — it is built for exactly this kind of image, and it is lossless.
And if you are converting a photograph, none of this is going to trouble you. That is the case the newer formats were designed around, and it is the case where they win by an enormous margin.