In a "hard knee" compression process, gain reduction is set to take effect once the signal exceeds the threshold by any amount (in theory). So even if you only go 1db over the threshold, a 4:1 ratio is saying the compressor should output 0.25db of signal.
Now, the reason I don't go into the ratio, attack, and release in extreme depth in the sticky post is because they don't exactly do what they theoretically do. A better way to think about the ratio control is how "tough" or "hard" the compressor works. There are very few real life scenarios where the actual input and output correspond to what the ratio mathematically yields based on the incoming signal.
I like to think of it as "hardness" because you get a fundamentally different sound by setting a low ratio with a low threshold, vs. setting a high ratio with a high threshold - even if mathematically you are performing the same amount of gain reduction.