If it wasn't working at all, wouldn't you notice getting sun burned?
Initially i thought it was going to be something advertised as spf 30 but actually 15. However spf 4 or less seems so low it should be noticable i would assume.
The returns on protection are very much diminishing by SPF 30.
Anything over SPF 30 buys you approximately no additional protection.
Using no sunscreen is SPF 1 (at 2 milligrams per square cm). Sunscreen SPF 2 would correspond to halving the rate of instantaneous damage.
SPF 30 compared to SPF 4 would indeed give (30/4)=7.5 times lower rate of instantaneous damage.
The SPF scale is more sensible than your blocking percentage scale.
As with most things, the dose makes the poison.
Source? All things being equal, I'd expect half the UV damage by going from 98% UV protection to 99% UV protection. That's significant even though the protection only went up by only 1%. Moreover as I mentioned in my previous comment, even if you assume that 2% UV exposure (from 98% protection) basically never results in skin cancer, that figure is only achieved if you use sunscreen perfectly, which no one really does.
So SPF 4 you are letting 25% of the sun through. I would assume that would be enough to still be sun burnt on a high uv index day if you spend most of it on the beach.
According to WikiPedia:
"For example, "SPF 15" means that 1⁄15 of the burning radiation will reach the skin, assuming sunscreen is applied evenly at a thick dosage of 2 milligrams per square centimeter[67] (mg/cm2)."
so assuming a linear dose response relationship (obviously oversimplified) when not using the sunscreen 15 times more instantaneous random damage is incurred compared to when using the sunscreen.
This does not translate directly into the rate of cancers though: just like the final damage of a meteorite storm isn't proportional, even though the instantaneous damage is.
Suppose a meteorite strikes a hospital, lots of damage. Then years later a meteorite strikes a school, lots of damage. Obviously if both happen in quick succession more damage will occur.
But if the whole human population takes up sunscreen use, selective pressure on cellular coping mechanisms will be relaxed, and eventually future generations won't be as resilient against sunburn. So just live your life, and don't allow scaremongers to separate you from your money, or thus indirectly scare you into doing your job for them.