Yes, typically it is 4% per surface, going in or out.
So, 4% gets reflected going in the first surface(and much greater if it is not perpendicular to the surface).
It arrives at the second surface on the way out, and 4% is reflected there.
Now this 4% gets shot back at the first surface, "going backwards".
This 4% that is "going backwards" to the first surface is then shot back where it came from. But 4% of the 4% is reflected forwards again (which at this point is 0.16% of the light).
So this 0.16% then arrives at the second face for the "second time", and 4% of this 0.16% is reflected back.
So we'd lost 8% but got 0.1664% back, which puts us at 7.8336%.
You can repeat this and get a slightly lower amount of loss.
But way back, we had about 4% bounce when we hit the first surface, going back to the source.
This initial bounce, goes back and hits the reflector for an 20-7% (7% loss for high end vacuum sputtered lab/telescope grade oxide overcoat to protect from oxidation). So lets say average is 10% (being low side for most reflectors) the 4% returning takes the hit in absorption, so we are get to 3.9%, on the way to the light source off the reflector.
Now we have a glass/quartz/saphire bulb surface we have to pass through, or the outside acrylic lens of the luxeon, then another interface from the acrylic lens to the silicone gel, and we finally get to the phosphor.
Then we hit this phosphor and I'd venture to guess see a 30% loss in absorption. Then it is outbound again.
The missing part is there is loss in the glass lens material, in the air, in the acrylic, in the silicone gel. I kinda look at it similar to the loss you see in a wire due to resistance.
Next, the surfaces are not perfectly perpendicular, but look like a mountain range under high power magnification. So you end up with a bit more loss than this simple "math".
The AR coating helps index match the materials, between the interfaces. From a EE perspective, its *alot* like impedance matching.
Lower index materials will have lower reflection, and higher
index materials will have a higher reflection loss. It's one of the reasons that diamonds sparkle so well. They have a fairly high index. Like in RF, where you often have a 50 ohm impedance, in optics, air has a Index of Refraction of 1.0.
Typically most AR coatings will reduce the reflection to under 0.5% This can drop to 0.2% with the skill of the coater, and the number of layers. High end coatings can drop below 0.1% reflection. Visible AR is typically a multitude of extremely thin layers.
From what I've seen, vacuum deposited AR tends to be much more durable than simple sputtered AR.
Silicon Dioxide AR tends to be a greenish hue in the reflection, where Magnesium Fluoride AR will have a purple hue. Other reflected hues are due to the lack of skill, and the coating will not be centered on the visible light spectrum, and for MgF(2), an improper coating will have a red or blue cast.
Just like the amount of reflection off a surface of glass increases as you move off perpendicular, then reaching the critical angle of 35-45 degrees, where you transition to a 100% reflection due to TIR, AR coatings also get more reflective off the perpendicular.
One bad thing about AR is you have to keep it clean. Unfortunately, even skin oil interfers with it's optimum properties. This can be significantly reduced by a final overcoating of hydrophillic/hygrophobic material. I cannot recall off hand which one helps with fingerprints and which one helps with fog.
Now remember that borofloat/borosilicate(crown glass) is water clear, looking edge on, and sodalime float glass (window glass) is green. You'll see additional losses to due the very low cost window glass. The green you see when looking edge on with sodalime, is an additional loss factor. And it significally reduces the multiple bounce light return.
There is a 0.2% typical penalty loss from absorption at each interface where you use a BBAR/HEA anti-reflective coating.
So, yup, I'd sure believe what you may have seen experimentally.
BTW, here is a quick and dirty on AR:
http://www.ocli.com/pdf_files/products/antireflection_coatings.pdf