Polarizers were sort of discussed earlier. In a nutshell, they are useful to control reflections. For a mid afternoon sports shooter, this could be beneficial. Are you talking water sports? Have you ever had a lot of reflection off the water? A polarizer could stomp that out. Similarly, if you’ve ever taken a photo of a racetrack where the asphalt is all shiney, that shinyness is due to reflections. Grass reflects, too.
A big drawback for polarizers is that they steal 2 stops of light – this means that it would be harder to stop action -> more motion blur as the athletes hit the ball (or whatever). Can be artistic, but… I have a polarizer on whenever I’m doing landscapes. Not so much when I’m doing portraiture or photos of the kids.
Multicoating. Hmmm. Was is a “UV” or a “Skylight” filter? Those filters are supposed to reduce a blue cast due to light being reflected by atmospheric particles. Supposed to be helpful in mountain photos where you have gobs of landscape going through tons of atmosphere. I’ve never noticed the difference (but I’ve never done a controlled test, either). I put my skylight filter on when I give my camera to someone who probably won’t treat the optics nice – it acts as a physical protector.
“Multicoating” as a term is something very desireable for a zoom lens or a filter for a zoom lens. It has to do with the “characteristic impedance of free space” – as light travels through space and hits a glass surface, an uncoated surface will reflect (due to impedance mismatch). A coated surface tries to better match the impedance, reducing the relfection, leading to more light hitting the imaging device (film, CCD). Multicoating just does it better. For a concrete example, have you ever seen someone’s eyeglasses that reflect gobs of light? Those glasses are not coated. Ones that don’t reflect are coated.
Note that I wrote “zoom lens”. Zooms tend to have many optical elements which all introduce light loss. Coating those elements mitigates that loss. Prime focus lenses are simpler and not as susecptible to light loss.
(I really like “characteristic impedance of free space” as a phrase and try to work it in whenever possible. Its harder than you may think)