I can't comment on flats specific, but I can on general use.
What causes haze is an excess of blue light, so cutting back on that is going to help you see better.
So, we've got three general shades we use.. Yellow, brown, and grey.

Grey is going to be the one that reproduces the most accurate colour tones, but it does the least of the three to reduce the excess blue light. If you buy photography filters, you will find a true Neutral Density filter is grey shaded.

Brown, or amber, is going to change colour reproduction from natural. However, because of its composition, it will cut back on blue light helping to reduce haze and increase clarity any time an excess of blue wavelengths are about. This is why as twilight recedes, or dusk encroaches, you may find that contrary to common sense, your sunglasses increase your ability to see details.

Finally, there's yellow lenses. Yellow will do more to reduce blue light versus brown, however it won't be as darkly shaded. This is why you often see things like driving, shooting, or other assorted glasses for activites sold with yellow lenses. Again, from a photography standpoint, a Wratten Yellow #8 is often used as the "standard" in B&W photography. The classic B&W films (I don't keep up much anymore) are blue sensitive, so using a yellow filter would help reproduce better contrast in your pictures. Many photographers, upon seeking more dramatic results, might switch out to a Wratten 25 red. Not that matters, but as an example of cutting back blue light.

So, with that said, the recommendation to anyone buying polarized lenses for sporting purposes, I always suggest amber.