I only know Sparta, but I think this works the same in the other Plarium games.

When you win a position/battleground/mission/infestation you get an equipment piece, the type you get depends on level you won.

Level 

1-20   Class I, Common

1-20  Class I, Uncommon

6-20  Class I, Rare

11-20 Class I, Legendary

21-40 Class II, Common

21-40 Class II, Uncommon

26-40 Class II, Rare

31-40 Class II, Legendary

41-60, Class III,  Common

41-60, Class III, Uncommon

46-60, Class III, Rare

51-Max, Class III, Legendary

61-Max, Class IV, Common

61-Max, Class IV, Uncommon

66-Max, Class IV, Rare

71-Max, Class IV, Legendary

I say this because I've done many hundreds of level 1-20 persians and I saw the pattern there. I've only done a moderate number of levels above that, but people who design software like this, tend to make things simple, so I have no reason to doubt that the same pattern is used in the higher level classes.

While it may infrequently occur, that a piece of the above types drops at a level outside those ranges, that could either be a designed-in very low probability event, or a bug. If people want to compile data for a 100 or so positions in one of the above given ranges, and find that something listed above needs to be altered, that would be great. However, anecdotal data, or just doing a handful or even a dozen positions in a range, is too small a number to draw conclusions from.

A couple years ago, someone tried to compile information on drops and posted it here, but they did not detect the pattern of levels within the common/uncommon/rare/legendary groups, so they gave much lower drop rates for legendary and rare items.

If you want legendary item within a certain class, about a dozen wins for positions in the range above should get you one, on average. Though I also wouldn't be surprised if above level 80, the odds are lower. Rare items are more frequent within their given level range. I wasn't paying as much attention to them, but I'd guess about 1 in 8. For a little while I was tracking frequencies for uncommon pieces and it was about 1 out of 6.

Also, chests are overwhelmingly more common for legendary equipment than their keys and pieces. It is not as bad with rare. I would guess this is because there is a smaller range of levels for legendary than there is for rare.

These ranges of levels is also important because if you clear all your levels below a certain number (and I think do this a few times), you will stop getting levels below that, or a certain % of your lowest level, or it has to do with your lowest and highest level. I haven't quite figured out more details on this, but suffice to say, if you want a legendary class I or legendary class II piece, but you've been doing only high levels, it seems that you will NEVER get a chance to get one again... unless somehow it comes in some package or tournament win. 

You may think that the higher the level the better, so that a class I or class II legendary is useless, but when you want to upgrade your higher level piece, it will take a lot of work/money.

So if you didn't get a fully maxed out legendary set for your lights or heavies for those times when you only want to attack or defend with lights or heavies, you won't be able to go back. Unless you can get a very special Delorean. ;-)