No problem, and I am hoping someone else will chime in. In a free run, especially if all the birds are one breed, then their eggs look similar, and it can be tricky to know who is laying what.
And I would like to be the first to point out, that I have only kept anecdotal records, as in, hmmmm the blue egg layer seems to be giving me an egg each day. So in a mixed flock, sometimes you can identify which egg goes with who. Take a couple of pictures of eggs, so that you know which is which, and keep a tally. Or separate you birds into individual pens say for 10 days, and keep track how many eggs in 10 days, give you a quick percentage. Two or three cages, and in 30 days, I would be able to test most of my hens.
But if it is egg laying that you would like to improve on, a much easier way, might be to look at the rooster. Get a rooster of a breed that is noted for it's egg laying. Then you don't have to separate anybody, and if you even keep fairly casual results of your hen's egg laying such as, keep a bowl of eggs on the counter, dating your eggs with a pencil, at the end of the period, say two weeks, sort your eggs, and the most prevalent group are the eggs you hatch.
Personally, I just bought a rooster, a Bielfeilder, which has some color patterns that I think will do better on the prairie, but can't really find out anything on their egg laying so hoping I did not shoot myself in the foot.
Mrs K
and this is a fascinating hobby with benefits! I have enjoyed it for years sometimes according to my plans, and sometimes not!