The chance increases if you have a happy hut, snuggle hut or nest box and no extra calcium is given.
I'd also say that smaller parrots - budgies and cockatiels etc - are more suspectable because they breed more often if given the chance.
2 Budgies, 3 Cockatiels, 6 GCC'S, 2 Crimson Bellie Conures, 9 Sun Conures, 2 Major Mitchells, 12 Eclectus parrots of various ages, 2 BF Amazons, 2 Hahn's Macaw's, 1 Red Tail Black Too
Personally my birds are fed a well balanced diet, have calcium at all times so they eat what they need. I don't think i have ever had a hen that was egg bound.
I just want to add, a excessive egg layer is prone to egg binding as well no matter how much calcium is being provided. Best to discourage them from laying period!