Taking a look at looting mob drop tables for mobs such as the zombie, its drop rates for rare player triggered drops, such as (I highlight) potatoes, iron and carrots, scale differently or incorrectly with looting and if a player manages to get the drop with a large looting value, only one potato drops.

Note
Do not do the procedure if rare loot drops only occur once regardless of looting value, even non-vanilla ones

Procedure
-Equip a Looting III sword (OR equip a non-vanilla, looting sword with a value > 1000 )
-Place two chests, to sort rare drops and normal ones
-Kill a number of unequipped, non-baby zombies (75-150)
-Between each kill, sort loot table drops including potatoes, iron and carrots from normal ones, be sure to log whether potato, iron and carrot drops also include other drops or multiples of the same drop.
-NOTE The term "drop" used means an individual zombies entire loot, not just the individual rare drops, so if rotten flesh is dropped with a rare drop, include that in the separate chest
-You should separate the carrot, potato and iron drops from regular rotten flesh drops:
Chest A: All items dropped from zombies that dropped rare items
Chest B: Normal, only rotten flesh drops

Notice that the rare drops only occur once, and things like rotten flesh almost never or never drop along with rare item drops.