There is a simple trick on how to get better results when farming stuff:
Just get a tool with a "fortune" enchantment and harvest your stuff!
The "fortune" enchantment seems to affect stuff like carrots, potatoes and so on as well while the tools don't get any damage while harvesting those materials.
Testing this on an 5x5 area with one water block inside I was able to get a better result of 68%.
So, don't throw your fortune Pickaxe away when it only has one more hitpoint left!!!

Here a Pic of the layout of my potatoe farm:
The results of farming the normal way without the little trick:
Here a pic of the results with the fortune tool, I used a fortune 3 puickaxe btw:
Best Regards,
SirSimpleton