These burgers have so many positives it's hard to know where to start.
First, the finely grated potato adds a great moisture factor to the ground chuck or ground round. So if you're using leaner mixtures (80/20 or 90/10), the potato will eliminate the dryness factor.
Secondly, if you need to streeeeeeetch that purchase of ground chuck just a little, once again, the potato will come to the rescue.
Thirdly, if you're looking for a way to add a little extra nutrition to a child's burger at home, here's the way to do it.
Begin with 1 pound of ground chuck or ground round and 1 medium russet potato. Break the meat up with a fork in a large bowl. Peel the potato and using the finest grating side of a box grater, grate the potato and add to the meat. Add about a 1/2 t. granulated garlic, a few grinds of black pepper and about 1/2 t. salt. Mix together well with the fork.
Shape into four patties. Heat a large cast iron skillet over medium high heat and add the burgers to the pan.
See the shreds of potato in there? Yummy goodness!
Cook until your desired level of doneness. The potatoes will also provide a nice "crunch" factor to the burgers. Enjoy!