Vegan patty binders

In case of vegan kitchen, you would need to use ingredients with high levels starch or binding proteins, such as gluten. One important thing to remember about starch is that it is removed (into the water) in the process of cooking. So, if you pre-cook your potatoes before adding them into patties, they will provide less starch than raw potatoes. The same goes for beans, chickpeas and any other starchy food.

Adding gluten, either in more or less pure form or in form of wheat flour, helps too but requires some 'development time' for its chemistry to work.

Also, the amount of water in your patty influences its consistency. The more water you have, the more starch/flour you would need.

For the specific case of chick peas, I can say that raw, soaked, ground (food processed) chickpeas need no binder, while pre-cooked (canned) ones do need a binder (from my falafel-making experiments.) I also found that "wetter than most recipes leaned" worked better for me in falafel. So that might fix the recipe that didn't work but tasted good.

If you are not dealing with a gluten-free vegan (far too many of whom seem to be trendy, rather than Celiac - I have much sympathy for Celiac, and little for trendy) plain old wheat flour is a good generic binder. Ground flaxseed (mentioned by Carmi in comments) is another, though it has more impact on flavor; it can be a good impact.

You could go a couple of routes here but what I recommend is to use potato mash as binder. Not salted, without any milk or butter substitute, spiced if you wish. This works perfectly both for baking and frying. The beauty is you can keep al your other "vegan ball" ingredients chunky and just use as much mash as you need to bind. Potatoes are also used in deserts (look up Irish dougnuts) so can be used in your sweets too. Just add cocoa powder and sugar! Best part is potatoes are gluten-free.

PS. steamed then grated potatoes add extra texture, though a bigger hassle to prepare.

Hope this helps :)

Legume flours (eg chickpea flour - inexpensively available at asian grocers, soybean flour, lentil flour ...) are strong protein based binders; at least chickpea flour (made into a batter with water) is strong enough to yield a usable pancake on its own (as is done in indian cuisine). Mind that these will need various degrees of cooking to be palatable (not long for chickpea flour, but it really does not taste good un-set or raw). Also, make sure that they are well hydrated but not overhydrated (similar to a flour-based batter).