Many of us don't really think much about balance but balance is extremely important in running - the better the balance, the more relaxed we will run. It's often taken for granted, an ability that we gain early and lose over time, especially after our mid forties, and that again is most of us here. I've recently read that many studies have shown that poor balance can be associated with serious health problems (and increased risks of falls as we get older) but that can be addressed and may well be fixed by proper training!
Some years ago I started practising standing on one leg and walking lunges (amongst other exercises) through practising martial arts ('Especially Tai Chi', as my wife helpfully chips in each and every time). That stuff will help strengthen our legs, improve flexibility, enhance our mental sharpness and focus so we are always aware of our position (or else we get punched in the face and walk away with a split lip or black eye).
Off road running will also help increase awareness of our positioning, thus helping maintain our balance.
Good and comfortable running is a mix of a lot of factors - diet, good running form, proper running gear, sleep, rest - and good balance! I never thought, until recently, that I would brush my teeth by standing on one leg like a flamingo (ignore snide comments coming from your kids, they are the ones who often cannot walk in straight lines).
So, if you see me out there being dressed up like a misplaced basketball player, approach me freely and join me in practice. The more, the merrier.