This is probably the most important component that people forget about or are just too lazy to incorporate into their programs. Single leg work (think lunges) serves several purposes. It helps to fix any weaknesses or imbalances that may exist between one limb or the other (in this case, one leg being stronger or weaker than the other). They also do a superb job at improving overall strength by forcing the hip adductors/abductors to fire and stabilize the body (namely the femur) while the body is breaking the frontal plane, which is especially beneficial for many athletes. This is also the reasoning as to why single leg work helps to improve coordination and balance, which many people (athletes aside) drastically lack.
I see it almost everyday with the clients that I work with. Kids who sit in front of the television all day playing video games or older adults who have sedentary jobs in front of the computer, can’t perform a simple reverse lunge without falling over every other repetition.
In the end, single leg work has a HUGE carryover to sports. How many sports can you think of that take place entirely on two feet? And no, competitive eating is not a sport. Additionally if there is anything that will help prevent the majority of knee problems that occur, single leg work may be it. So do yourself a favor and start incorporating them into your programming. Your knees will thank you.
On an aside, I like to categorize single leg work in the same fashion as Mike Boyle: check out this article which shows a few videos of the movement I am referring to.
Knee Dominant Single Leg Training: basically entails any squat variation on one leg (lunges, step-ups, split squats, Bulgarians, one-legged squats (pistols)
Static, Un-supported: consist of single leg movements done on one leg with no movement forward or backward (these would be your true one-legged squats). The non working extremity is not allowed to touch the ground.
Static, Supported: still no movement forward or backward, but now the non working extremity is supported (by the ground or a bench). These would entail your split squats or Bulgarian split squats.
Dynamic: Walking Lunges, step-ups
Hip Dominant Single Leg Training: involves more of the hamstrings and glutes. One-legged Romanian Deadlifts, Reverse Lunges. etc.
Unfortunately, I can’t include videos of all movements listed above. If you have any more questions, feel free to e-mail me and I can send you some links/videos.