If I could do only one upper body exercise it would have to be pull-ups. Grappling is much more about pulling than pushing, and pull-ups are a convenient way to develop strength and endurance in your lats, biceps, and other pulling muscles.
You can do pull-ups in the gym, on a tree branch, or on monkey bars in a playground. I try to do pull-ups using three different hand positions: palms facing away from me, palms facing towards each other, and palms facing me. This develops strength in slightly different ways, and on the mat you never know exactly how your arms are going to be positioned.
Here are some additional pullup variations you may want to experiment with:
- Pull-ups with extra weight (tuck a dumbbell into your lifting belt)
- Pullups with static hangs: pause in mid-pullup
- Pullups gripping a gi or towel draped over the bar
- Upside-down pull-ups (pike up so that your feet face the ceiling)
Don’t get too hung up on the number of repetitions you can do. The maximum number of pull-ups achievable really depends on how fast you go. If I go up and down really fast, and bounce a bit at the bottom of my pullup, I can probably do twice as many as if went through each pullup slowly and smoothly. They are tough no matter how fast you do them.