One thing I have noticed over the last few years coaching combat athletes is that very often, 9/10 of them are very WEAK overhead, both with pushing (overhead press variations) and pulling (chin up variations).
Pressing overhead is difficult because the muscles involved are smaller when pressing on a vertical axis, compared to pressing on a horizontal axis.
However, getting strong at pressing overhead is a wise investment. And what's really cool about vertical pushing is that you can peak it perfectly for fight nights / comps / tournaments (much more so than horizontal pressing).
Here's how;
During your BASE strength phase (around 10 weeks out), choose a press variation that puts you in a disadvantageous position, for example; Seated Z Press, Half Kneeling Single Arm Landmine Press, Seated OHP (with no backrest) etc.
Because it's the BASE phase, you'll want to work in the 5 to 8 rep range, @ 75-85% of your 1RM. 3-4 sets.
When you transition into your Max Strength phase (around 7 weeks out), you're going to IMPROVE your pressing position by choosing a press variation that allows you to press MORE weight.
For example; OHP, Seated OHP (with backrest), Standing Single Arm Landmine Press, etc.
Because it's the Max Strength phase, you'll now want to focus on the 3-5 rep range, @ 80-90% of your 1RM. 3 sets.
Now to peak the vertical push series, we need a FULL BODY pressing option, that allows us to ACCELERATE the bar as fast as possible, with moderate to heavy loads.
Enter the Power phase (around 4 weeks out).
My favourite candidate here is the Push Press. Landmine Push Presses are great, too, especially if your shoulders don't love vertical pressing.
Because it's the Power phase, you'll now want to hit 5-6 reps of the Push Press, using around 110-115% of what you could STRICT press for the same number of reps.
For example, if you strict press 135lb for 5 reps, then 135 x 115% = 155lbs, so you would do 5 reps of Push Press with 155lb (as a rough guide).
As always, make sure to taper during the WEEK OF your important fight night or competition.
Invest your strength training time into developing solid overhead strength and you will be a problem to deal with, I promise you.