No you don't havt to be tall to be a good striker. And you are only at a disadvantage against a taller striker if you allow yourself to be. Now if you try to stand on the outside and hang and bang with a fighter that has a reach advantage over you then yes, your at a major disadvantage but once you get inside and your working from the inside you neutralize his reach advantage and in fact now the man with the shorter arms has the advantage. This of coarse is not taking into account knees and elbows your opponent could throw while your on the inside.
As I have see stated, the major key for the shorter fighter in a standup war is footwork and good movement. Slip in and out of his range. Slip in take your shots and slip back out before he can return damage. Utilize movement to keep him constantly readjusting and try to beat him to the punch. Take him out of his game and make him play yours, by your rules. Don't let him dictate the pace nor the distance. The fighter with the reach advantage is gonna need to work his jab or a leg kick to keep the shorter fighter where he wants him. As the shorter fighter you have to deny him that. Every time the taller guy even thinks leg kick he should be feeling yours. Keep him on the defensive, good movement in and out. Never come straight in but being working those angles. Everytime he throws a jab out there make him pay for it. Teach him to keep his hands to himself. If everytime he throws his jab you counter with an attack, whether it be a leg kick or stepping in and unleashing a punch of your own, you wil actually be training him not to throw his jab and you will see, he starts throwing it less and less giving you even more opportunity to get inside and start really getting the work done. In MMA, you have a futher advantage and that is the potential for a takedown. Even if that is the furthest thing from your mind, don't let him now that. You want him thinking you could go for the takedown at any second. The more he is thinking about what your gonna do, the less he is thinking about what he should be doing.
Fighting a man with a longer reach is only a disadvantage if you let it be, especially in MMA where your possibilities to neutralize that advantage is endless. In the end, it'll come down to you. Your skill level and your training. Just knowing you have this potential disadvantage and training to neutralize it give you the advantage.
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