Rockin' knows of what he speaks.
First off, only boxing will get you in shape for boxing. Boxing will help get you cut and fit if you're a weightlifter, but no amount of weightlifting in the world will make you into a good boxer.
If you just want to get fit, boxing is a great physical and mental workout to complement a weightlifting program. If you want to learn to box and use weightlifting to supplement it, though, then the gym routine you outlined above is too specialized, IMO. You want to concentrate on compound movements like squats and cleans, that make you use a dozen or more muscles in concert; not isolating exercises like dumbell flyes and curls.
I'm on the weight pile 3 days a week for around 90 minutes, and in the boxing gym 3 or 4 days a week for 2 hours or so, alternating days. My weight routine is:
1 day -- 8 sets of squats (+ warmup set)
1 day -- 8 sets of deadlifts (+ warmup set)
1 day -- 8 sets of cleans (+ warmup set)
I jump rope for 5-10 minutes between every couple of sets. I usually pyramid down, i.e., use a lighter weight each set, and do 6-8 reps per set. By the time I hit that 8th set of squats, I'm usually just using the bar plus maybe 20 lbs, and I'm hitting failure or my physical pain threshhold; I'm that burned out. (I used to bodybuild, so I know that my body responds well to pyramid drop sets and 6-8 sets of 6-8 reps. Your mileage may vary. If you haven't lifted before, start with 3 sets.) Warm-up sets are done with 50% of my max for about 15 reps.
I've been on this for a few weeks, now, and it's made a huge difference in my mobility in the ring.
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