Power absolutely is directly related to strength. The equation for power is force multiplied by distance (work) divided by time. Strength underpins power, which is why stronger athletes can express greater power outputs. This is backed up by hundreds and hundreds of scientific studies. Being stronger also improves technique as there is less diffusion in the brain for the same movement, meaning it's less taxing/demanding. I don't even know what you're trying to say with all your arrows.
You have to understand that boxers are 100% different to every other athlete, therefor the same rules do not apply.
Seems to me like it would be better to just go ahead with the squats then. Probably safer and easier to continuously add weight while squatting rather than doing it with the barbell step up.
I agree, bilateral exercises are better for increasing strength because you can load up more. Unilateral exercises should always be used primarily as accessory exercises (to provide balance etc.) rather than a main strength building exercise. I do think unilateral work is quite important for a boxer as each leg moves a bit differently from the other (and independently) so there is potential for asymmetry and other issues to come into play. Do both if you can.
The first boxer I ever saw lift weights in training was Victor Galindez back in the late 70's. Vito Antuerfermo also lifted weights although he denied it. Galindez was doing presses behind the neck with a pretty light barbell. I still think pressing will increase punching power. Of course, Nothing will replace proper balance and leverage.
DW is correct about squats a recent study by the British Journal of Sports Medicine the maximum effort in squats determines sprint performances and height in elite soccer players. In 2009 researchers at appalachia state university found significant correlations between squat 1rm 5, 10 and 40 yard dash; the shorter the dash the stronger the correlation between 1-AA football players.
There is no reason not to substitute the barbell squat with the less risky hex bar deadlift. http://www.asbweb.org/conferences/2003/pdfs/93.pdf
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Unable to post sites since my membership is less than 90 days. See the Appalachian state university study. Influence of power and strength- power training on load velocity performance. That should start you. There is quite a lot of material to cover.
I am not asking this question to be a wise guy, serious question: Does anyone actually know a boxer who went from being a light puncher to being a heavy puncher after taking up weight training? I honestly can't think of one.