This is simply another one of those topics, like politics, abortion et al, that no matter how many points are made by either side it it all comes down to personal choice. Strength train, or don't strength train. Personally strength training bores me to death, the things I already do keep me in fine shape. As for pullups, when I was heavily into rock climbing, I had a huge pullup workout I did twice a week, regular, weighted, unevens, and a few more. Is there irrefutable evidence that strength training will make you a faster triathlete? Well I can tell you that I've beaten many very muscular guys half my age, so I'll just stick with swim, bike, run, surf.

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I'm not a complete idiot, some of the parts are missing.