Well, my take is a bit different. Yes, the races can and are won on the run. BUT, you must be a good cyclist to stay in contention (non-drafting) AND to feel good enough to have a good run. SAME TOO, you must be able to swim good enough to put yourself in contention for the aforementioned bike. So, the most important is to put the three together in a way that you are in position to close with a successful run.
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David
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Disclaimer: I have personal and professional relationships with many athletes, vendors, and organizations in the triathlon world.