Plain and simple, beets contains nitrates. Our body converts nitrates to nitric oxide, which is a vasodilation substance that opens blood vessels to move more oxygen and nutrients to working muscle groups. It helps us to do the same amount of work while using less oxygen. Or even better, doing more work while using the same amount of oxygen. Some studies have even found that after drinking a cup of beet juice, athletes can do the same work load utilizing almost 20% less oxygen. Its not exactly fair to say that beet juice will increase speed of power out put, but you can potentially do more work for the sam oxygen utilization.
A fantastic 2017 meta-analysis found that "The available results suggest that supplementation with beetroot juice can improve cardiorespiratory endurance in athletes by increasing efficiency, which improves performance at various distances, increases time to exhaustion at submaximal intensities, and may improve the cardiorespiratory performance at anaerobic threshold intensities and maximum oxygen uptake (VO2max)."
That sounds great, so bring on the beet supplements? Not quite. Its been found that non-vegetable sources of nitrates may have detrimental health effects. This would be the added nitrates in processed and cured deli meats or any beet root powder or tablet. Those are to be avoided as best as you can. If you want to improve our performance, you should ideally obtain nitrates from whole vegetables. Try adding some beets to your salads, sandwiches, wraps, stir-frys, and soups.