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The true extreme spread of a population is about 6 times the standard deviation," explains Engleman. That is thanks to the power of a normal distribution, which we talked about in the
last article. In a normal distribution, we know 99.9% of our shots will be within 3 SD (3 times the SD) from our average velocity. That means our slowest shot would be 3 times our SD below the average, and the fastest shot would be 3 times our SD above the average – and the difference between the min and the max would be very close to 6 times our SD. So, in our example where our SD is 9.6 fps, we should expect our ES to eventually grow to 58 fps if we continued to fire shots (9.6 fps SD x 6 = 57.6 fps ES). How many shots would it take before measured ES got to 58 fps? Who knows! It might take 100+ rounds, but we also might luck into that spread in a different 20-shot string. But, by 1,000 shots our data would take the shape of a normal distribution and our ES would likely land near 60 fps, yet our SD would very likely remain between 8 and 13 fps. This illustrates why SD is a more reliable statistical indicator of variation.