Baseball leads off, followed by the NFL, NBA, NHL, and MLS, respectively. Each Voronoi territory contains every place closer to that stadium or arena than to any other active U.S. venue in its league. Canadian teams, Alaska, and Hawaii are excluded.
I tested a familiar baseball idea: with two outs, a runner on second can run immediately on contact and without worrying about getting doubled-off.
Using 47,653 MLB regular-season balls in play from 2021-2025 with second occupied, first and third empty, and home runs excluded, I measured whether the runner scored on that same play (i.e., not whether they advanced to third and scored later). Below are the probabilities the runner scores:
A two-proportion hypothesis test evaluated the null hypothesis that the scoring probabilities were equal (2 outs vs fewer than 2 outs). The result was statistically significant (p < 0.001), so I reject the null and conclude that two outs are associated with a higher probability of scoring on the play compared to 0 or 1 outs.
The increase may reflect larger leads, running on contact, and more aggressive third-base coaching. This is a strong statistical result but not necessarily causal: runners, contact, defense, and game situations likely have an influence.