Why does it suck to wait for things? In a previous post I analyzed a NYC subway dataset and found that at some point, quite early, it's worth just giving up. This isn't a proof that the subway doesn't run on time — in fact it might actually proves that the subway runs really well.

Erik Bernhardsson

A mathematical exploration of why subway waiting times are so sensitive to variance in train arrival intervals. Using NYC MTA data, the analysis shows that even a 1% chance of a 10x delay can increase average waiting time by 1.83x. The key insight is that average waiting time scales with the variance of inter-train intervals, not just the mean frequency. Real MTA data shows variance roughly doubles average waiting times across most lines, meaning trains running more evenly spaced — without adding any new trains — could cut average wait times in half.

Subway waiting math

How much does the variance matter in reality?