What makes a record unbreakable? Sometimes, the game changes and records move out of reach. Sometimes, the game remains the same, but a truly exceptional player has a single-season performance so dominant that it is unlikely to ever be surpassed.

And the records that seem unlikeliest to fall are a combination of an extraordinary player and fundamental shifts in the game. By using something called extreme value theory — often used for modeling extreme weather events and floods — we can approximate how many seasons of baseball similar to the most recent era it would take for there to be a 50 percent chance that the single-season records below will have been broken.

Of course, unforeseeable changes in baseball’s rules make these numbers tentative at best. But they serve to highlight some of the best performances in baseball’s modern era (since 1901), and the ones that are likely to remain on baseball’s record books for decades, and centuries, to come.