Ted Williams entered the final two games of the 1941 season batting .39955. If he’d sat them out, the average would’ve been rounded up to .400, making him the only MLB player in the modern era to bat the milestone. Manager Joe Cronin told Williams the decision to play and risk it or simply sit on the record was up to Williams, who famously said, “If I can’t hit .400 all the way, I don’t deserve it.” He went six for eight in the season-ending double-header and finished with a .406 batting average.

"But many players make the other choice,” said Devin Pope, behavioral scientist at the University of Chicago’s Booth School of Business, when I interviewed him for my book, Brain Trust. Though no one’s recently had the good fortune to confront the decision while camped at .400, many players have entered their last at bat with a .300 average. “More than 30 percent of those batters send in a pinch hitter,” says Pope. On the flip side of the .300 fence, Pope explains that batters at .299 never send in pinch hitters – and they never walk. For better or for worse, players who go into their final at-bat with a .299 average swing, trying to get the hit that puts them over the .300 hump.

The same is true of the diamond market. “You can’t find any .99-carat diamonds,” says Pope. Dealers know their customers will pay significantly more for a 1-carat diamond than they would for a .99-carat one, and so cut the stones accordingly.

So too with SAT scores. If a student scores xx90 – like 1,590 or 1,690 -- they’re about 20 percent more likely to retake the test than someone who scored lower in the last two digits. Next time – certainly -- they’ll hit that next hundred-point marker!

Thanks to our irrational human brains, we value these milestones – a .300 hitter, a 1-carat diamond, an 1,800 SAT score – disproportionately more than if they were just a tick lower. This means that batters have incentive to ride the pine at .300 or swing for a single at .299, trying to get to the high side of a value fence and thus likely earn a higher salary after the next contract negotiation. Conversely, advertisers exploit the low side of the value fence, pricing a gallon of milk at $3.99 and a car at $19,995. To our brains, the savings looks much larger than it actually is.

This also means that every time your car’s odometer gains a digit in the hundreds spot, it loses twenty dollars in resale value. Devin Pope showed that a car with 50,799 miles is worth twenty dollars more than a car with 50,800 miles. That’s an expensive mile. But a car with 50,899 miles is still worth as much as it was at 50,800. In respect to miles, your car doesn’t lose value smoothly – it ratchets downward with the hundreds digit.

The effect is a little stronger when you tick a thousand miles. That’ll cost you $250. But, “While all the 10,000-mile marks were huge,” says Pope, “it seemed like people caught on to the 100,000-mile game.” Even with the human mind’s inability to see $3.99 milk as $4.00, with used cars, it’s too obvious that a seller is trying to unload a car just before it charts 100,000 miles, so the price starts dropping at about 99,900.

So if you’re buying a car, your best deals will be just after it’s hit a round number – following 50,000 or 100,000 is ideal. And if you’re selling, make sure you do it before the car reaches those milestones that make it seem old. If that looming milestone is the big 100,000, sell it before 99,900.

Or at least before the odometer’s last two digits roll from 99 to 100. It’ll bring an extra twenty dollars.