Before his last plate appearance of the 2007 season, with the postseason looming and his catcher’s body disintegrating like a ’72 Impala, Victor Martinez came to the plate and noticed the scoreboard taunting him.

On it read his batting average: .299.

He had gone two for three that day and figured he had clawed his average up to .300. But Martinez was still at .299465, which is about the closest one can dance with .300 without sharing its dress.

“The only way I was going to walk,” Martinez recalled recently with a laugh, “was a pitch in the dirt or over my head.”

Normally a selective hitter, Martinez rapped a 2-1 fastball through the infield and finished the season at .301. In doing so, he contributed not only to the back of his baseball card, but also to a study of behavior that goes well beyond baseball.

Two economists at the Wharton School of the University of Pennsylvania, while investigating how round numbers influence goals, examined the behavior of major-league hitters from 1975 to 2008 who entered what became their final plate appearance of the season with a batting average of .299 or .300 (in at least 200 turns at bat).

They found that the 127 hitters at .299 or .300 batted a whopping .463 in that final at-bat, demonstrating a motivation to succeed well beyond normal (and in what was usually an otherwise meaningless game).

Most deliciously, not one of the 61 hitters who entered at .299 drew a walk — which would have fired those ugly 9s into permanence because batting average considers bases on balls neither hit nor at-bat.

Martinez said that “.299 doesn’t look as good as that 3 in front.”

Now, hitting .300 carries less prestige than it once did. Offensive metrics more founded in science have turned batting averages of .300 (prince), .350 (king) and .200 (court jester) into ranks within an increasingly irrelevant royal family.

Yet even today’s hitters will clearly try much harder when a .300 average is at stake, said Devin Pope, who co-wrote the study with Wharton’s Uri Simonsohn. (The paper has been accepted for publication by the journal Psychological Science.) What they found could intrigue behavioral economists from academia to Las Vegas, as well as add a little spice to today’s final regular-season games.

Pope and Simonsohn found that the percentage of hitters who end a season at various averages from .280 to .320 — those hitting .294, .295, .302 and so on — decreases, as expected, in a relatively smooth fashion. The percentage plummets at .299 and skyrockets at .300, before settling into its normal, steady decline.

“Usually when you look at sports, the opponent is motivated, too — like in the World Series, pitchers are trying just as hard,” said Pope, who recently took a position at the University of Chicago. “What you have here is asymmetric motivation, and it results in a wild divergence from what would otherwise be expected.”

As part of their round-number study, Pope and Simonsohn also examined the behavior of high school students taking the SAT. They found that those who received scores ending with 90 were significantly more likely to retake the test than if their score ended in 00, clearly striving for the ladder’s next rung. (Imagine if the students could take their scores to salary arbitration.)

“We don’t think of numbers in a continuous fashion — we react to round numbers differently,” Pope said. “There’s a ton of literature on pricing, where $2.99 seems much cheaper than something priced at $3. We think this is a similar psychology — for the same reason stores price at $2.99, hitters want to hit that target of .300.”

At Yankee Stadium a week ago, in the Boston Red Sox clubhouse a few lockers down from Martinez, David Ortiz laughed at baseball players’ aversion to 9s. (Strange, given the sport’s skeletal use of 3s and 9s.) Five years ago, in a meaningless 162nd game against the Yankees, Ortiz entered batting .299 for the season; he struck out in the first inning to drop to .298 and walked in the third, knowing he still had a few more chances to swing for .300.

One inning later, Ortiz singled to reach .300. He batted one more time in the sixth — he walked, refusing to swing at anything that might result in an out — and was, because of the statistical awareness of his manager, Terry Francona, replaced on the bases to make sure that .300 season average would last forever.

“In baseball, that one point, that one number, makes a huge difference,” Ortiz said. “We were talking the other day, the guys were saying that this was the first year since 2007 that I get 100 RBI (runs batted in).

“They forget that I got 99 last year. I’m like, what happened to those 99? They don’t count?”