As major league baseball reaches the end of its regular season, you get the feeling that Los Angeles Dodgers designated hitter Shohei Ohtani and New York Yankees captain Aaron Judge are just getting started in their collision course with history.

Mr. Ohtani is destined to reach a once unthinkable milestone by becoming the first player in baseball history to collect 50 home runs and 50 stolen bases in a season. Mr. Judge, meanwhile, could flirt with his American League record of 62 home runs in a season, having hit 51 on the year heading into Friday’s games.

While their regular-season performances have been nothing short of extraordinary, their year will be defined by what they do in the fast-approaching post-season and how they respond to the pressure of October baseball.

“The most important thing is to be able to contribute to winning the game,” Mr. Ohtani told reporters earlier this week. “Obviously the closer I get to 50/50 the more I’m contributing to the team win. If that’s how it is then I’m happy for that.”

Before a recent homerless drought where Mr. Judge did not belt a single home run in the 15 games before Friday, it might have been difficult deciding whether he or Mr. Ohtani was having the better season. 

After a slow start where Mr. Judge, 32, managed just four homers in his first 27 games, the Yankees outfielder homered on back-to-back nights against the Milwaukee Brewers to trigger a 102-game stretch where he belted 47 home runs. The surge of power-hitting was capped by a two-homer game against the Colorado Rockies. Mr. Judge has not homered in the 15 games since then but had 11 hits and three doubles. The long-ball drought is something no one seems overly concerned about as the Yankees try to fend off the Baltimore Orioles in the American League East.

“It’s another historic season, he’s putting together,” Yankees manager Aaron Boone said. “We saw in April and now the last couple of weeks where he’s not dominating like his usual self. I’m confident he’ll get rolling.”

Mr. Judge, who carried 126 RBI and a .320 batting average into Friday, seems certain to win the AL Most Valuable Player Award for the second time after winning it in 2022.

Mr. Ohtani, 30, is a lock for his third MVP Award overall and first in the National League. In his first campaign with the Dodgers after playing six years with Los Angels, Mr. Ohtani is making good on the ten-year $700 million contract he signed to move to Hollywood.

Heading into Friday’s games, the team’s designated hitter had 47 home runs and 48 stolen bases with three weeks remaining in the season to create his own 50/50 club.

He became the sixth player in major league history and the fastest ever to reach 40 homers and 40 stolen bases when he did that in the same game last month.  Now he’s on the cusp of doing something that has never been done before.

“He’s playing tremendous baseball,” Dodgers manager Dave Roberts said recently. “You can see he’s picking us up bigtime. Obviously, I hope he does it regardless of where. But hopefully he does it at home.”

Mr. Ohtani, who had 104 RBI and .292 batting average after 143 games, has made a seamless transition playing for the Dodgers despite being engulfed in a sports gambling controversy during spring training. Mr. Ohtani’s long-time interpreter and confidant Ippei Mizuhara pleaded guilty to bank and tax fraud for stealing $17 million from Mr. Ohtani’s bank account. Mr. Mizuhara said he spent the bulk of the money covering gambling debts.

An investigation by Major League Baseball revealed no evidence Mr. Ohtani was aware of any illegal sports betting, calling him “a victim of fraud.” The incident is declared closed and all but forgotten amid his already historical season.

“As a player you feel very supported and appreciative of the fans behind me and behind the team,” Mr. Ohtani said after a warm reception in his return to Anaheim. “It makes a difference that they’re out here.”

The Dodgers are comfortably ahead in the NL West, ensuring Mr. Ohtani will reach the post-season for the first time in his MLB career. Playing in the spotlight of October baseball and potentially a World Series will introduce him to a new legion of fans. Mr. Judge is hoping the Yankees reach the post-season after failing to qualify last year. Then he’ll have to a chance to be the Yankees latest Mr. October.