The Post Sports Live crew assesses the Nationals at the midway point of the season, and look at which players need to lead the team down the stretch to a potential National League East crown. (Post Sports Live/The Washington Post)

The phrases permeate baseball — “He’s on fire,” “I’m seeing the ball well” or “He’s locked in” — but, really, what do they all mean? For decades, research — primarily involving basketball — has disproved the existence of the “hot hand,” the theory that a player on a streak is more likely to perform better on the next play.

Just don’t tell baseball players that.

“Hot streaks are real,” Washington Nationals hitting coach Rick Schu said. “Totally. One-hundred percent.”

“That’s a real thing,” Nationals right fielder Jayson Werth added. “No doubt about it. It’s been talked about over and over and over. Michael Jordan’s talked about it. It’s real.”

Baseball players believe that eight hits in the past 10 at-bats, for example, will help determine the outcome in their 11th at-bat. Managers often sit a cold player in favor of a hot one, or call for a pitcher to pitch around a hot opposing batter. But until recently, there was little hard evidence to prove hot streaks.

A 1985 study by Cornell psychology professor Thomas Gilovich and Stanford professors Robert Vallone and Amos Tversky found no evidence of streak shooting when studying statistics from a Philadelphia 76ers season, free throw shooting data from the Boston Celtics and an experiment with Cornell players. The study found that Julius Erving was nearly as likely to make a free throw after three misses (52 percent) than after hitting three straight free throws (48 percent).

But according to newer research — such as a working study conducted by Brett Green, an assistant professor at California-Berkeley’s business school, and Jeffrey Zwiebel, a finance professor at Stanford — there is evidence that hot streaks exist.

As a sports fan, Zwiebel was motivated to address the claims of older studies and their statistical flaws. He believed baseball was different than basketball because of the breadth of data and nature of the sport. In basketball, for example, a hot shooter may draw a double team by the opposing defense; that’s not possible in baseball.

Green and Zwiebel studied two million MLB at-bats from 2000 to 2011. They neutralized for the abilities of the hitter and pitchers — such as lefty-on-lefty matchups and stadium sizes — and focused on 10 major statistical categories, such as batting averages, home run percentages and strikeout rates.

They found that a hitter’s past 25 at-bats were a significant predictor of his next at-bat. When a player is hot, they found his expected on-base percentage to be 25 to 30 points higher than it would if he were cold. Home run rates jumped 30 percent and strikeout rates dropped. For pitchers in hot streaks, future performance was improved, too.

“The effect is fairly large,” Zwiebel said. “It’s highly significant not just in the statistical sense but the strategic sense. The effect is large enough where it makes sense for managers to sit a cold hitter or play a hot hitter, or perhaps the strategical adjustments for a pitcher to pitch around a hot hitter.”

Another recent basketball study presented this spring by Andrew Bocskocsky, John Ezekowitz and Carolyn Stein of Harvard found that hot-shooting players were 1.2 to 2.4 percentage points more likely to hit their next shot, a small but noticeable difference. Recent studies like these two finally found evidence for a belief that players have long held.

“It matters a lot mentally if you’ve been successful in your last at-bats,” said Baltimore Orioles designated hitter Nelson Cruz, who has been one of baseball’s hottest hitters all season and is second in the majors with 28 home runs. “Your confidence definitely goes up and you’re more likely to get a hit in your next at-bat.”

The study conducted by Green and Zwiebel, however, stops short of offering explanations. Zwiebel said he believes a player’s change in hitting is likely a combination of physical and mental factors. Players, too, can’t pinpoint reasons. Werth, currently the Nationals’ hottest hitter, talks about hitting streaks as if they were independent beings that come and go uncontrollably.

“If I knew the answer to that, I’d be a first-ballot Hall of Famer,” he said. “What’s that Yogi Berra saying? ‘The game is 90 percent half mental.’ It’s pretty accurate. It doesn’t make any sense. If you can find it and hold on to it, you can have a really good year or career. It’s those guys that are able to harness it for long periods of time and not fall into the pitfalls of slumps. If you do go into a slump, you come out of it quicker. That’s the name of the game: trying to hold on to it for as long as possible. It’s not easy.”

Werth knows from personal experience that hitting can turn in either direction quickly. After a solid May, he went cold in June, hitting .212 with only six extra-base hits. Through the slump, Werth still felt good. Earlier this month, he made a minor adjustment — standing taller in the batter’s box, which allowed him to see pitches better and make his swing more compact — and he took off.

Werth is hitting .375 with 12 extra-base hits in July. Though he’s played just 11 games, he’s already hit six home runs, more than he hit in April, May or June. So what changed?

“That whole thing happens in the fraction of a second when the ball leaves the pitcher’s hand until it hits your bat,” Werth said. “It doesn’t happen for a very long time but when you’re locked in that instant, you’re able to like, when you’re going good, the universe slows down. The earth stops spinning. The 100 miles an hour is not 100 miles an hour. It’s that ability to make that small little window be a lot longer.”

There is undoubtedly a major physical component to hitting. If a player is injured or even slightly weakened or tired, his swing in compromised. Even when healthy, bad habits can deteriorate a player’s swing. But imagine the player is fully healthy and his swing is normal; players say the frame of mind is just as important, perhaps more.

“Your state of mind matters a lot,” Cruz said. “If you feel good, the chances of doing well improve.”

Players may be 0 for their past 10 but are hitting line drives right at opposing defenders. The numbers may show a mini-slump but, in the player’s mind, he is hitting the ball well and is hot.

“There are times like that,” Werth said. “There are also time where you’re 0 for 20 and you don’t have a chance in hell. When you’re locked in or hot, in the zone, you’ve got a high rate for success.”