Every game has a turning point, when one team takes a big leap toward victory, whether it's a towering home run, a squeeze bunt, a bases-loaded strikeout or a run-saving catch.
Thanks to a metric called win expectancy, we can attach numbers to these swings in fortune. Win expectancy, expressed as a percentage, shows a team's chances of victory at a particular point in time. This is based on historical data showing how clubs have fared in different situations, based on factors such as the score, the inning, how many outs there were and which bases were occupied.
Using win expectancy as a guide, here is a look at three plays that served as turning points in Monday's games:
Shaw's 451-foot blast for Brewers
Game: Brewers at Cardinals
Situation: Milwaukee's Travis Shaw was batting against Cardinals reliever Seung Hwan Oh with runners at first and second and two outs in the top of the 10th inning of a 4-4 tie.
Result: Shaw, who was out of the lineup on Sunday after being hit by a pitch on the right hand Saturday night, found himself in a 1-2 hole. Oh then threw a slider below the strike zone, but Shaw was able to golf it well over the right-center-field wall for a go-ahead three-run shot, as the Brewers hung on to win, 7-5.
Win expectancy for Brewers: +48.5 percentage points (47.8% to 96.3%)
Facts to know:
• According to Statcast™, Shaw's homer had a 109.4 mph exit velocity and traveled a projected 451 feet, making it the second-longest homer of his career. The longest was a 458-foot blast on April 20.
• The blast was the longest homer Oh has allowed, by a margin of 29 feet.
They said it: Shaw: "That was pure reaction right there. Down-and-in slider, for me it was just trying to put the ball in play. I reacted and backspun it."
Result: Hamilton pulled a soft line drive just over Pirates first baseman Josh Bell for a walk-off double, as Alcantara scored the winning run in a 4-3 walk-off.
Win expectancy for Reds: +39.1 percentage points (60.9% to 100%)
Facts to know:
• The ball came off Hamilton's bat at just 65.9 mph, according to Statcast™, making it the Reds' softest extra-base hit this season.
• At 95.0 mph, Hudson's pitch was the third-fastest Hamilton has turned into a hit this year, and the fastest he's taken for extra bases.
• This was the second walk-off hit of Hamilton's career, following a single off the Cubs' Hector Rondon on July 8, 2014.
They said it: Hamilton: "When I hit it, I thought 'Josh is a tall guy over there. I hope it gets over his head.' That's one where it's not hit hard enough where it gets in the outfield and they have a chance to throw it home. It's just enough over the first baseman's head where we can get a chance to score. It's a fun game for us, even though it got cold towards the end, it was a big win for us."
Error spurs crooked number for Astros Game: Rangers at Astros
Result: On a 3-2 pitch, Aoki bounced a ground ball to the left side. Shortstop Elvis Andrus moved to his right to field it and tried to make a jump throw to second for a forceout. But his throw sailed past second baseman Rougned Odor and rolled all the way into foul territory down the right-field line. By the time the dust settled, the Astros had runners at second and third with no outs, setting up a five-run inning en route to a 6-2 win.
Win expectancy for Astros: +22.5 percentage points (43.0% to 65.5%)
Facts to know:
• Statcast™ shows that Bregman took a modest 14.2-foot secondary lead off first base and made it to second in 3.37 seconds, tied for his fastest first-to-second time this season on a play with a secondary lead of less than 15 feet.
• Aoki got a single on the play despite his batted ball having a 13 percent Hit Probability, according to Statcast™.
They said it: Rangers manager Jeff Banister: "Throw to second base, Elvis was trying to make a baseball play, and the ball gets away. That put us in a tough situation."
Andrew Simon is a research analyst for MLB.com. Follow him on Twitter @AndrewSimonMLB. This story was not subject to the approval of Major League Baseball or its clubs.